oxideav-opus 0.0.12

Opus audio codec — orphan-rebuild scaffold pending clean-room re-implementation.
Documentation
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# oxideav-opus

Pure-Rust Opus audio codec (SILK + CELT).

## Status — 2026-06-15 (clean-room round 50)

**Packet header + §3.2 frame-packing parser + RFC 6716 Appendix B
self-delimiting framing (`parse_self_delimited` — Figures 25..29 for
codes 0/1/2 and CBR/VBR code 3, with a `consumed` byte count so a
multistream demuxer can chain calls; reuses the §3.2.1 length
encoding via the shared `decode_length` helper) + §3.1 / §4.2 framing
dispatch (`OpusFrameRouting`: SILK-only / Hybrid / CELT-only mode +
SILK internal bandwidth pinned to WB for Hybrid + §4.2.2 SILK-frame
count + §4.2.4 per-frame LBRR-flag presence gate + channel-count
multiplier) + §3.4 R1..R7 malformed-input rejection audit
(`tests/malformed_input.rs`: 20 integration tests sweeping every
R1..R7 violation shape + TOC-byte total-function determinism +
§4.2.3 / §4.2.4 SILK-header truncation safety property) + §4.1
range decoder (incl. the §4.1.2 public two-step symbol path
`ec_decode(ft)` + `ec_dec_update(fl, fh, ft)` for run-time-computed
frequency models — the building block for the §4.3.2.1 coarse-energy
Laplace decoder and the §4.3.3 allocation search) +
§4.2.3 SILK header bits (VAD + LBRR flag per channel) + §4.2.4
per-frame LBRR flags (Table 4 PDFs at 40/60 ms) +
SILK §4.2.7.1–§4.2.7.5.1 frame-header decoder + §4.2.7.4 subframe
gains (log_gain decode + the §4.2.7.4 tail-end
`gain_Q16 = silk_log2lin((0x1D1C71*log_gain >> 16) + 2090)` dequant
mapping `0..=63 → [81920, 1_686_110_208]`) + §4.2.7.5.2 LSF Stage-2 residual + §4.2.7.5.3 NLSF
reconstruction + §4.2.7.5.4 NLSF stabilization + §4.2.7.5.5 NLSF
interpolation + §4.2.7.5.6 NLSF→LPC core conversion (`silk_NLSF2A`) +
§4.2.7.5.7 LPC range-limiting bandwidth expansion + §4.2.7.5.8 LPC
prediction-gain stability limiting (`silk_LPC_inverse_pred_gain_QA`) +
§4.2.7.6 LTP parameters (pitch lags + LTP filter coefficients +
LTP scaling) + §4.2.7.7 LCG seed + §4.2.7.8 excitation (rate level +
pulses per shell block + recursive pulse-location split + LSBs + signs
+ §4.2.7.8.6 LCG-driven reconstruction) + §4.2.7.9.1 LTP synthesis
filter (voiced 5-tap Q7 LTP convolution + out[]/lpc[] rewhitening
with the §4.2.7.9.1 LSF-interpolation-split branch; unvoiced `res[i]
= e_Q23[i]/2^23` normalised copy) + §4.2.7.9.2 LPC synthesis filter
(per-subframe short-term predictor with `d_LPC` history carry-over
and `out[i] = clamp(-1, lpc[i], 1)`) + §4.2.8 stereo unmixing
(`silk_stereo_MS_to_LR`: low-passed `p0` + delayed mid + §4.2.7.1 Q13
weights → clamped L/R, with 8 ms weight interpolation across frames) +
§4.2.9 resampler delay budget (Table 54: NB = 0.538 ms, MB = 0.692 ms,
WB = 0.706 ms; internal SILK rates 8/12/16 kHz; supported output rates
8/12/16/24/48 kHz) + first CELT-layer fragment: §4.3 Table 56
pre-band header symbols (`silence` `{32767, 1}/32768`, §4.3.7.1
post-filter parameter group: logp=1 enable + `octave` uniform[0,6)
+ `period = (16<<octave) + fine_pitch - 1` from `4+octave` raw bits
`15..=1022` + `gain` 3 raw bits → `G = 3*(gain_index+1)/32` +
`tapset` `{2,1,1}/4`, §4.3.1 `transient` `{7,1}/8`, §4.3.2.1 `intra`
`{7,1}/8`) + §4.3 Table 55 CELT MDCT-band layout
(`celt_band_layout`: 21-band partition with `bins_per_channel` at
2.5 / 5 / 10 / 20 ms, band-edge frequencies `0..=20000 Hz`,
`celt_band_at_hz` reverse lookup, the §4.3 "first 17 bands not
coded in Hybrid mode" rule baked into `celt_first_coded_band` /
`HYBRID_FIRST_CODED_BAND = 17`, column-sum helper
`celt_total_bins_per_channel`) + §4.3.4.5 TF-resolution adjustment
lookup (`celt_tf_adjust`: Tables 60–63 keyed by `(frame_size,
transient, tf_select, tf_change[b])``i8 ∈ [-3, 3]` + §4.3.1
`tf_select` "only decoded if it can affect at least one band" gate +
`TfDirection::{Unchanged, IncreaseTime(N), IncreaseFrequency(N)}`
classification for the §4.3.4.5 Hadamard-transform step) + §4.5.1
CELT redundancy / mode-transition side information
(`celt_redundancy::decode_redundancy`: §4.5.1.1 implicit signalling
for SILK-only Opus frames at the 17-bit remaining gate + §4.5.1.1
explicit signalling for Hybrid Opus frames at the 37-bit gate
with the Table 64 `{4095, 1}/4096` flag + §4.5.1.2 Table 65
`{1, 1}/2` position flag → `End` / `Beginning` placement +
§4.5.1.3 redundancy size: SILK-only = remaining whole bytes,
Hybrid = `2 + dec_uint(256)` with the §4.5.1.3 "claimed > whole
bytes remaining" overflow routed to `RedundancyDecision::Invalid`) +
§4.5.2 SILK + CELT decoder state-reset policy
(`mode_transition_reset::decide_state_resets`: rule 1 SILK reset on
CELT-only → SILK/Hybrid transitions + rule 2 CELT reset on every
mode change into Hybrid or CELT-only + rule 3 carve-out placing the
CELT reset *before the redundant CELT frame* on SILK/Hybrid →
CELT-only with redundancy + rule 4 carve-out suppressing the CELT
reset on CELT-only → SILK/Hybrid with redundancy; `StateReset {
silk, celt: CeltResetPlacement::{None, BeforeFrame,
BeforeRedundantOnly} }` driving the full 3×3-mode × redundancy
matrix and cross-checked against the non-normative §4.5.3 Figure
18 reset markers) + §4.5.1.4 redundant-CELT-frame decode parameters
and cross-lap placement (`redundancy_decode_params`:
`RedundantFrameParams { duration_tenths_ms: 50 (fixed 5 ms),
channels, bandwidth (with §4.5.1.4 "MB SILK → WB" override),
position, size_bytes, cross_lap }` derived from
`OpusFrameRouting` + `RedundancyDecision`; `CrossLapPlacement::
{FirstHalfAsIs, SecondHalfAsIs}` mapping `Beginning`"first 2.5 ms of redundant as-is + second 2.5 ms cross-lap" (CELT
→ SILK/Hybrid) and `End` → "discard first 2.5 ms + second 2.5 ms
cross-lap" (SILK/Hybrid → CELT); `Invalid` overflow + `NotPresent`
both route to `None` per §4.5.1.3) + §4.3.2.1 CELT coarse-energy
Laplace-model parameter surface (`celt_e_prob_model`: `E_PROB_MODEL`
— the 336-byte `[LM ∈ 0..4][mode ∈ {inter, intra}][band × 2]` Q8
`{prob, decay}` table feeding `ec_laplace_decode` +
`EnergyPredictionMode::{Inter, Intra}` selector driven by the §4.3.2.1
CELT-header `intra` flag + `e_prob_pair(lm, mode, band) -> EProbPair`
/ `e_prob_row(lm, mode) -> &[u8; 42]` accessors + intra-mode
prediction-coefficient constants `INTRA_PRED_ALPHA_Q15 = 0` /
`INTRA_PRED_BETA_Q15 = 4915` against `Q15_ONE = 32768` per RFC 6716
§4.3.2.1 p. 108 + per-LM inter-mode coefficients
`INTER_PRED_ALPHA_Q15 = {29440, 26112, 21248, 16384}` /
`INTER_PRED_BETA_Q15 = {30147, 22282, 12124, 6554}` with the
`energy_pred_coef(lm, mode) -> EnergyPredCoef` accessor, the Q15
numerators fixed by the RFC 6716 Appendix A normative reference code)
+ §4.3.3 intensity-stereo reservation parameter
surface (`celt_log2_frac_table`: `LOG2_FRAC_TABLE` — the 24-byte Q3
(1/8-bit) conservative `log2` table feeding the §4.3.3
`intensity_rsv = LOG2_FRAC_TABLE[end − start]` reservation +
`log2_frac(coded_bands) -> u8` accessor + `log2_frac_row() -> &[u8;
24]` full-row borrow + `Q3_BITS_PER_WHOLE_BIT = 8` unit-denominator
constant; covers the CELT-only `end − start = 21` and Hybrid `end −
start = 4` reachable indices per RFC 6716 §4.3.3 p. 113) + §4.3.3
allocation-trim parameter surface (`celt_alloc_trim`: `ALLOC_TRIM_PDF`
— the 11-cell Table-58 PDF `{2, 2, 5, 10, 22, 46, 22, 10, 5, 2,
2}/128` + derived `ALLOC_TRIM_ICDF = [126, 124, 119, 109, 87, 41, 19,
9, 4, 2, 0]` for `RangeDecoder::dec_icdf` consumption +
`ALLOC_TRIM_DEFAULT = 5` / `ALLOC_TRIM_MIN = 0` / `ALLOC_TRIM_MAX =
10` per the RFC's "an integer value from 0-10" and "the default value
of 5 indicates no trim" wording + `ALLOC_TRIM_SIGNAL_COST_EIGHTH_BITS
= 48` (6 whole bits in 1/8-bit precision) + the §4.3.3 signalling
gate `alloc_trim_is_signalled(ec_tell_frac, frame_eighth_bits,
total_boost) -> bool` evaluating `(ec_tell_frac + 48) ≤
(frame_eighth_bits − total_boost)` with saturating arithmetic on the
malformed-input edges + the typed wrapper `decode_alloc_trim(rd,
ec_tell_frac, frame_size_bytes, total_boost) -> Result<u8,
AllocTrimError>` fusing the gate, the gate-fail-returns-5 rule, and
the `dec_icdf` read into one call + `AllocTrimError::{FrameSizeOverflows,
TotalBoostExceedsFrame}`) + §4.3.3 band-boost decoder
(`celt_band_boost::decode_band_boosts`: §4.3.3 per-band
`quanta = min(8*N, max(48, N))` lookup via `band_boost_quanta` in 1/8
bits + per-band inner loop reading `dec_bit_logp(dynalloc_loop_logp)`
bits while `(dynalloc_loop_logp * 8) + tell < total_bits + total_boost`
AND `boost < cap[band]` with the §4.3.3 `dynalloc_loop_logp = 1`
drop after the first boost + cross-band `dynalloc_logp ∈
DYNALLOC_LOGP_MIN..=DYNALLOC_LOGP_INIT = 2..=6` decrement on every
boosted band + `BandBoostOutcome { per_band, total_boost_eighth_bits,
total_bits_remaining_eighth_bits, dynalloc_logp_final }` bundling the
§4.3.3 boost accumulator that feeds the §4.3.3 allocation-trim gate
at `decode_alloc_trim` + the §4.3.3 invariant `total_bits +
total_boost = frame_eighth_bits` conserved across boost steps) +
§4.3.3 reservation block (`celt_reservations::reserve_block`: §4.3.3
`total = frame_size_bytes * 64 − ec_tell_frac − 1` setup +
`anti_collapse_rsv = 8` iff transient && `LM > 1` && `total ≥
(LM + 2) * 8` + `skip_rsv = 8` iff `total > 8` after anti-collapse +
stereo `intensity_rsv = LOG2_FRAC_TABLE[end − start]` with the §4.3.3
"reset to 0 if greater than total" branch + `dual_stereo_rsv = 8` iff
`total > 8` after intensity, gating dual-stereo on intensity having
been successfully reserved + `ReservationOutcome { anti_collapse_rsv,
skip_rsv, intensity_rsv, dual_stereo_rsv, total_remaining_eighth_bits }`
typed outcome + `ONE_BIT_EIGHTH_BITS = 8` /
`CONSERVATIVE_DEDUCTION_EIGHTH_BITS = 1` /
`ANTI_COLLAPSE_LM_MIN_EXCLUSIVE = 1` /
`ANTI_COLLAPSE_HEADROOM_MULT_EIGHTH_BITS = 8` /
`ANTI_COLLAPSE_HEADROOM_LM_OFFSET = 2` cost + gating constants +
`ReservationError::{FrameSizeOverflows, TellExceedsFrame,
TotalBoostExceedsFrame, LogFracLookupFailed}`) +
§4.3.3 per-band minimum-allocation vector
(`celt_band_thresh::{band_min_thresh, compute_band_min_thresh,
band_min_thresh_vec, standard_band_window}`: §4.3.3 §4.3.3
`thresh[b] = max((24 * N) / 16, 8 * channels)` in 1/8 bits — one whole
bit per channel or 48 128th-bits per MDCT bin, whichever is greater +
the §4.3.3 "band-size term not scaled by channel count" carve-out +
`BAND_THRESH_BINS_MULTIPLIER = 24` / `BAND_THRESH_BINS_DIVISOR = 16` /
`BAND_THRESH_PER_CHANNEL_EIGHTH_BITS = 8` /
`BAND_THRESH_MONO_CHANNELS = 1` / `BAND_THRESH_STEREO_CHANNELS = 2`
formula constants + `BandThreshError::{InvertedBandWindow,
BandWindowOutOfRange, OutputBufferTooSmall}` caller-side bookkeeping
errors) + §4.3.3 static allocation table
(`celt_static_alloc::STATIC_ALLOC` — the 21-band × 11-quality-column
Q5 grid `alloc[band][q]` in 1/32-bit per MDCT bin units transcribed
from RFC 6716 §4.3.3 Table 57 (p. 112), `STATIC_ALLOC_Q_COUNT = 11` /
`STATIC_ALLOC_Q_MIN = 0` / `STATIC_ALLOC_Q_MAX = 10` /
`STATIC_ALLOC_TOTAL_CELLS = 231` / `STATIC_ALLOC_RIGHT_SHIFT = 2` /
`STATIC_ALLOC_INTERP_STEPS = 64` layout / conversion constants +
`static_alloc_cell(band, q) -> u8` raw-cell lookup + `static_alloc_row(band)
-> &[u8; 11]` row borrow + `static_alloc_eighth_bits(band, q, channels,
n_bins, lm) -> u32` applying the §4.3.3
`channels * N * alloc[band][q] << LM >> 2` unit fold from Q5 to Q3
1/8-bit units + `StaticAllocError::{BandOutOfRange, QualityOutOfRange,
ChannelsOutOfRange, LmOutOfRange}` caller-side bookkeeping errors);
the §4.3.2.1 Laplace decoder itself + 2-D `(time, frequency)` predictor
+ §4.3.3 1/64-step interpolated search over Table 57 + the §4.3.4 band
loop + the §4.3.7 inverse MDCT transform proper and its weighted
overlap-add still deferred (the §4.3.4.2 PVQ shape read path landed in
round 49).

Round 41 adds the §4.3.4.2 *PVQ codebook-size function*
(`celt_pvq_v::pvq_codebook_size(n, k) -> Result<u32, PvqVError>`)
evaluating the RFC 6716 §4.3.4.2 bivariate recurrence
`V(N, K) = V(N - 1, K) + V(N, K - 1) + V(N - 1, K - 1)` with base
cases `V(N, 0) = 1` / `V(0, K) = 0 (K != 0)` over two rolling rows
of length `K + 1`, plus `PVQ_V_N_MAX = 352` / `PVQ_V_K_MAX = 4096`
caller-side bookkeeping bounds and the `PVQ_V_MAX = 2**32 − 1`
overflow guard inherited from RFC 6716 §4.1.5's `ec_dec_uint(ft)`
upper bound (`PvqVError::OverflowsDecUintRange` reports
stream-impossible inputs). Both the §4.3.4.2 PVQ index decode
(`ec_dec_uint(V(N, K))`) and the §4.3.4.1 *Bits-to-Pulses* search
consume this primitive at their respective consumer sites.

Round 42 adds the §4.3.2.2 *fine-energy quantization* primitive
(`celt_fine_energy`): the §4.3.2.2 correction `(f + 1/2) / 2**B_i −
1/2 = (2f + 1 − 2**B_i) / 2**(B_i + 1)` exposed as an exact reduced
ratio (`fine_correction_ratio`), in Q15 (`fine_correction_q15`,
exact for every reachable `B_i`, strictly within `(−16384, +16384)`),
and in an arbitrary Q-format (`fine_correction_q`, e.g. CELT's
`DB_SHIFT = 10`), plus the §4.3.2.2 *final* fine-energy bit planner
(`plan_final_fine_bits`: one extra bit per band per channel,
priority-0 bands band-0-upward then priority-1, leftover unused).

Round 43 adds the §4.3.4.2 *PVQ index-to-vector decode*
(`celt_pvq_decode`): `decode_pvq_vector(n, k, index) -> Vec<i32>` /
`decode_pvq_vector_into(n, k, index, &mut [i32])` implementing the
§4.3.4.2 five-step recovery (`p = (V(N-j-1,k) + V(N-j,k))/2`, sign on
`i < p`, the `p -= V(N-j-1,k)` magnitude walk, `X[j] = sgn*(k0-k)`)
that consumes the round-41 `pvq_codebook_size` `V(N, K)` and turns a
codeword index into the integer pulse vector with `sum |X[j]| = K`,
plus `pvq_l1_norm` / `pvq_l2_norm_squared` invariant helpers (the
final unit-L2 normalization is a float step deferred to the §4.3.4
consumer) and `PvqDecodeError::{CodebookSize, IndexOutOfRange,
OutputBufferTooSmall}`.

Round 44 adds the §4.3.4.3 *spreading (rotation)* layer
(`celt_spreading`): the Table 56 per-frame "spread" symbol decode
(`decode_spread` with `SPREAD_PDF = {7, 2, 21, 2}/32` /
`SPREAD_ICDF`), the Table 59 `spread → f_r` map (`spread_f_r` /
`SPREAD_F_R`: 0 → no rotation, 1 → 15, 2 → 10, 3 → 5), the §4.3.4.3
rotation gain `g_r = N/(N + f_r*K)` (`rotation_gain`) and angle
`theta = pi*g_r^2/4` (`rotation_angle`, composed as `spread_theta`),
the back-and-forth 2-D rotation series (`rotate_in_place`), the
multi-block interleave stride `round(sqrt(N/nb_blocks))`
(`spreading_stride`) with the strided per-set variant
(`rotate_strided`), and the composed `apply_spreading` (per-block
rotation + the `(pi/2 − theta)` strided pre-rotation when
`nb_blocks > 1` and blocks span ≥ 8 samples).**

Round 45 adds the §4.3.2.1 per-LM *inter*-mode coarse-energy
prediction coefficients (`celt_e_prob_model`):
`INTER_PRED_ALPHA_Q15 = {29440, 26112, 21248, 16384}` /
`INTER_PRED_BETA_Q15 = {30147, 22282, 12124, 6554}` (Q15 against
`Q15_ONE = 32768`, indexed by `LM = log2(frame_size/120)`), plus the
`energy_pred_coef(lm, mode) -> EnergyPredCoef { alpha_q15, beta_q15 }`
accessor unifying the intra carve-out (`(0, 4915)` for every LM) and
the per-LM inter pairs. This closes the round-29 deferral: the values
come from the `pred_coef[4]` / `beta_coef[4]` data in `quant_bands.c`
of the RFC 6716 Appendix A normative reference code, which is embedded
in the staged RFC text itself (§A.1 extraction procedure, SHA-1
verified; §A.2: "it is the code in this document that shall remain
normative").

## Round 50 — §4.3.7.1 pitch post-filter response (2026-06-15)

Round 50 lands the RFC 6716 §4.3.7.1 *post-filter response*
(`celt_post_filter`) — the pitch comb filter the CELT decoder applies to
the inverse-MDCT / overlap-add output (§4.3.7) just before the
round-48 §4.3.7.2 de-emphasis. The §4.3.7.1 post-filter *parameters*
(enable bit, octave, fine pitch, gain index, tapset) already landed in
`celt_header` (round 20); this round owns their *application*.

RFC 6716 §4.3.7.1 (p. 121) states the response as the five-tap symmetric
comb

```text
  y(n) = x(n) + G*( g0*y(n-T) + g1*(y(n-T+1)+y(n-T-1))
                              + g2*(y(n-T+2)+y(n-T-2)) )
```

a recursive filter over past *output* samples `y` (state = the trailing
`T + 2` outputs, carried across frames, reset only on a §4.5.2 CELT
state reset). The ASCII equation prints each pair term with a repeated
index (`y(n-T+1)+y(n-T+1)`); the symmetric reading `y(n-T±1)` /
`y(n-T±2)` is the only one consistent with the surrounding "g0, g1, g2"
symmetric-tap-set prose, and the module documents that the literal
repeated-index form would degenerate the comb into a non-symmetric
single tap. The three tapsets, the gain map `G = 3*(gain_index+1)/32`,
and the `T ∈ 15..=1022` pitch bound are exact facts from the text.

New public surface (`celt_post_filter`):

* `POST_FILTER_TAPS` (the three §4.3.7.1 `(g0, g1, g2)` tapsets),
  `tapset_coefficients(tapset)`, `post_filter_gain(gain_index)`, and the
  formula constants (`POST_FILTER_{MIN,MAX}_PERIOD`,
  `POST_FILTER_GAIN_{NUMERATOR,DENOMINATOR}`, `POST_FILTER_TAPSET_COUNT`,
  `POST_FILTER_GAIN_INDEX_MAX`).
* `PostFilterCoeffs { period, a0, a1, a2 }` (gain folded into each tap),
  built via `new(period, gain_index, tapset)` or `from_header(&CeltPostFilter)`.
* `PostFilter` — a single-channel filter carrying the output history:
  `new()` / `reset()` / `step(x, &coeffs)` / `process_in_place` /
  `process` and the §4.3.7.1 gain-transition crossfade
  `process_gain_transition(input, output, old, new, overlap)` that mixes
  the two coefficient sets' comb responses with the squared
  [`celt_mdct_window`] weights `(1-W(n)^2)` / `W(n)^2`, pushing the
  *mixed* value into the shared feedback history per the §4.3.7.1
  "interpolated one at a time … the past value of y(n) used is
  interpolated" rule.
* `crossfade_transition(old_out, new_out, out, overlap)` — the
  non-recursive squared-window crossfade for callers that produced the
  two branches separately.
* `PostFilterError::{TapsetOutOfRange, PeriodOutOfRange,
  GainIndexOutOfRange, OutputBufferTooSmall, TransitionLengthMismatch,
  Window}` with `From<MdctWindowError>`.

Twenty-six new unit tests (1064 lib tests total, up from 1038 at
round-49 close; 20 integration tests unchanged) pin the tapset decimals
and `g2 = 0` for tapsets 1/2, the gain formula + monotonicity, the
gain-fold, the period bounds, header round-trip, fresh-history
pass-through, a hand-expanded impulse response placing each tap at its
exact lag, impulse-response symmetry about `T`, history carry across
split blocks, the buffer paths, `reset`, the gain-transition endpoints +
old==new identity + length checks, the standalone crossfade convexity,
and every error `Display`.

What's deferred at the §4.3.7 consumer site: the inverse MDCT transform
proper + weighted overlap-add (which produce this filter's `x(n)` input
and consume the round-47 `celt_mdct_window` ramp; the FFT layout defers
to the staged twiddle/bitrev tables whose run mapping is not yet
traced), and the exact transition-region length / placement the encoder
chooses per §4.5 mode change.

Source: RFC 6716 §4.3.7.1 (pp. 120–121) — held in-repo at
`docs/audio/opus/rfc6716-opus.txt`. No external library source was
consulted; the comb response, tapsets, gain map, and squared-window
transition rule are stated directly in the standards-track text.

## Round 49 — §4.3.4.2 PVQ shape read path (2026-06-15)

Round 49 lands the RFC 6716 §4.3.4.2 *PVQ shape* read path
(`celt_pvq_decode`), composing the three steps the standards-track text
states in sequence (§4.3.4.2, p. 116–117) into a single call from the
range decoder to the band's normalized float "shape":

1. `i = ec_dec_uint(V(N, K))` — the uniformly-distributed codeword
   index, read with the round-3 [`RangeDecoder::dec_uint`] on the
   round-41 `V(N, K)` codebook size.
2. The round-43 five-step index-to-vector walk
   (`decode_pvq_vector_into`), producing the integer pulse vector `X`
   with `sum |X[j]| == K`.
3. The §4.3.4.2 final normalization: *"The decoded vector X is then
   normalized such that its L2-norm equals one."*

This closes the round-43 deferral of the unit-L2 normalization (then
left to the consumer site because it depends on the float scaling) and
the round-43 deferral of the up-front `ec_dec_uint(V(N, K))` index read
(then noted as the wiring of [`RangeDecoder::dec_uint`] to the decode).
The result is exactly the vector the §4.3.4.3 spreading rotation
(`celt_spreading`) operates on — its RFC prose opens *"The normalized
vector decoded in Section 4.3.4.2 is then rotated…"* — and the vector
§4.3.6 denormalization later multiplies by the square root of the
decoded band energy.

New public surface (`celt_pvq_decode`):

* `pvq_unit_normalize(&[i32], &mut [f64]) -> Result<(), PvqShapeError>`
  — the §4.3.4.2 unit-L2 scaling `out[j] = X[j] / sqrt(sum X[j]**2)`.
  The `K = 0` all-zero codeword has no defined direction, so it is left
  all-zeros (a band that carries no shape); every `K > 0` codeword
  yields `sum out[j]**2 == 1` to float precision.
* `decode_pvq_shape(rd, n, k) -> Result<Vec<f64>, PvqShapeError>` — the
  full read path; returns the unit-norm `f64` shape of length `N`.
* `decode_pvq_shape_into(rd, n, k, &mut [f64]) -> Result<usize,
  PvqShapeError>` — the same into a caller buffer of length `≥ N`.
* `PvqShapeError::{CodebookSize, RangeDecoder, PulseVector,
  OutputBufferTooSmall}` with `From<PvqVError>` / `From<PvqDecodeError>`
  (the latter flattening a codebook-size sub-error so the variant set
  stays orthogonal).

Fourteen new unit tests (1038 lib tests total, up from 1024 at round-48
close; 20 integration tests unchanged) pin: the unit-L2 norm over every
codeword of `(N, K) ∈ 1..=6 × 1..=6`, exact direction preservation
(`(3,0,-4) → (0.6, 0, -0.8)`), single-pulse ±1, the zero-vector
carve-out, and the normalize buffer paths (short rejection, over-long
tail preserved); the full-path `decode_pvq_shape` ↔ `decode_pvq_vector`
+ `pvq_unit_normalize` consistency from fixed range-decoder buffers, the
`_into` ↔ allocating parity, the `K = 0` all-zero + no-bit-consumption
edge (`dec_uint(1)` reads nothing), the `N = 1` signed-unit shape,
codebook-size error propagation, and every error conversion / `Display`.

What's deferred at the §4.3.4 consumer site: the §4.3.4.1
*Bits-to-Pulses* search that supplies `K` from the §4.3.3 allocation —
still a **docs gap** (the precomputed pulse-cache layout that selects
the permitted-`K` set per `(band, LM)` lives in `rate.c`'s
`compute_pulse_cache()`, which the RFC names but does not embed; the
`docs/audio/opus/tables/cache-bits50.csv` / `cache-index50.csv` values
are staged but no trace describes the run layout, per-entry bits units,
or the `(band, LM) → run` index calculation, and the allocation must be
recovered bit-exactly), and the §4.3.4 band loop that feeds each band's
`(N, K)` through this shape decode then the spreading rotation.

Source: RFC 6716 §4.3.4.2 (p. 116–117) — held in-repo at
`docs/audio/opus/rfc6716-opus.txt`. No external library source was
consulted; the index read, the index-to-vector walk, and the unit-L2
normalization are all stated directly in the standards-track text.

## Round 48 — §4.3.7.2 de-emphasis filter (2026-06-14)

Round 48 lands the RFC 6716 §4.3.7.2 *de-emphasis filter*
(`celt_deemphasis`) — the last stage of the CELT decode pipeline,
applied after the §4.3.7 inverse MDCT + weighted overlap-add and the
§4.3.7.1 pitch post-filter, just before the time-domain samples leave
the decoder. RFC 6716 §4.3.7.2 (p. 122) specifies it as the inverse of
the encoder's pre-emphasis filter:

```text
    1            1
   ---- = ---------------
   A(z)                -1
          1 - alpha_p*z
```

with `alpha_p = 0.8500061035`. The encoder's pre-emphasis is the FIR
`A(z) = 1 - alpha_p*z^-1` (`x(n) = s(n) - alpha_p*s(n-1)`); inverting
that one pole gives the decoder-side one-pole IIR recurrence

```text
  y(n) = x(n) + alpha_p * y(n-1)
```

The pole `≈ 0.85` is just inside the unit circle (stable), and its
single state element `y(n-1)` carries across frame boundaries — the
recurrence is continuous over the whole decoded stream, reset only on a
§4.5.2 CELT state reset. Each channel carries its own independent
memory.

New public surface (`celt_deemphasis`):

* `DEEMPHASIS_ALPHA_P = 0.8500061035` — the §4.3.7.2 coefficient,
  exactly the decimal the RFC prints.
* `DeemphasisFilter` — a single-channel filter carrying the one-pole
  memory: `new()` (zeroed), `with_memory(mem)` (seeded), `memory()`,
  `reset()`, `step(x) -> y` (one-sample recurrence advancing state),
  `process_in_place(&mut [f64])`, and `process(input, output) ->
  Result<usize, DeemphasisError>` (state left unchanged on error).
* `DeemphasisError::OutputBufferTooSmall`.

Fifteen new unit tests (1024 lib tests total, up from 1009 at round-47
close; 20 integration tests unchanged) pin the `alpha_p` constant and
its stability bound, fresh-filter zero memory, first-sample
pass-through, a hand-computed recurrence run, constant-input
convergence to the DC gain `1/(1 - alpha_p)`, the
**pre-emphasis-round-trip inverse property** (pre-emphasise then
de-emphasise recovers the original signal to `1e-12`), memory carry
across split blocks (two-block filtering == whole-stream filtering),
`with_memory` seeding, `reset`, the `process_in_place` ↔ `step` parity,
the output-buffer write path + over-long-buffer acceptance +
short-buffer rejection (state unchanged on error), the empty-input
no-op, and the error `Display`.

The §4.3.7.1 pitch post-filter *response* (the §4.3.7.1
`y(n) = x(n) + G*(g0*y(n-T) + ...)` filter that feeds this stage; the
post-filter *parameters* land in `celt_header` at round 20) and the
§4.3.7 inverse MDCT transform proper + weighted overlap-add (which
consume the round-47 `celt_mdct_window` ramp) remain deferred to their
consumer sites.

Source: RFC 6716 §4.3.7.2 (p. 122) — held in-repo at
`docs/audio/opus/rfc6716-opus.txt`. The recurrence is the textbook
inverse of the stated one-pole transfer function. No external library
source was consulted; the filter and its single coefficient are stated
directly in the standards-track text.

## Round 47 — §4.3.7 inverse-MDCT overlap window (2026-06-14)

Round 47 lands the RFC 6716 §4.3.7 *inverse-MDCT overlap window*
(`celt_mdct_window`) — the windowed overlap ramp the CELT decoder
applies after the inverse MDCT, before weighted overlap-add. §4.3.7
(p. 121) gives the basic full-overlap 240-sample window directly as a
squared-double-sine "derived from the window used by the Vorbis
codec":

```text
  W(n) = sin( (pi/2) * sin( (pi/2) * (n + 1/2) / L )^2 )
```

The ASCII figure's `2` superscript squares the *inner* sine. The
module fixes this nesting from the §4.3.7 power-complementarity
requirement (the window "still satisfies power complementarity",
`[PRINCEN86]`): only the inner-squared form yields
`W(n)^2 + W(L-1-n)^2 = 1`, because with `s(n) = sin((pi/2)t)^2` the
reflected index gives `s(L-1-n) = 1 - s(n)` and the outer sine maps a
`(sin, cos)` pair back to a complementary `(sin, cos)` pair. The
module proves the identity algebraically in its header and pins it in
tests on both the basic window and arbitrary overlaps.

New public surface (`celt_mdct_window`):

* `window_tap(n, len)` — the amplitude window tap for window length
  `L = len`; range `[0, 1]`.
* `basic_window() -> [f64; 240]` — the §4.3.7 full-overlap window.
* `mdct_window(overlap) -> Vec<f64>` — the §4.3.7 "low-overlap" rising
  ramp for an arbitrary even `overlap`, built by evaluating the same
  shape with `L = overlap`. This expresses the RFC's "zero-pad the
  basic window and insert ones in the middle" construction as a
  per-overlap ramp: the consumer applies the ramp to the leading
  `overlap` samples (and its time-reverse to the trailing `overlap`),
  with the `2N - 2*overlap` centre samples at unity.
* `celt_overlap_window() -> [f64; 120]` — the fixed CELT overlap at
  48 kHz (the 2.5 ms look-ahead "fixed by the decoder", RFC 6716 §1).
* `BASIC_WINDOW_LEN = 240` / `CELT_OVERLAP_48K = 120` constants and
  `MdctWindowError::{PositionOutOfRange, ZeroLength, OddOverlap}`.

Eighteen new unit tests (1009 lib tests total, up from 991 at
round-46 close; 20 integration tests unchanged) pin the inner-squared
formula spot-check, the `[0, 1]` bound, the monotone-increasing ramp,
power complementarity on the basic window and on overlaps `2/4/16/120/
240`, the half-power centre pair, the endpoint shape, the
`mdct_window` ↔ `window_tap` and `celt_overlap_window` ↔
`mdct_window(120)` parities, and every error path.

The §4.3.7 inverse MDCT transform proper ("no special
characteristics … `2*N` time-domain samples, while scaling by 1/2")
and the weighted overlap-add that consumes this ramp remain deferred
to the §4.3.7 consumer site.

Source: RFC 6716 §4.3.7 (p. 121) and the §1 fixed-overlap statement
(p. 10) — held in-repo at `docs/audio/opus/rfc6716-opus.txt`. No
external library source was consulted; the window equation is stated
directly in the standards-track text.

## Round 45 — §4.3.2.1 per-LM inter-mode (alpha, beta) prediction coefficients (2026-06-12)

Round 45 lands the per-LM *inter*-mode `(alpha, beta)` coarse-energy
prediction parameterisation deferred since round 29 (RFC 6716
§4.3.2.1, p. 108). The RFC prose fixes the intra case
(`alpha = 0`, `beta = 4915/32768`) and states that the inter
coefficients "depend on the frame size in use", but defers the numeric
values to the normative Appendix A reference code. Those values —
`pred_coef[4] = {29440, 26112, 21248, 16384}` and
`beta_coef[4] = {30147, 22282, 12124, 6554}` (Q15, indexed by
`LM = log2(frame_size/120) ∈ 0..=3`) — are numeric facts read from
`quant_bands.c` inside the Appendix A source embedded in the staged
`docs/audio/opus/rfc6716-opus.txt` (extracted with the RFC's own §A.1
command; the tarball SHA-1 matched the value printed in §A.1, and the
`beta_intra = 4915` declaration in the same file confirms the p. 108
intra constant). RFC 6716 §1 includes Appendix A in the normative
text and §A.2 states the in-document code remains normative, so these
constants carry spec weight; no external reference distribution or
other implementation was consulted.

New API surface in `celt_e_prob_model`:

* `INTER_PRED_ALPHA_Q15: [u16; 4]` — time-domain predictor weight per
  LM; `alpha` shrinks as frames grow (exactly `1/2` at 20 ms) because
  a longer inter-frame gap weakens the previous-frame predictor.
* `INTER_PRED_BETA_Q15: [u16; 4]` — frequency-leakage coefficient per
  LM (`≈ {0.920, 0.680, 0.370, 0.200}`).
* `EnergyPredCoef { alpha_q15, beta_q15 }` with exact-binary-fraction
  `alpha()` / `beta()` float views.
* `energy_pred_coef(lm, mode) -> Result<EnergyPredCoef,
  EProbModelError>` — one range-checked contract for both modes;
  intra returns the LM-independent `(0, 4915)`.

Ten new unit tests (986 lib tests, up from 976; 20 integration tests
unchanged): Appendix A value pins for both arrays, the exact-half
`LM = 3` alpha, strict monotone decrease of both coefficient sets in
LM, inter-beta > intra-beta for every LM, accessor↔table agreement,
intra LM-independence, out-of-range `lm` rejection in both modes,
exact float views, and the 3-decimal doc-comment approximations.

A consequence worth recording for §4.3.4.1 (Bits-to-Pulses, still
deferred): the same Appendix A carve-out stages the normative
pulse-cache construction (`rate.c`), so the `cache-bits50` /
`cache-index50` run layout that round 44 recorded as a docs gap is now
reachable through the staged RFC text; a future round can consume it
under the same grounding.

Source: RFC 6716 §4.3.2.1 (p. 108), §1 (p. 5), §A.1–A.3
(pp. 163–164), and the Appendix A `quant_bands.c` coefficient data —
all held in-repo at `docs/audio/opus/rfc6716-opus.txt`. No external
library source was consulted.

## Round 44 — §4.3.4.3 spreading (rotation) (2026-06-11)

Round 44 lands RFC 6716 §4.3.4.3 *Spreading* — the rotation applied
to the §4.3.4.2-decoded shape vector "for the purpose of avoiding
tonal artifacts" (RFC 6716 §4.3.4.3, pp. 117–118). The procedure is
stated directly in the standards-track prose: the rotation gain
`g_r = N / (N + f_r*K)` with `f_r` from Table 59 (spread value 0 →
infinite, i.e. no rotation; 1 → 15; 2 → 10; 3 → 5), the angle
`theta = pi * g_r^2 / 4`, the 2-D step `x_i' = cos(theta)*x_i +
sin(theta)*x_j` / `x_j' = -sin(theta)*x_i + cos(theta)*x_j`, and the
N-D composition as a back-and-forth series of adjacent-pair 2-D
rotations (`R(x_1, x_2) … R(x_{N-1}, x_N)` then back down to
`R(x_1, x_2)`). The "spread" symbol itself is the Table 56 per-frame
PDF `{7, 2, 21, 2}/32`.

New public surface (`celt_spreading`):

* `decode_spread(&mut RangeDecoder) -> u8` — the Table 56 symbol
  read (`SPREAD_PDF` / `SPREAD_ICDF` / `SPREAD_FTB = 5`).
* `spread_f_r(spread) -> Result<Option<u32>, …>` / `SPREAD_F_R`  the Table 59 map; `None` is the "infinite (no rotation)" row.
* `rotation_gain(n, k, f_r)` / `rotation_angle(g_r)` /
  `spread_theta(n, k, spread)``g_r` and `theta`.
* `rotate_in_place(&mut [f64], theta)` — the §4.3.4.3
  back-and-forth 2-D rotation series (orthogonal; preserves the L2
  norm).
* `spreading_stride(len, nb_blocks)``round(sqrt(N/nb_blocks))`
  (round-half-up documented; the RFC does not pin the tie rule).
* `rotate_strided(&mut [f64], stride, theta)` — the same series
  applied independently to each interleaved set
  `S_k = {stride*n + k}`.
* `apply_spreading(&mut [f64], k, spread, nb_blocks)` — the composed
  process: no-op for spread 0; per-block rotation by `theta`
  (`N` = block length per "applied separately on each time block");
  and, when `nb_blocks > 1` with blocks ≥ 8 samples
  (`SPREAD_PRE_ROTATION_MIN_BLOCK_LEN`), the extra `(pi/2 − theta)`
  rotation applied first, interleaved over the whole vector. The
  module doc records the reading of the §4.3.4.3 multi-block
  paragraph (whose prose reuses `N` for both the full vector and a
  block); the primitives are exact transcriptions so the §4.3.4
  consumer site can recompose if fixture-level verification pins a
  different reading.
* `SpreadingError::{SpreadOutOfRange, ZeroDimensions, ZeroBlocks,
  ZeroStride, BlocksDoNotDivideLength}`.

Twenty-eight new unit tests (976 lib tests total, up from 948 at
round-43 close; 20 integration tests unchanged) pin: the Table 56
PDF/iCDF consistency and an exhaustive first-byte sweep showing
`decode_spread` always yields a Table 59 row; the Table 59 map and
its out-of-range rejection; worked `g_r` / `theta` points
(`g_r(16, 4, 5) = 4/9`, `theta = 4*pi/81`, `K = 0 ⇒ g_r = 1`,
`g_r = 1 ⇒ theta = pi/4`) and the monotonicities (more pulses ⇒
smaller `theta`; Table 59 spread 1 < 2 < 3 in rotation strength);
the 2-D step against the RFC definition; the `N = 3` series against
an explicit-matrix composition; L2-norm preservation, zero-angle
identity, and sign-linearity of the series; stride worked points
including the 2.5-tie; strided-rotation equivalence to
gather-rotate-scatter, set independence, norm preservation, and the
singleton-set no-op; and the composed `apply_spreading` paths
(spread-0 identity, single-block equivalence, small-block
pre-rotation skip, multi-block pre-rotation effect + exact
composition, zero-vector fixed point, and every error path).

What's deferred: the §4.3.4 band loop that feeds decoded shape
vectors through this rotation, and the §4.3.4.1 Bits-to-Pulses
conversion. §4.3.4.1 is a **docs gap**: the staged
`docs/audio/opus/tables/cache-bits50.csv` / `cache-index50.csv`
carry the precomputed pulse-cache *values* (392 + 105 entries), but
no staged trace describes the table's internal layout — how a
`(band, LM)` pair selects a run inside `cache-bits50`, the
per-entry bits units/bias, and the permitted-`K` mapping the RFC
alludes to ("the search is performed against a precomputed
allocation table that only permits some K values for each N", RFC
6716 §4.3.4.1, p. 116). RFC prose alone does not pin the layout,
and the allocation must be recovered bit-exactly.

Source: RFC 6716 §4.3.4.3 (pp. 117–118), Table 59 (p. 117), and the
Table 56 "spread" row (p. 107) — held in-repo at
`docs/audio/opus/rfc6716-opus.txt`. No external library source was
consulted.

## Round 43 — §4.3.4.2 PVQ index-to-vector decode (2026-06-11)

Round 43 lands the RFC 6716 §4.3.4.2 *PVQ index-to-vector decode* —
the consumer of round 41's `V(N, K)` codebook-size primitive that
turns a decoded codeword index `i ∈ 0..V(N, K)` into the
integer-magnitude pulse vector `X` with `|X_0| + ... + |X_{N-1}| =
K`. RFC 6716 §4.3.4.2 (p. 116–117) states the recovery as a
five-step per-coordinate walk: for `j = 0..N-1`,

1. `p = (V(N-j-1, k) + V(N-j, k)) / 2`;
2. if `i < p` then `sgn = 1`, else `sgn = -1` and `i = i - p`;
3. `k0 = k`; `p = p - V(N-j-1, k)`;
4. while `p > i`: `k = k - 1`; `p = p - V(N-j-1, k)`;
5. `X[j] = sgn * (k0 - k)`; `i = i - p`.

The two halves of step 1 split the count of configurations whose
`j`-th coordinate is strictly positive (`sgn = +1`) from the rest;
the step 3–4 loop walks the per-coordinate magnitude `k0 - k` down to
the slice the index falls into. The arithmetic is `V(N, K)`-counting
only — no probability model, no range-coder interaction beyond the
single up-front `ec_dec_uint(V(N, K))` read that supplies `i`.

New public surface (`celt_pvq_decode`):

* `decode_pvq_vector(n, k, index) -> Result<Vec<i32>, PvqDecodeError>`
  — allocating decode; the returned vector has length `N` and
  satisfies `sum |X[j]| == K`.
* `decode_pvq_vector_into(n, k, index, &mut [i32]) -> Result<usize,
  PvqDecodeError>` — in-place decode into a caller buffer of length
  `≥ N`; returns the count written (`N`).
* `pvq_l1_norm(&[i32]) -> u64` / `pvq_l2_norm_squared(&[i32]) -> u64`
  — invariant helpers; the §4.3.4.2 final "L2-norm equals one"
  normalization is a floating-point step left to the §4.3.4 consumer
  site (it depends on the band's energy scaling).
* `PVQ_DECODE_N_MAX` / `PVQ_DECODE_K_MAX` — caller-side bookkeeping
  bounds mirrored from `celt_pvq_v`.
* `PvqDecodeError::{CodebookSize(PvqVError), IndexOutOfRange,
  OutputBufferTooSmall}`.

Twenty-seven new unit tests (948 lib tests total, up from 921 at
round-42 close; 20 integration tests unchanged) pin: the
full-index-range bijection (`L1 == K` for every codeword `i ∈ 0..V(N,
K)` over `(N, K) ∈ 1..=6 × 0..=6`, plus injectivity over the same
sweep — combined with the codebook size `V(N, K)` this is a counting
proof of surjectivity onto the K-pulse lattice); hand-enumerated full
codebooks at `(1,1)/(1,3)/(2,1)/(2,2)`; the `K = 0` all-zero codeword;
the index-0 leading-positive-pulse and last-index
leading-non-positive properties; the L1/L2 helpers against manual
values; `decode_into` parity with the allocating variant and its
short-buffer rejection; index-out-of-range rejection at and above
`V(N, K)`; the `V(0, K)` empty-codeword edges; a larger-band
(`N = 16, K = 4`) strided spot check; the §4.1.5 overflow propagation
at `V(176, 176)`; and the error-`Display` / `From<PvqVError>`
plumbing.

The up-front `ec_dec_uint(V(N, K))` index read (wiring the round-3
[`RangeDecoder::dec_uint`] to this decode) and the §4.3.4.1
Bits-to-Pulses search that supplies `K` from the §4.3.3 allocation
remain deferred to the §4.3.4 consumer site.

Source: RFC 6716 §4.3.4.2 (p. 116–117) — held in-repo at
`docs/audio/opus/rfc6716-opus.txt`. No external library source was
consulted; the five-step index-to-vector procedure is stated verbatim
in the standards-track text.

## Round 42 — §4.3.2.2 fine-energy quantization (2026-06-10)

Round 42 lands the RFC 6716 §4.3.2.2 *fine-energy quantization*
primitive. After the §4.3.2.1 coarse-energy predictor reconstructs
each band's log-energy in 6 dB steps, §4.3.2.2 (p. 109) refines it
with a small uniform correction: "Let `B_i` be the number of fine
energy bits for band `i`; the refinement is an integer `f` in the
range `[0, 2**B_i − 1]`. The mapping between `f` and the correction
applied to the coarse energy is equal to `(f + 1/2) / 2**B_i − 1/2`."
Algebraically that is `(2f + 1 − 2**B_i) / 2**(B_i + 1)` — a
zero-mean fraction of a 6 dB step whose `2**B_i` reconstruction
levels tile the open interval `(−1/2, +1/2)` symmetrically about
zero.

§4.3.2.2 also specifies the *final* fine-energy step: "When some
bits are left 'unused' … these bits are used to add one extra fine
energy bit per band per channel. … remaining bits are first assigned
only to bands of priority 0, starting from band 0 and going up. If
all bands of priority 0 have received one bit per channel, then bands
of priority 1 are assigned an extra bit per channel … If any bits are
left after this, they are left unused."

New public surface (`celt_fine_energy`):

* `fine_correction_ratio(bits, f) -> Result<(i32, i32), …>` — the
  exact reduced `(numerator, denominator)` = `(2f + 1 − 2**B_i,
  2**(B_i + 1))`; numerator is always odd (lowest terms).
* `fine_correction_q15(bits, f) -> Result<i32, …>` — the correction
  in Q15, exact for every reachable `B_i` (denominator divides
  `2**16`), strictly within `(−16384, +16384)`.
* `fine_correction_q(bits, f, shift) -> Result<i64, …>` — the
  correction in an arbitrary Q-format (e.g. CELT's `DB_SHIFT = 10`).
* `fine_energy_levels(bits) -> Result<u32, …>``2**B_i`.
* `plan_final_fine_bits(priorities, channels, leftover_bits) ->
  FinalFineBitPlan { granted, bits_used, bits_unused }` — the
  §4.3.2.2 priority-0-then-priority-1, band-0-upward final-bit sweep;
  `None`-priority bands are excluded; `bits_used + bits_unused ==
  leftover_bits` always.
* `FineEnergyChannels::{Mono, Stereo}`, `FinalBitPriority::{Priority0,
  Priority1}`, constants `FINE_ENERGY_MAX_BITS = 14` /
  `FINE_ENERGY_Q15_ONE = 32768` / `FINE_ENERGY_HALF_Q15 = 16384`,
  and `FineEnergyError::{BitsOutOfRange, RefinementOutOfRange}`.

Thirty-three new unit tests (921 lib tests total, up from 888 at
round-41 close; 20 integration tests unchanged) pin the correction at
worked `(B_i, f)` points (`B_i = 1 ⇒ ±1/4`; `B_i = 2 ⇒ ±1/8, ±3/8`),
the odd-numerator-lowest-terms / zero-mean-symmetry / uniform-step /
strictly-within-`±1/2` / monotone-in-`f` invariants, the Q15
exactness against the ratio form, the `DB_SHIFT = 10` parity, and the
final-bit priority sweep (priority ordering, band order within a
priority, the stereo two-bit-per-band cost, leftover-unused,
`None`-band exclusion, zero-budget, empty-priorities, and the
`bits_used + bits_unused == leftover` conservation law).

The §4.3.2.2 range-decoder reads — `dec_bits(B_i)` producing `f` and
`dec_bits(channels)` reading the final extra bits — and the addition
of the correction onto the §4.3.2.1 reconstructed log-energy run at
the consumer site once the §4.3.3 allocator produces the per-band
`B_i` and priority vectors.

Source: RFC 6716 §4.3.2.2 (p. 109) — held in-repo at
`docs/audio/opus/rfc6716-opus.txt`. No external library source was
consulted; the correction formula and the final-allocation priority
rule are both stated verbatim in the standards-track text.

## Round 41 — §4.3.4.2 PVQ codebook-size function `V(N, K)` (2026-06-08)

Round 41 lands the RFC 6716 §4.3.4.2 *PVQ codebook-size function*
`V(N, K)`. RFC 6716 §4.3.4.2 (p. 116) defines it directly:

> The number of combinations can be computed recursively as
> `V(N, K) = V(N-1, K) + V(N, K-1) + V(N-1, K-1)`, with `V(N, 0) = 1`
> and `V(0, K) = 0, K != 0`. There are many different ways to compute
> `V(N, K)`, including precomputed tables and direct use of the
> recursive formulation. […] Implementations MAY use any methods they
> like, as long as they are equivalent to the mathematical definition.

`V(N, K)` is the number of integer-magnitude lattice points
`{ x ∈ Z^N : |x_0| + |x_1| + ... + |x_{N-1}| = K }` — the size of
the §4.3.4 PVQ codebook for `N` MDCT bins and `K` pulses. The
§4.3.4.2 PVQ index is decoded with `ec_dec_uint(V(N, K))`, and the
§4.3.4.1 *Bits-to-Pulses* search picks `K` by searching the codebook
size against the §4.3.3 per-band allocation. Both consume this
primitive at their consumer site.

RFC 6716 §4.1.5 (p. 29) caps `ec_dec_uint`'s `ft` parameter at
`2**32 − 1`; the §4.3.3 bit-allocation procedure keeps the
reachable `(N, K)` pairs inside that bound. This module short-
circuits with `PvqVError::OverflowsDecUintRange` the moment any
intermediate recurrence cell crosses `2**32 − 1`, since such a
PVQ index could not be transmitted by a conforming Opus stream.

New public surface (`celt_pvq_v`):

* `pvq_codebook_size(n, k) -> Result<u32, PvqVError>` — evaluates
  the §4.3.4.2 bivariate recurrence in `u64` over two rolling rows
  of length `K + 1`, returning a `u32` (the `ec_dec_uint` natural
  width). Constant-space (over `K`), `O(N · K)` time.
* `PVQ_V_N_MAX = 352` — caller-side bookkeeping bound on `N`
  covering joint-stereo bands at the 20 ms frame size
  (`2 × CELT_MAX_BINS_PER_BAND = 2 × 176 = 352`).
* `PVQ_V_K_MAX = 4096` — conservative caller-side bookkeeping
  bound on `K` so fuzz callers can sweep wide envelopes.
* `PVQ_V_MAX = 2**32 − 1` — the RFC 6716 §4.1.5 `ec_dec_uint(ft)`
  ceiling, inherited as the overflow guard's threshold.
* `PvqVError::{NOutOfRange{provided, max}, KOutOfRange{provided,
  max}, OverflowsDecUintRange{n, k}}` — caller-side bookkeeping
  errors and stream-impossibility reports.

Twenty-three new unit tests (888 lib tests total, up from 865 at
round-40 close; 20 integration tests unchanged) pin the four
§4.3.4.2 base cases (`V(0, 0) = 1`, `V(N, 0) = 1` for every
`N ∈ 0..=PVQ_V_N_MAX`, `V(0, K) = 0` for every `K ∈ 1..=PVQ_V_K_MAX`,
`V(1, K) = 2` for every `K ≥ 1`, `V(N, 1) = 2N` for every
`N ∈ 1..=PVQ_V_N_MAX`), cross-check the bivariate recurrence over a
`(N, K) ∈ 1..=12` sweep, pin a 7×7 hand-computed table of `V(N, K)`
values, pin two specific worked points (`V(3, 3) = 38`, `V(4, 2) =
32`) that demonstrate the `V(N, K) ≠ V(K, N)` asymmetry (matching
the spec's strictly-ordered coordinate convention), validate the
monotone-non-decreasing-in-`N` invariant for every fixed `K`,
validate the monotone-non-decreasing-in-`K` invariant for `N ≥ 2`
(the `N = 1` carve-out where `V(1, K) = 2` for every `K ≥ 1` is the
documented exception), exercise the §4.1.5 overflow guard on
`V(176, 176)` (well above `2**32`), confirm the guard does *not*
trip on values just under the ceiling (`V(2, K) = 4K` over the full
`K ∈ 0..=100` window), exercise both `PVQ_V_N_MAX` and `PVQ_V_K_MAX`
boundary-rejection paths, validate the three module constants
(`PVQ_V_N_MAX = 352`, `PVQ_V_K_MAX = 4096`, `PVQ_V_MAX = 4_294_967_295
= 2**32 − 1`), and pin every error-Display message at the failing
input.

The §4.3.4.2 PVQ index decode itself (`ec_dec_uint(V(N, K))` then
the §4.3.4.2 index-to-vector conversion) and the §4.3.4.1
*Bits-to-Pulses* search are the natural downstream consumers; both
remain deferred to subsequent rounds.

Source: RFC 6716 §4.3.4.2 (p. 116) — held in-repo at
`docs/audio/opus/rfc6716-opus.txt`. No external library source was
consulted; the recurrence is given directly in the standards-track
text.

## Round 40 — §4.3.3 1/64-step interpolated allocation search (2026-06-08)

Round 40 lands the RFC 6716 §4.3.3 *1/64-step interpolated static-
allocation search* that consumes the round-39 Table 57 surface. RFC
6716 §4.3.3 (p. 111, lines 6223–6230) is explicit: "The allocation
is obtained by linearly interpolating between two values of q (in
steps of 1/64) to find the highest allocation that does not exceed
the number of bits remaining." This round owns the *interpolation +
search* half; the orchestrated §4.3.3 allocator that folds in the
round-31 per-band cap, the round-33 boosts, the round-34
reservations, the round-35 per-band minimum, the round-36 trim
offsets, and the skip / dual-stereo / intensity-stereo flag reads
runs at the consumer site once every piece of the §4.3.3 parameter
surface is composed.

New public surface (`celt_alloc_search`):

* `Q_FP_MAX = 640` — the §4.3.3 fixed-point quality bound packing
  `q'_fp = q_lo * 64 + frac` with `q_lo ∈ 0..=9`, `frac ∈ 0..=63`,
  plus the saturation endpoint `(q_lo = 9, frac = 64)` representing
  `q' = 10.0`.
* `STATIC_ALLOC_INTERP_RIGHT_SHIFT = 8` — the combined right shift
  the §4.3.3 conversion applies to the Q11 per-band cell × step
  product (`>> 2` Q5→Q3 fold plus `>> 6` Q6 step-weight reduction).
* `QFpComponents { q_lo, frac }` — the decomposed `(q_lo, frac)`
  form of the fixed-point quality index.
* `q_fp_to_components(q_fp) -> Result<QFpComponents, …>` /
  `q_fp_from_components(q_lo, frac) -> Result<u32, …>` — invertible
  accessors that round-trip every `q_fp ∈ 0..=640`.
* `per_band_eighth_bits_at_q_fp(band, q_fp, channels, n_bins, lm) ->
  Result<u64, …>` — per-band Q3 allocation under the §4.3.3 linear
  interpolation `cell_q11 = alloc[b][q_lo] * (64 - frac) +
  alloc[b][q_lo + 1] * frac` followed by the
  `(channels * N * cell_q11) << LM >> 8` unit fold. Reduces to the
  round-39 `static_alloc_eighth_bits` at every integer `q_fp = q *
  64`.
* `total_eighth_bits_at_q_fp(q_fp, channels, frame_size, is_hybrid)
  -> Result<u64, …>` — total allocation summed across coded bands,
  respecting the §4.3 first-coded-band rule (`0` for CELT-only /
  `17` for Hybrid).
* `search_q_fp(budget_eighth_bits, channels, frame_size, is_hybrid)
  -> Result<AllocSearchOutcome, …>` — the §4.3.3 "highest
  allocation that does not exceed the number of bits remaining"
  linear scan from `q_fp = Q_FP_MAX` downwards.
* `AllocSearchOutcome { q_fp, total_eighth_bits }` — chosen
  fixed-point quality plus its evaluated total.
* `AllocSearchError::{ChannelsOutOfRange, QFpOutOfRange,
  BandOutOfRange}` — caller-side bookkeeping errors.

Twenty-seven new unit tests (865 lib tests total, up from 838 at
round-39 close; 20 integration tests unchanged) pin: the
`Q_FP_MAX = 640` and `STATIC_ALLOC_INTERP_RIGHT_SHIFT = 8`
derived constants; the `(q_lo, frac)` decomposition at every
integer column, the mid-step `q_fp = 352 ⇒ (5, 32)`, and the
saturation endpoint `q_fp = 640 ⇒ (9, 64)`; the round-trip
`q_fp_from_components(q_fp_to_components(q_fp)) == q_fp` over
the full `0..=640` range; the four invalid `(q_lo, frac)` shapes
the recomposer rejects; the per-band parity check that
`per_band_eighth_bits_at_q_fp(band, q * 64, …)` exactly
reproduces the round-39 `static_alloc_eighth_bits(band, q, …)`
across a representative sweep; the saturation parity check that
`q_fp = Q_FP_MAX` reproduces the pure column-10 lookup; the
column-zero pin; the §4.3.3 monotonicity invariant that per-band
allocations are monotone non-decreasing in `q_fp`; every
caller-bookkeeping error path; the total-across-coded-bands
properties (`total(q_fp = 0) = 0`; monotone in `q_fp`; CELT-only
exceeds Hybrid at saturation; stereo bounded by `2 * mono` and
`2 * mono + 21` to capture per-band `>> 8` rounding slack); and
the search behaviour (zero budget converges to `q_fp = 0`;
`u64::MAX` budget reaches `q_fp = Q_FP_MAX`; exact-target probes
return at least the target; one-less-than-target probes fall
strictly below; the self-consistency invariant that the returned
total recomputes correctly AND if `q_fp < Q_FP_MAX` the next
step's total strictly exceeds the budget).

The orchestrated §4.3.3 allocator that ties the search output to
the per-band cap, minimum, trim, boosts, and reservation block —
plus the §4.3.3 skip / dual-stereo / intensity-stereo flag reads —
runs at the consumer site and is the natural next round.

Source: RFC 6716 §4.3.3 (pp. 111–112) — held in-repo at
`docs/audio/opus/rfc6716-opus.txt`. No external library source was
consulted.

## Round 39 — §4.3.3 static allocation table (Table 57) (2026-06-08)

Round 39 lands the RFC 6716 §4.3.3 *static allocation table* — Table
57's 21-band × 11-quality-column Q5 grid `alloc[band][q]` that the
§4.3.3 *Bit Allocation* search interpolates over to derive each band's
static shape allocation. RFC 6716 §4.3.3 (p. 111) describes the
conversion as
`channels * N * alloc[band][q] << LM >> 2`, where the result is in
1/8 bits — the same units every other §4.3.3 budget quantity uses
(compatible with the round-34 [`celt_reservations`] output, the
round-35 [`celt_band_thresh`] floor, the round-36
[`celt_trim_offsets`] tilt bias, the round-33 boosts, and the
round-31 [`celt_cache_caps50`] per-band cap at the consumer site).

New public surface (`celt_static_alloc`):

* `STATIC_ALLOC: [[u8; 11]; 21]` — the §4.3.3 Table 57 grid
  reproduced inline; row `b ∈ 0..=20` indexes the §4.3 Table 55
  band; column `q ∈ 0..=10` indexes the §4.3.3 quality parameter;
  each cell is a Q5 value in 1/32-bit per MDCT bin units.
* `STATIC_ALLOC_Q_COUNT = 11` / `STATIC_ALLOC_Q_MIN = 0` /
  `STATIC_ALLOC_Q_MAX = 10` / `STATIC_ALLOC_TOTAL_CELLS = 231`  layout constants for the table.
* `STATIC_ALLOC_RIGHT_SHIFT = 2` — the `>> 2` half of the §4.3.3
  `<< LM >> 2` unit fold from Q5 to Q3.
* `STATIC_ALLOC_INTERP_STEPS = 64` — the §4.3.3 1/64-step
  interpolation denominator the orchestrated search will multiply
  by inside its inner loop.
* `static_alloc_cell(band, q) -> Result<u8, StaticAllocError>`  raw-cell lookup before the unit conversion.
* `static_alloc_row(band) -> Result<&[u8; 11], StaticAllocError>`  full-row borrow for the §4.3.3 per-band inner-loop search shape.
* `static_alloc_eighth_bits(band, q, channels, n_bins, lm) ->
  Result<u32, StaticAllocError>` — applies the §4.3.3
  `channels * N * alloc[band][q] << LM >> 2` conversion, returning
  the per-band static shape allocation in 1/8 bits.
* `StaticAllocError::{BandOutOfRange, QualityOutOfRange,
  ChannelsOutOfRange, LmOutOfRange}` — caller-side bookkeeping errors.

Twenty-eight new unit tests (838 lib tests total, up from 810 at
round-38 close; 20 integration tests unchanged) pin the table shape
(21 × 11 = 231 cells; column 0 uniformly zero; column 10 at 200 for
bands 0..=7 then declining monotonically to 104 at band 20), the
monotone-non-decreasing-in-`q` invariant the §4.3.3 search depends
on, hand-picked corner cells (band 0 / q 1 = 90; band 0 / q 10 =
200; band 8 / q 10 = 198; band 13 / q 1 = 0 / q 2 = 20; band 20 / q
5..=8 = 1; band 20 / q 10 = 104), worked-example traces of the
`<< LM >> 2` unit conversion at LM = 0 and LM = 3, the `<< LM`
doubling property across the four CELT frame sizes (`2.5 / 5 / 10
/ 20 ms`), a cross-check against the round-24
[`celt_band_layout::celt_band_bins_per_channel`] band-width lookup
(band 0 at 20 ms = 8 / band 20 at 20 ms = 176 traced through to the
final 1/8-bit allocation), and every out-of-range guard.

The §4.3.3 1/64-step interpolated search over Table 57 itself — the
loop that converges on a quality `q` whose interpolated allocation
fits the working budget (after the round-34 reservations, the
round-35 minimum threshold, the round-36 trim offsets, the round-33
boosts, and the round-31 per-band cap have applied their
constraints) — remains deferred to a subsequent round; this round
owns only the *parameter surface* (the table plus the per-band /
per-cell unit conversion).

Source: RFC 6716 §4.3.3 Table 57 (pp. 111–112) — held in-repo at
`docs/audio/opus/rfc6716-opus.txt`. No external library source was
consulted; the §4.3.3 RFC text identifies the table by its
`(band, q)` indexing rule and gives the values directly in the
standards-track text.

## Round 38 — §4.5.3 normative + recommended-non-normative transition table (2026-06-07)

Round 38 lands the RFC 6716 §4.5.3 *Summary of Transitions* (Figure 18 +
Figure 19) — the configuration-switch lookup that closes the §4.5
chain after the round-26 §4.5.1 redundancy side information, the
round-28 §4.5.1.4 cross-lap placement, and the round-27 §4.5.2
state-reset policy. §4.5.3 enumerates the exhaustive set of
*normative* transitions (nine rows in Figure 18) the encoder is
allowed to use, plus the *recommended non-normative* shapes (seven
rows in Figure 19) for transitions without redundancy where PLC is
allowed.

New public surface (`celt_transitions`):

* `NormativeTransition::{SilkToSilkWithRedundancy,
  NbOrMbSilkToHybridWithRedundancy, WbSilkToHybrid,
  SilkToCeltWithRedundancy, HybridToNbOrMbSilkWithRedundancy,
  HybridToWbSilk, HybridToCeltWithRedundancy,
  CeltToSilkWithRedundancy, CeltToHybridWithRedundancy}` — one
  variant per row of Figure 18.
* `RecommendedNonNormativeTransition::{SilkToSilkAudioBandwidthChange,
  NbOrMbSilkToHybrid, SilkToCeltWithoutRedundancy,
  HybridToNbOrMbSilk, HybridToCeltWithoutRedundancy,
  CeltToSilkWithoutRedundancy, CeltToHybridWithoutRedundancy}` — one
  variant per row of Figure 19.
* `BoundaryOp::{SilkReset, SilkAndCeltReset, CeltReset,
  WindowedCrossLap, DirectMix, CeltOverlapExtract,
  PacketLossConcealment, StreamJoin}` — the §4.5.3 figure key
  markers (`;`, `|`, `!`, `&`, `+`, `c`, `P`, `>`) lifted to a
  typed list so a consumer can cross-check its per-seam dispatch
  decisions against the figure.
* `classify_normative_transition(prev_mode, prev_silk_bandwidth,
  next_mode, next_silk_bandwidth, redundancy_present) ->
  Option<NormativeTransition>` — pure-function lookup against
  Figure 18 rows. The SILK-bandwidth split between rows 2 and 3
  ("NB or MB SILK to Hybrid with Redundancy" vs "WB SILK to
  Hybrid"), between rows 5 and 6 (the symmetric Hybrid → SILK
  case), and the §4.5 "audio-bandwidth change is the glitch
  source" reading that rules out same-bandwidth SILK→SILK from
  row 1, are baked into the classifier.
* `recommended_non_normative(prev_mode, prev_silk_bandwidth,
  next_mode, next_silk_bandwidth) -> Option<RecommendedNonNormativeTransition>`
  — the Figure-19 companion lookup; mutually exclusive with
  Figure 18's two no-redundancy rows (WB-SILK → Hybrid and
  Hybrid → WB-SILK) so consumers can chain the two classifiers
  without overlap.
* `NormativeTransition::seam_operations() -> &'static [BoundaryOp]`
  and the matching method on `RecommendedNonNormativeTransition`
  — the ordered marker list at the transition seam, transcribed
  from the §4.5.3 figure for each row.
* `NormativeTransition::carries_redundancy() -> bool``true`
  for the seven `WithRedundancy` rows, `false` for `WbSilkToHybrid`
  and `HybridToWbSilk` (the two no-redundancy normative
  exceptions §4.5 calls out).
* `redundancy_is_present(decision)` — bridge from the round-26
  `RedundancyDecision` to the boolean the classifier consumes,
  matching the round-27 `mode_transition_reset` convention that
  treats `RedundancyDecision::Invalid` as "no usable redundancy"
  per the §4.5.1.3 stop-and-discard recommendation.

Forty-two new unit tests (810 lib tests total, up from 768 at
round-37 close; 20 integration tests unchanged) pin every Figure-18
and Figure-19 row, the SILK-bandwidth splits, the same-mode
exclusions, the §4.5 first-paragraph carve-outs that exempt same-
configuration CELT→CELT / Hybrid→Hybrid transitions, the seam-op
ordering for every row, and a cross-check that the §4.5.3 figure-
reset markers (`;`, `|`, `!`) agree with the §4.5.2 state-reset
policy already encoded in [`crate::mode_transition_reset`]. The
§4.5.3 invariant that "no-redundancy Figure-18 rows do not appear
on Figure 19" is asserted by sweeping the full
`(prev_mode, prev_bw, next_mode, next_bw)` cross-product.

The actual §4.3.7 power-complementary MDCT cross-lap, the §4.4 PLC
algorithm interior, and the §4.5 mid/side overlap-buffer arithmetic
remain deferred — this round owns only the *boundary classification*
(which seam markers fire for which transition), not the arithmetic
at the seam.

Source: RFC 6716 §4.5.3 (pp. 128–130) — held in-repo at
`docs/audio/opus/rfc6716-opus.txt`. No external library source was
consulted; the §4.5.3 figures and key are the only source.

## Round 36 — §4.3.3 per-band allocation-trim offsets (2026-06-07)

Round 36 lands the §4.3.3 *per-band allocation-trim offsets* — the
per-band tilt vector that biases the §4.3.3 Table 57
static-allocation search after the round-35 `band_min_thresh` floor
is applied. RFC 6716 §4.3.3 (p. 115) specifies the formula:

```text
base = (alloc_trim - 5 - LM)
     * channels
     * n_shortest
     * remaining_bands
     * (1 << LM)
     * 8
     / 64
trim_offsets[b] = base - (if n_per_channel == 1 { 8 * channels } else { 0 })
```

with `alloc_trim ∈ [0, 10]` the round-32 trim signal,
`LM ∈ {0, 1, 2, 3}` the §4.3 frame-size scale,
`channels ∈ {1, 2}`,
`n_shortest = celt_band_bins_per_channel(band, Ms2_5)` (Table 55
column 0 — the shortest §4.3 frame size for the standard CELT mode),
`n_per_channel = celt_band_bins_per_channel(band, frame_size)`, and
`remaining_bands` the band-position-dependent factor. All arithmetic
is signed; the output is in 1/8 bits (the §4.3.3 universal currency).

The §4.3.3 narrative attaches the width-1 carve-out to the per-band
result: "width 1 bands receive greater benefit from the coarse energy
coding", so the trim is backed off by one whole bit per channel for
them. The "number of remaining bands" choice is deferred to the
consumer site (the round that lands the §4.3.3 Table 57
static-allocation search): the RFC narrative phrases it as a
per-band-iteration quantity, and this module accepts `remaining_bands`
as an explicit caller-supplied parameter — both readings of the spec
phrasing fit through the same signature.

New public surface (`celt_trim_offsets`):

* `band_trim_offset(alloc_trim, lm, is_stereo, n_shortest,
  n_per_channel, remaining_bands) -> Result<i32, TrimOffsetError>`  per-band primitive; validates `alloc_trim ≤ ALLOC_TRIM_MAX`.
* `band_trim_offset_for_band(band, alloc_trim, frame_size, is_stereo,
  remaining_bands) -> Result<i32, TrimOffsetError>` — convenience
  that derives `n_shortest` and `n_per_channel` from the round-24
  Table 55 layout; rejects `band ≥ CELT_NUM_BANDS`.
* `band_n_shortest(band) -> Option<u16>` — Table 55 column-0 lookup
  helper.
* `shortest_frame_size() -> CeltFrameSize` — returns `Ms2_5` for the
  standard §4.3 CELT mode (which covers all four frame sizes).
* Formula constants `TRIM_OFFSETS_BIAS = 5` (§4.3.3 "subtract 5"),
  `TRIM_OFFSETS_NUMERATOR_SCALE = 8` (§4.3.3 "multiply by 8"),
  `TRIM_OFFSETS_DIVISOR = 64` (§4.3.3 "divide by 64"),
  `TRIM_OFFSETS_WIDTH_ONE_BINS_PER_CHANNEL = 1` (§4.3.3 width-1
  trigger), `TRIM_OFFSETS_WIDTH_ONE_PER_CHANNEL_EIGHTH_BITS = 8`
  (§4.3.3 per-channel subtraction = one whole bit), and
  `TRIM_OFFSETS_MONO_CHANNELS = 1` / `TRIM_OFFSETS_STEREO_CHANNELS = 2`
  channel multipliers matching the round-35
  `BAND_THRESH_{MONO,STEREO}_CHANNELS` pins.
* `TrimOffsetError::{AllocTrimOutOfRange{provided, max},
  BandOutOfRange{band}}` — caller-side bookkeeping bug variants.

Forty-two new unit tests (751 lib tests total, up from 709 at
round-35 close; 20 integration tests unchanged) pin the seven §4.3.3
formula constants to their narrative sources (including the
`TRIM_OFFSETS_BIAS == ALLOC_TRIM_DEFAULT == 5` cross-check between
the round-32 trim default and the §4.3.3 trim-cancel value), exercise
the §4.3.3 single-band formula at six worked points (default-trim /
LM 0 / no-width-1 ⇒ 0; default-trim / LM 0 / width-1 mono ⇒ -8;
default-trim / LM 0 / width-1 stereo ⇒ -16; max-trim / LM 0 / large
factors ⇒ +577; min-trim / LM 3 / large factors mono ⇒ -3 696;
min-trim / LM 3 / width-1 stereo ⇒ -352), cross-check
LM-factor-doubles (40 → 64 → 96 → 128 across the four LMs with
`trim_term` adjusted per LM), validate the channel /  n_shortest /
remaining_bands linear-scaling invariants in isolation, pin the
truncating-toward-zero integer-division behaviour at three numerator
cells (`-512/64 = -8` exact, `-8/64 = 0` truncating-positive-zero,
`-80/64 = -1` truncating-toward-zero), check the kernel-cancel paths
(`alloc_trim - 5 == LM` ⇒ result = width-1 correction only), validate
the width-1 trigger fires only at `n_per_channel == 1` (verified at
`{0, 2, 3, 22, 176}` exclusion edges), exercise the
`band_trim_offset_for_band` Table-55 wrapper over the full 21 × 4 × 2
matrix and on `band ≥ CELT_NUM_BANDS` rejection, the wrapper's
width-1 trigger at band 0 / 2.5 ms (N = 1) and width-1 inactive at
band 20 / 20 ms (N = 176 ⇒ -1 386), the
output-fits-well-within-`i32` guarantee at worst-case input edges,
plus a determinism sweep over five `alloc_trim` × four frame sizes ×
21 bands × 2 channels × 4 `remaining_bands` values, and `Debug`
rendering for both error variants.

What's still deferred: the §4.3.3 Table 57 static-allocation search
that consumes `trim_offsets[]` (against the round-31 `cap[]`
per-band maximum, the round-33 `boosts[]`, and the round-35
`thresh[]` floor) is the responsibility of the §4.3.3 allocator and
runs in a downstream round. With round 36 now landed, every input to
that search is in tree: per-band `cap[]` from round 31, the
`alloc_trim` signal from round 32, per-band `boosts[]` from round 33,
the reservation block from round 34, per-band `thresh[]` from round
35, and per-band `trim_offsets[]` from this round.

## Round 35 — §4.3.3 per-band minimum-allocation vector (2026-06-06)

Round 35 lands the §4.3.3 *per-band minimum-allocation vector* — the
hard lower bound on shape allocation that lets the §4.3.3 Table 57
static-allocation search *drop* low-rate bands rather than code them
with a sub-floor allocation. RFC 6716 §4.3.3 (p. 115) specifies the
formula:

```text
thresh[band] = max((24 * N) / 16, 8 * channels)
```

with `N = celt_band_bins_per_channel(band, frame_size)` (round 24's
Table 55) and `channels ∈ {1, 2}` the channel count. Both terms are
in 1/8 bits — the §4.3.3 universal currency. The `(24 * N) / 16` term
is 48 128th-bits per MDCT bin (= 1.5 1/8 bits per bin = 3/8 whole bits
per bin); the `8 * channels` term is one whole bit per channel.

The §4.3.3 narrative is explicit that the band-size dependent term
`(24 * N) / 16` is *not* scaled by the channel count: at the very low
rates where this floor binds, the §4.3.3 allocator concentrates the
budget on the mid channel, so the per-band minimum tracks the mid
only. This module pins that carve-out in its constants and tests.

New public surface (`celt_band_thresh`):

* `band_min_thresh(band, frame_size, is_stereo) -> Option<u32>`  per-band `thresh[band]` lookup; `None` when `band ≥ 21` (Custom
  mode is out of scope).
* `compute_band_min_thresh(start, end, frame_size, is_stereo,
  &mut thresh)` — in-place vector fill over the §4.3 coding window
  `start..end` (`0..21` for CELT-only, `17..21` for Hybrid).
* `band_min_thresh_vec(start, end, frame_size, is_stereo) ->
  Result<Vec<u32>, BandThreshError>` — allocating convenience.
* `standard_band_window(is_hybrid) -> (usize, usize)` — helper
  producing the §4.3 full-frame window via
  `celt_first_coded_band(is_hybrid)` +
  `celt_end_coded_band()`.
* Formula constants `BAND_THRESH_BINS_MULTIPLIER = 24`,
  `BAND_THRESH_BINS_DIVISOR = 16`,
  `BAND_THRESH_PER_CHANNEL_EIGHTH_BITS = 8`,
  `BAND_THRESH_MONO_CHANNELS = 1`,
  `BAND_THRESH_STEREO_CHANNELS = 2`.
* `BandThreshError::{InvertedBandWindow, BandWindowOutOfRange,
  OutputBufferTooSmall}` — caller-side bookkeeping bug variants
  (the band layout itself is total over `band < 21`; an out-of-range
  window cannot come from a corrupt bitstream).

Thirty-eight new unit tests (709 lib tests total, up from 671 at
round-34 close; 20 integration tests unchanged) pin the five §4.3.3
constants to their narrative sources, cross-check the function
against `max((24 * N) / 16, 8 * channels)` over every (band,
frame_size, channels) cell of the standard 21-band × 4-frame-size ×
2-channel matrix, validate the §4.3.3 "not scaled by channel count"
invariant at bin-term-dominated cells, validate the
channel-term-doubles-with-stereo invariant at channel-term-dominated
cells, exercise the full CELT-only / Hybrid driver windows plus a
partial NB 2.5 ms window, and check the `band_min_thresh_vec` ⇔
slice-form agreement, the §4.3.3 "at least one whole bit per
channel" floor across every cell, the thresh-monotonic-in-frame-size
invariant, the `stereo ≥ mono` invariant, a units cross-check
pinning the §4.3.3 "48 128th bits per MDCT bin" wording, and the
three `BandThreshError` paths.

What's still deferred: the §4.3.3 *use* of `thresh[]` (the Table 57
static-allocation search competing `thresh[]` against the round-31
`cap[]` per-band maximum and the upcoming `trim_offsets[]` per-band
tilt) runs at the §4.3.3 allocator's consumer site in a downstream
round. The `trim_offsets[]` vector itself is the next §4.3.3 piece;
its formula (RFC 6716 §4.3.3 p. 115) depends on `alloc_trim`, the
shortest frame size for the mode, and the number of remaining
bands, and lives in a separate module.

## Round 34 — §4.3.3 reservation block (2026-06-04)

Round 34 lands the §4.3.3 *reservation block* — the fixed-cost
preamble that runs immediately after the §4.3.3 band-boost loop
(round 33) and the §4.3.3 allocation-trim decode (round 32) but
before the Table 57 static-allocation search. RFC 6716 §4.3.3 (p. 114)
specifies four reservations skimmed off the working `total` budget:

1. `anti_collapse_rsv` (8 1/8 bits) — reserved iff the §4.3.1
   `transient` flag is set, LM > 1 (i.e. CELT frame size ≥ 10 ms),
   and `total ≥ (LM + 2) * 8` at the time of the check.
2. `skip_rsv` (8 1/8 bits) — reserved iff `total > 8` after the
   anti-collapse deduction.
3. `intensity_rsv` (stereo only) — equal to
   `LOG2_FRAC_TABLE[end − start]` Q3 bits from round 30's
   `celt_log2_frac_table::log2_frac` lookup, except reset to 0 if
   that value would exceed the current `total` (in which case
   `dual_stereo_rsv` is also skipped).
4. `dual_stereo_rsv` (stereo only, 8 1/8 bits) — reserved iff
   `total > 8` after the intensity-stereo deduction.

The §4.3.3 working `total` starts at
`frame_size_bytes * 64 − ec_tell_frac − 1` (the trailing `-1` is the
§4.3.3 "one (8th bit) is subtracted to ensure that the resulting
allocation will be conservative" deduction).

New public surface:

* `ReservationOutcome { anti_collapse_rsv, skip_rsv, intensity_rsv,
  dual_stereo_rsv, total_remaining_eighth_bits }` — typed outcome
  in 1/8 bits, with `reserved_total_eighth_bits()` summing the four
  reservation costs for the §4.3.3 invariant check
  `total_remaining + reserved = frame_eighth − ec_tell − 1`.
* `reserve_block(frame_size_bytes, ec_tell_frac, total_boost, lm,
  is_transient, is_stereo, coded_bands) -> Result<ReservationOutcome,
  ReservationError>` — pure-function evaluator over the §4.3.3
  reservation arithmetic. `lm` is typed `CeltFrameSize`; `coded_bands`
  is `end − start` for the §4.3 band-coding window (0..=21 normally,
  ≤ 4 in Hybrid mode), used directly as the
  `crate::celt_log2_frac_table::LOG2_FRAC_TABLE` index for the
  intensity-stereo lookup.
* `ReservationError::{FrameSizeOverflows, TellExceedsFrame{…},
  TotalBoostExceedsFrame{…}, LogFracLookupFailed(Log2FracError)}`  caller-side bookkeeping bugs. The range coder's sticky error flag
  is the right channel for a corrupt bitstream signal; this return
  type captures only frame-arithmetic violations.
* `ONE_BIT_EIGHTH_BITS = 8` — the §4.3.3 cost of each
  anti-collapse / skip / dual-stereo reservation.
* `CONSERVATIVE_DEDUCTION_EIGHTH_BITS = 1` — the §4.3.3 "one (8th
  bit) is subtracted" rule.
* `ANTI_COLLAPSE_LM_MIN_EXCLUSIVE = 1` — the strict `LM > 1` floor.
* `ANTI_COLLAPSE_HEADROOM_MULT_EIGHTH_BITS = 8` and
  `ANTI_COLLAPSE_HEADROOM_LM_OFFSET = 2` — the
  `(LM + 2) * 8` 1/8-bit-headroom test.
* `EIGHTH_BITS_PER_BYTE = 64` (module-local; mirrors round 32's
  `celt_alloc_trim::EIGHTH_BITS_PER_BYTE`).

The §4.3.3 *use* of the reservations — the actual `dec_bit_logp(1)`
reads of the anti-collapse / skip / dual-stereo flags and the
`ec_dec_uint(end − start)` read of the intensity-stereo band — runs
at the §4.3.3 allocator's consumer site after the Table 57 static
allocation search produces the per-band shape allocation. This module
owns only the bookkeeping that decides *whether* each reservation
slot is occupied and *how many 1/8 bits* it claims.

Forty-one new unit tests (671 lib tests total, up from 630 at round-33
close; 20 integration tests unchanged, grand total 691) cover: the
five RFC constants pinned to their narrative sources; the
`EIGHTH_BITS_PER_BYTE` agreement with `celt_alloc_trim`; the
`CeltFrameSize::column_index() → LM` cross-check at every frame size;
the four anti-collapse predicate paths (non-transient ⇒ no rsv,
LM ∈ {0, 1} ⇒ no rsv even with transient, LM = 2 / LM = 3 with budget
⇒ rsv = 8); the §4.3.3 anti-collapse threshold inequality at exact
match and one short; the §4.3.3 skip gate at `total = 8` (rsv = 0)
and `total = 9` (rsv = 8); a strict-ordering check that the
anti-collapse deduction precedes the skip gate; the mono branch
skipping all stereo reservations even with budget; the stereo
intensity-reset-on-overflow path with `dual_stereo_rsv = 0` follow-on;
the stereo intensity-just-fits path with `dual_stereo_rsv ∈ {0, 8}`
depending on the remaining budget vs the `total > 8` gate; the
§4.3 Hybrid 4-band window producing `intensity_rsv = 19` from
`LOG2_FRAC_TABLE[4]`; the `coded_bands ∈ {0, 1}` boundary cells; the
§4.3.3 invariant `total_remaining + reserved = frame_eighth − ec_tell
− 1` across mono / stereo / transient / non-transient / nonzero-tell
permutations; the four `ReservationError` paths (frame-byte overflow,
tell exceeding frame, total_boost exceeding frame, coded_bands above
the `LOG2_FRAC_TABLE` coverage); the mono short-circuit on out-of-range
`coded_bands` (the intensity-stereo lookup is *not* attempted for mono
frames, so the input is harmless); the zero-byte and one-byte frame
edge cases; the §3.4 R5 1275-byte max-frame headroom assertion with
every reservation reserved at its maximum
(`anti_collapse + skip + intensity + dual_stereo = 8 + 8 + 37 + 8 =
61`); the `ReservationOutcome::default()` all-zero pattern;
determinism across repeats; debug formatting; and the
`From<Log2FracError>` round-trip.

Provenance: RFC 6716 §4.3.3 (p. 114) in
`docs/audio/opus/rfc6716-opus.txt`; cross-referenced by
`docs/audio/celt/spec/celt-coarse-energy-and-allocation.md` §2.5
(steps 1–4 of the allocation initial-conditions list). No external
numeric table is required for this module: the four reservation
costs (8, 8, `LOG2_FRAC_TABLE[…]`, 8) and the §4.3.3 gating
predicates are inlined in the RFC body.

The §4.3.3 *use* of the reservations — the actual `dec_bit_logp(1)`
reads of the anti-collapse / skip / dual-stereo flags and the
`ec_dec_uint(end − start)` read of the intensity-stereo band — runs
at the §4.3.3 allocator's consumer site once the Table 57 search
produces the per-band shape allocation; the per-band `trim_offsets[]`
derivation that biases the Table 57 search is the responsibility of
the §4.3.3 allocator and runs in a downstream round.

## Round 33 — §4.3.3 band-boost decoder (2026-06-04)

Round 33 lands the §4.3.3 *band boost* decode loop — the third §4.3.3
fragment after round 30's `LOG2_FRAC_TABLE` and round 31's
`CACHE_CAPS50` parameter surfaces, and the structural piece that
bridges round 31's `cap[]` lookup (consumed as the §4.3.3 inner-loop
upper bound) with round 32's allocation-trim gate (consumed as
`total_boost`). Lives in a new `celt_band_boost` module.

The §4.3.3 narrative (RFC 6716 §4.3.3, pp. 113–114) is the full
band-boost procedure:

> The band boosts are represented by a series of binary symbols that
> are entropy coded with very low probability. […] To decode the band
> boosts: First, set 'dynalloc_logp' to 6, the initial amount of
> storage required to signal a boost in bits, 'total_bits' to the size
> of the frame in 8th bits, 'total_boost' to zero, and 'tell' to the
> total number of 8th bits decoded so far. For each band from the
> coding start (0 normally, but 17 in Hybrid mode) to the coding end
> (which changes depending on the signaled bandwidth), the boost
> quanta in units of 1/8 bit is calculated as `quanta = min(8*N,
> max(48, N))`. […] Set 'boost' to zero and 'dynalloc_loop_logp' to
> dynalloc_logp. While dynalloc_loop_logp […] in 8th bits plus tell is
> less than total_bits plus total_boost and boost is less than `cap[]`
> for this band: Decode a bit from the bitstream with
> dynalloc_loop_logp as the cost of a one and update tell to reflect
> the current used capacity. If the decoded value is zero break the
> loop. Otherwise, add quanta to boost and total_boost, subtract
> quanta from total_bits, and set dynalloc_loop_log to 1. […] If boost
> is non-zero and dynalloc_logp is greater than 2, decrease
> dynalloc_logp.

The module owns:

* `DYNALLOC_LOGP_INIT = 6` — §4.3.3 initial first-boost cost in whole
  bits (`p = 1/64`).
* `DYNALLOC_LOGP_MIN = 2` — §4.3.3 minimum first-boost cost floor
  (`p = 1/4`).
* `DYNALLOC_LOOP_LOGP_AFTER_FIRST = 1` — §4.3.3 within-band cost for
  the second and subsequent boost bits.
* `BAND_BOOST_QUANTA_FLOOR_EIGHTH_BITS = 48` and
  `BAND_BOOST_QUANTA_CEIL_MULT = 8` — §4.3.3 quanta-rule constants
  (48 1/8 bits = 6 whole bits = one full boost step;
  `8*N` 1/8 bits = 1 bit/sample ceiling).
* `band_boost_quanta(n_bins_per_channel) -> u32` — §4.3.3
  `min(8*N, max(48, N))` quanta lookup, total over `u32` (the §4.3
  Table 55 bin counts fit in `u16` by a wide margin).
* `decode_band_boosts(rd, start, end, caps, n_bins, frame_size_bytes)
  -> Result<BandBoostOutcome, BandBoostError>` — the §4.3.3 band-boost
  decode driver. Walks `start..end` (the §4.3 coding window: `0..end`
  normally, `17..end` in Hybrid mode), running the §4.3.3 inner loop
  on each band with the supplied per-band `caps[band - start]` upper
  bound and `n_bins[band - start]` quanta input, and accumulates the
  §4.3.3 `total_boost` consumed by `celt_alloc_trim::decode_alloc_trim`
  downstream.
* `BandBoost { boost_eighth_bits, bits_read }` — per-band outcome.
* `BandBoostOutcome { per_band, total_boost_eighth_bits,
  total_bits_remaining_eighth_bits, dynalloc_logp_final }` — full
  driver outcome.
* `BandBoostError::{CapsLengthMismatch, NBinsLengthMismatch,
  EmptyBandWindow, InvertedBandWindow}` — caller-side bookkeeping
  bugs (the range coder's sticky error flag is the right channel
  for a corrupt bitstream signal).

Thirty-seven new unit tests (630 lib tests total, up from 593 at the
round-32 close; 20 integration tests unchanged, grand total 650)
cover: the five §4.3.3 RFC constants pinned to their narrative
sources; the `quanta = min(8*N, max(48, N))` rule sampled at the
`N = 48` boundary, in the `N > 48` linear regime, in the `6 ≤ N <
48` floor regime, in the `N < 6` ceiling regime, at `N = 0`, and as
a total function over every `u16`; the four `BandBoostError` paths
against an unchanged range-coder state; the no-room-for-any-boost
path (`frame_size_bytes = 0`) returning all-zero boosts and the
unchanged §4.3.3 invariant; the stop-bit-biased payload
(`[0x00; 64]` whose §4.1.1 init `val = 127 - (b0 >> 1) = 127`
biases `dec_bit_logp` toward the §4.3.3 stop branch) decoding zero
boosts with `bits_read = 1` per band and the §4.3.3
`dynalloc_logp_final = DYNALLOC_LOGP_INIT` no-decrement rule; the
boost-bit-biased payload (`[0xFF; 64]` ⇒ `val = 0`) actually
boosting at least one band and decrementing `dynalloc_logp` below
its initial value; the `per_band` vector alignment with the
`start..end` window (including the §4.3 Hybrid `17..21` four-band
window); the §4.3.3 invariant `total_bits + total_boost =
frame_size_bytes * 64` conserved across both the stop and boost
paths; the §4.3.3 `dynalloc_logp` cross-band floor at
`DYNALLOC_LOGP_MIN`; the `boost = 0` short-circuit on a `cap = 0`
band (no range-coder bits read); the `BandBoostOutcome` debug /
equality / determinism cross-check on identical runs; and the
§3.4 R5 `1275 * 64` max-frame headroom assertion.

Provenance: RFC 6716 §4.3.3 (pp. 113–114) in
`docs/audio/opus/rfc6716-opus.txt`; cross-referenced by §2.3 of
`docs/audio/celt/spec/celt-coarse-energy-and-allocation.md`. No
external numeric table is required: the §4.3.3 constants (init = 6,
floor = 2, step = 48, `min(8*N, max(48, N))` quanta rule) and the
narrative state-machine are all inlined in the RFC body.

## Round 32 — §4.3.3 allocation-trim parameter surface (2026-06-03)

Round 32 lands the §4.3.3 *allocation trim* — the Table-58 PDF, the
§4.3.3 signalling gate, and the typed decode wrapper that fuses the
two — behind a new `celt_alloc_trim` module. The §4.3.3 narrative
(RFC 6716 §4.3.3, pp. 114–115) reads:

> The allocation trim is an integer value from 0-10. The default
> value of 5 indicates no trim. The trim parameter is entropy coded
> in order to lower the coding cost of less extreme adjustments.
> Values lower than 5 bias the allocation towards lower frequencies
> and values above 5 bias it towards higher frequencies. Like other
> signaled parameters, signaling of the trim is gated so that it is
> not included if there is insufficient space available in the
> bitstream. To decode the trim, first set the trim value to 5,
> then if and only if the count of decoded 8th bits so far
> (ec_tell_frac) plus 48 (6 bits) is less than or equal to the
> total frame size in 8th bits minus total_boost (a product of the
> above band boost procedure), decode the trim value using the PDF
> in Table 58.

Table 58 is the 11-cell PDF `{2, 2, 5, 10, 22, 46, 22, 10, 5, 2,
2}/128`. The symbol `k ∈ 0..=10` reads as the trim integer `k`; the
PDF is symmetric around `k = 5` (the no-trim default), with the
heaviest mass on that cell, and falls off as 22, 10, 5, 2, 2 either
side — matching the §4.3.3 "less extreme adjustments cheapened" rule.

The module owns:

* `ALLOC_TRIM_PDF: [u8; 11]` — the Table-58 PDF reproduced inline.
* `ALLOC_TRIM_ICDF: [u8; 11]` = `[126, 124, 119, 109, 87, 41, 19,
  9, 4, 2, 0]` — the derived iCDF by the §4.1.3.3
  `icdf[k] = (1<<ftb) − fh[k]` rule, ready for
  `RangeDecoder::dec_icdf`.
* `ALLOC_TRIM_PDF_LEN = 11`, `ALLOC_TRIM_FTB = 7`,
  `ALLOC_TRIM_PDF_DENOMINATOR = 128` — shape constants.
* `ALLOC_TRIM_DEFAULT = 5`, `ALLOC_TRIM_MIN = 0`, `ALLOC_TRIM_MAX
  = 10` — trim-integer range, per the §4.3.3 wording.
* `ALLOC_TRIM_SIGNAL_COST_EIGHTH_BITS = 48` (the §4.3.3 "plus 48
  (6 bits)" budget) and `EIGHTH_BITS_PER_BYTE = 64` — gate
  constants.
* `alloc_trim_is_signalled(ec_tell_frac, frame_eighth_bits,
  total_boost) -> bool` — the §4.3.3 signalling-gate predicate.
* `frame_eighth_bits(frame_size_bytes) -> Result<u32,
  AllocTrimError>` — byte-to-1/8-bit conversion with `u32`
  overflow rejection.
* `decode_alloc_trim(rd, ec_tell_frac, frame_size_bytes,
  total_boost) -> Result<u8, AllocTrimError>` — the composite
  wrapper: evaluate the gate, return `5` on gate failure
  (consuming no bits), or `dec_icdf(&ALLOC_TRIM_ICDF, 7)` on gate
  success.
* `alloc_trim_pdf()` / `alloc_trim_icdf()` — full-table borrows.
* `AllocTrimError::{FrameSizeOverflows, TotalBoostExceedsFrame{
  frame_eighth_bits, total_boost }}` — error variants for
  caller-side bookkeeping bugs.

Thirty-three new unit tests (593 lib tests total, up from 560 at the
round-31 close; 20 integration tests unchanged, grand total 613)
cover: the `ALLOC_TRIM_PDF_LEN = 11` / `ALLOC_TRIM_FTB = 7` /
`ALLOC_TRIM_PDF_DENOMINATOR = 128` / `ALLOC_TRIM_DEFAULT = 5` /
`ALLOC_TRIM_MIN..=ALLOC_TRIM_MAX = 0..=10` /
`ALLOC_TRIM_SIGNAL_COST_EIGHTH_BITS = 48` /
`EIGHTH_BITS_PER_BYTE = 64` constants; the Table 58 PDF cells pinned
against the RFC body verbatim; the PDF sums-to-128 invariant; the
PDF symmetry around `k = 5`; the heaviest-mass-at-default cell
(`PDF[5] = 46`); the iCDF strict-monotone-decreasing invariant; the
iCDF-from-PDF derivation cross-check (every cell of the 11-cell
table); four iCDF spot pins (`[0] = 126`, `[1] = 124`, `[5] = 41`,
`[10] = 0`); the `frame_eighth_bits` scaling at `0`, `1`, `1275`
(§3.4 R5 max) and `u32` overflow rejection on `boundary + 1` and
`u32::MAX`; the §4.3.3 signalling gate at the six-bit boundary
(`ec_tell_frac = frame − 48` passes, `frame − 47` fails); the gate
under non-zero `total_boost`; the gate underflow / `u32` overflow
safety paths; the `decode_alloc_trim` gate-fail returns
`ALLOC_TRIM_DEFAULT` and consumes no range-coder bits (via
`tell()` before/after); the gate-pass returns an in-range value and
advances `tell_frac()`; both error paths leave the range coder
untouched; and the worst-case-symbol-cost-matches-gate-budget
math `log2(128 / 2) = 6` whole bits = 48 1/8 bits.

Provenance: the §4.3.3 narrative (the §4.3.3 trim integer range, the
"default value of 5 indicates no trim" wording, the signalling-gate
predicate `(ec_tell_frac + 48) ≤ (frame_size_bytes * 8 −
total_boost)`, and the §4.3.3 reference function names) is
transcribed from RFC 6716 §4.3.3 in
`docs/audio/opus/rfc6716-opus.txt` (pp. 114–115). The 11-cell Table
58 PDF is inlined in the RFC body on p. 115; no separate CSV is
required (the `docs/audio/celt/tables/` set holds only the §4.3.3
tables the RFC does *not* inline). The
`docs/audio/celt/spec/celt-coarse-energy-and-allocation.md` §2.4
narrative cross-references both. The iCDF is derived from the
inlined PDF by the §4.1.3.3 `icdf[k] = (1 << ftb) − fh[k]` rule.
The §4.3.3 *use* of the trim — the per-band `trim_offsets[]`
derivation (RFC 6716 §4.3.3 p. 115: `(alloc_trim − 5 − LM) *
channels * MDCT_bin_count * remaining_bands * 2**LM * 8 / 64`, with
the width-1-band carve-out subtracting `8 * channels`) that biases
the Table 57 static allocation search — is the responsibility of
the §4.3.3 allocator and runs at the call site of
`decode_alloc_trim`; it is out of scope for this parameter surface.

## Round 31 — §4.3.3 per-band maximum-allocation parameter surface (2026-06-03)

Round 31 lands the §4.3.3 *bit allocation* `cache_caps50` lookup plus
the §4.3.3 `init_caps()` convert rule (RFC 6716 §4.3.3, pp. 113–114)
behind a new `celt_cache_caps50` module. This is the second of the
two §4.3.3 table dependencies round 24 noted as blocking the
allocator: round 30 landed `LOG2_FRAC_TABLE` (the §4.3.3
intensity-stereo reservation log₂), and this round lands
`CACHE_CAPS50` (the §4.3.3 per-band maximum allocation cap). With
both tables in tree the §4.3.3 allocator's table-dependency wall is
closed; what remains is the orchestration itself (boost / trim /
anti-collapse / skip / dual-stereo reservations, the Table 57
static-allocation search, and the reallocation / fine-vs-shape split
/ band-priority computation).

The §4.3.3 narrative reads (RFC 6716 §4.3.3, p. 113):

> The maximum allocation vector is an approximation of the maximum
> space that can be used by each band for a given mode. The value is
> approximate because the shape encoding is variable rate […]. The
> maximums specified by the codec reflect the average maximum. In
> the reference implementation, the maximums in bits/sample are
> precomputed in a static table […] for each band, for each value
> of LM, and for both mono and stereo.

The §4.3.3 indexing and convert rule (RFC 6716 §4.3.3 p. 113):

> To convert the values in cache.caps into the actual maximums:
> first, set `nbBands` to the maximum number of bands for this mode,
> and `stereo` to zero if stereo is not in use and one otherwise.
> For each band, set `N` to the number of MDCT bins covered by the
> band (for one channel), set `LM` to the shift value for the frame
> size. Then, set `i` to `nbBands*(2*LM+stereo)`. Next, set the
> maximum for the band to the `i`-th index of `cache.caps + 64` and
> multiply by the number of channels in the current frame (one or
> two) and by `N`, then divide the result by 4 using integer
> division. The resulting vector will be called `cap[]`. The
> elements fit in signed 16-bit integers but do not fit in 8 bits.
> This procedure is implemented in the reference in the function
> `init_caps()` in `celt.c`.

So the §4.3.3 allocator needs three things from this module: the
flat `cache_caps50` byte for a `(LM, stereo, band)` triple, the
`init_caps()` `(value + 64) * channels * N / 4` convert step, and
the §4.3.3 `i = nbBands*(2*LM + stereo) + band` row-stride indexing
rule. All three are owned here; the §4.3.3 band loop that walks
across bands and produces the full `cap[]` vector is the
allocator's responsibility and runs at the call site.

The module owns:

* `CACHE_CAPS50: [u8; 168]` — the per-band maximum-allocation table
  in Q0 bits/sample units, laid out as eight 21-byte rows in the
  §4.3.3 `(LM, stereo)` row-stride convention. Row `r` is
  `(LM = r/2, stereo = r%2)`; the row matches CSV row `r` in
  `docs/audio/celt/tables/cache_caps50.csv`.
* `CACHE_CAPS50_LM_COUNT = 4`, `CACHE_CAPS50_STEREO_COUNT = 2`,
  `CACHE_CAPS50_TOTAL_BYTES = 168` — shape constants for downstream
  callers.
* `CACHE_CAPS50_STEREO_MONO = 0`, `CACHE_CAPS50_STEREO_STEREO = 1`  the §4.3.3 stereo-axis index constants.
* `INIT_CAPS_BIAS = 64`, `INIT_CAPS_DIVISOR = 4`,
  `INIT_CAPS_MAX_CHANNELS = 2``init_caps()` convert-rule constants.
* `CacheCapsStereo::{Mono, Stereo}` — the typed stereo-axis
  selector, with `axis_index() -> usize` (yielding `0` / `1` for the
  row-stride rule), `channels() -> u32` (yielding `1` / `2` for the
  `init_caps()` multiplier), and `from_is_stereo(bool) -> Self` for
  decoding the TOC stereo-flag boolean.
* `cache_caps_offset(lm, stereo, band) -> usize` — the §4.3.3
  `nbBands * (2*LM + stereo) + band` flat-offset helper.
* `cache_caps_value(lm, stereo, band) -> Result<u8, CacheCaps50Error>`
  — the typed per-cell accessor with `LmOutOfRange` /
  `BandOutOfRange` bounds checks.
* `cache_caps_row(lm, stereo) -> Result<&'static [u8], CacheCaps50Error>`
  — the typed per-row borrow for the §4.3 band loop.
* `init_caps(caps_value, channels, n_bins) -> u32` — the §4.3.3
  `((value + 64) * channels * N) / 4` convert step on a single byte
  (named for the §4.3.3 reference function).
* `cap_for_band_bits(lm, stereo, band, channels, n_bins) -> Result<u32,
  CacheCaps50Error>` — composite lookup + convert, with the
  `ChannelsOutOfRange` check on the §4.3.3 `channels ∈ {1,2}`
  range.
* `CacheCaps50Error::{LmOutOfRange, BandOutOfRange,
  ChannelsOutOfRange}` — the three error variants.

The §4.3.3 narrative invariant that the per-band cap "fits in signed
16-bit integers but does not fit in 8 bits" is checked across the
full §4.3 band loop at 20 ms stereo (the headline CELT-only frame
size at the maximum channel count): every `cap_for_band_bits` call
is `≤ i16::MAX`, and at least one cell exceeds `i8::MAX`.

Twenty-nine new unit tests (560 lib tests total, up from 531 at the
round-30 close; 20 integration tests unchanged, grand total 580)
cover: the `CACHE_CAPS50_LM_COUNT = 4` / `CACHE_CAPS50_STEREO_COUNT
= 2` / `CACHE_CAPS50_TOTAL_BYTES = 168` shape constants pinned
against the array's actual length; the `INIT_CAPS_BIAS = 64` /
`INIT_CAPS_DIVISOR = 4` / `INIT_CAPS_MAX_CHANNELS = 2` convert-rule
constants; the `CACHE_CAPS50_STEREO_MONO = 0` /
`CACHE_CAPS50_STEREO_STEREO = 1` axis-index constants plus the
`CacheCapsStereo::axis_index()` / `channels()` /
`from_is_stereo(bool)` round-trip; eight CSV-cell spot-checks at
`(row 0, band 0)` / `(row 1, band 20)` / `(row 2, band 0)` /
`(row 3, band 8)` / `(row 4, band 12)` / `(row 5, band 17)` /
`(row 6, band 20)` / `(row 7, band 0)` (covering every CSV row plus
the high-band tail of the 2.5 ms stereo / 20 ms mono rows, mid-band
plateau of the 10 ms mono row, and the Hybrid-reachable band of the
10 ms stereo row); the §4.3.3 `cache_caps_offset()` rule against
every `(LM, stereo, band)` triple (168 cells) plus the two endpoints
(`offset(0, Mono, 0) == 0` and
`offset(3, Stereo, 20) == TOTAL_BYTES − 1`); the
`cache_caps_value()` total-function sweep; the `cache_caps_row()`
per-cell mirror; the `LmOutOfRange` / `BandOutOfRange` /
`ChannelsOutOfRange` error paths on both accessors and the composite
helper; four `init_caps()` formula pins including the
`(caps=255, channels=2, N=192) → 30624` upper-bound cell and the
floor-division corner at `caps ∈ {1,2,3}` (all yielding
`(value + 64) / 4 = 16`); a `cap_for_band_bits()` composite
cross-check against the manual lookup-plus-`init_caps()` sequence
at `(LM=2, stereo=Stereo, band=17)` driven by the §4.3 Table 55 bin
count for that band; the §4.3.3 narrative `cap fits in i16 but not
i8` invariant (sweep at 20 ms stereo for the i16 bound + an explicit
`at_least_one_cap_exceeds_i8` pin); and two §4.3.3-reachable-cell
sanity pins (CELT-only 20 ms stereo band 0 → `caps = 204` →
`cap = 134 * n_bins`; Hybrid 20 ms mono band 17 → `caps = 173` →
`cap = (237 * n_bins) / 4`).

Provenance: the §4.3.3 narrative (the convert rule, the §4.3.3
`i = nbBands * (2*LM + stereo) + band` indexing, the bits/sample
table description, the `cap` fits-in-`i16` invariant, and the
`init_caps()` function name) is transcribed from RFC 6716 §4.3.3
in `docs/audio/opus/rfc6716-opus.txt` (pp. 113–114). The 168 Q0
byte values are reproduced from
`docs/audio/celt/tables/cache_caps50.csv` (one CSV row per `(LM,
stereo)` cell, 21 bytes per row — see the `cache_caps50.meta`
sidecar for the canonical layout). The narrative
`docs/audio/celt/spec/celt-coarse-energy-and-allocation.md` §2.2
cross-references both. The rest of the §4.3.3 allocation algorithm
(boost / trim / anti-collapse / skip / dual-stereo reservations,
the Table 57 static-allocation search consuming the `cap[]` vector,
the reallocation / fine-vs-shape split / band-priority computation)
is out of scope for this module.

## Round 30 — §4.3.3 intensity-stereo reservation parameter surface (2026-06-02)

Round 30 lands the §4.3.3 *bit allocation* `LOG2_FRAC_TABLE` lookup
(RFC 6716 §4.3.3, p. 113) behind a new `celt_log2_frac_table` module.
This is a narrow parameter-surface piece — the 24-byte conservative
`log2` table the §4.3.3 *intensity-stereo reservation* uses, plus a
typed accessor pairing it with the §4.3.3 `coded_bands = end − start`
indexing rule — not the rest of the §4.3.3 allocation algorithm
(anti-collapse / skip / dual-stereo reservations, the Table 57
static-allocation search, boost / trim decoding, or the `cache_caps50`
per-band maximum vector). Round 24 noted the §4.3.3 allocator as
blocked on `cache_caps50` + `LOG2_FRAC_TABLE`; this round delivers
the smaller of the two table dependencies so subsequent rounds can
build up the §4.3.3 reservation pre-amble against it.

The §4.3.3 narrative (RFC 6716 §4.3.3 sub-step §2.5 "intensity
stereo") reads:

> For stereo, bits are reserved for intensity stereo and dual stereo.
> Intensity stereo requires `ilog2(end − start)` bits, reserved if
> there is room […]. The number of bits actually reserved is given
> by the `LOG2_FRAC_TABLE` in `rate.c`.

So the §4.3.3 caller indexes the table by the number of coded bands
in the frame (`end − start` over the §4.3 Table 55 band loop) and
reserves that many 1/8-bit units from `total` before the Table 57
static allocation search runs. For CELT-only frames the band loop is
`0..=20` so `end − start = 21`; for Hybrid frames the SILK layer
covers the first 17 bands so `end − start = 4` (the §4.3 carve-out of
bands `17..=20`). The table's 24-entry depth covers both with
headroom.

The module owns:

* `LOG2_FRAC_TABLE: [u8; 24]` — the conservative `log2` table in Q3
  (1/8-bit) units, laid out exactly as
  `docs/audio/celt/tables/log2_frac_table.csv` (one CSV row per
  `(index, log2_8thbits)` pair).
* `LOG2_FRAC_TABLE_LEN = 24` — the shape constant for downstream
  callers.
* `Q3_BITS_PER_WHOLE_BIT = 8` — the §4.3.3 unit-denominator,
  toggling between whole bits and 1/8-bit units.
* `log2_frac(coded_bands) -> Result<u8, Log2FracError>` — the typed
  accessor that does the §4.3.3 `LOG2_FRAC_TABLE[end − start]`
  lookup with a bounds check that catches the `coded_bands ≥ 24`
  case (which the §4.3.3 band loop cannot reach but a buggy caller
  could).
* `log2_frac_row() -> &'static [u8; 24]` — the full-row borrow when
  a downstream sub-decoder wants to iterate the table without
  per-call indexing.
* `Log2FracError::CodedBandsOutOfRange { coded_bands }` — the one
  error variant.

Seventeen new unit tests (531 lib tests total, up from 514 at the
round-29 close; 20 integration tests unchanged, grand total 551)
cover: the `LOG2_FRAC_TABLE_LEN = 24` shape constant pinned against
the array's actual length; the `Q3_BITS_PER_WHOLE_BIT = 8` unit
constant; seven CSV-row spot-checks at indices 0 / 1 / 2 / 4 / 14 /
15 / 21 / 23 (covering the §4.3.3 base case, the 1-bit floor, the
upward-rounded conservative entry, the Hybrid reachable index, the
32-byte plateau pair, the CELT-only reachable index, and the final
entry); a monotone-non-decreasing property over every adjacent pair
of entries (the §2.5 narrative's "conservative log2" implies
monotonicity); a conservative-bound property `LOG2_FRAC_TABLE[n] ≥
8 × floor(log2(n))` for every `n ∈ 1..24` (formulated as a leading-
zero-count check to avoid floating-point); a total-function sweep
over every in-range index (24 cells); `CodedBandsOutOfRange` error
paths for `LOG2_FRAC_TABLE_LEN` and `u32::MAX`; a row-vs-pair
cross-check on every cell that `log2_frac_row()` agrees with
`log2_frac(n)`; and two §4.3.3-reachable-index sanity pins
(CELT-only `end − start = 21` → `36` Q3; Hybrid `end − start = 4` →
`19` Q3).

Provenance: the §4.3.3 narrative (the conservative `log2`
characterisation, the `intensity_rsv = LOG2_FRAC_TABLE[end − start]`
formula, the §4.3.3 §2.5 sub-step the table participates in, and the
Q3 / 1-8-bit unit) is transcribed from RFC 6716 §4.3.3 in
`docs/audio/opus/rfc6716-opus.txt` (pp. 112–114). The 24 Q3 byte
values are reproduced from `docs/audio/celt/tables/log2_frac_table.csv`
(one CSV row per `(index, log2_8thbits)` pair — see the
`log2_frac_table.meta` sidecar for the canonical layout). The
narrative `docs/audio/celt/spec/celt-coarse-energy-and-allocation.md`
§2.5 cross-references both. The rest of the §4.3.3 allocation
algorithm (boost / trim / anti-collapse / skip / dual-stereo
reservations, the Table 57 static-allocation search, the
`cache_caps50` per-band maximum, the §4.3.3 reallocation /
fine-vs-shape split / band-priority computation) is out of scope for
this module.

## Round 29 — §4.3.2.1 CELT coarse-energy Laplace-model parameter surface (2026-06-01)

Round 29 lands the first §4.3.2.1 *Coarse Energy Decoding* fragment
(RFC 6716 §4.3.2.1, pp. 108–109) behind a new `celt_e_prob_model`
module. This is the parameter-surface piece — the table lookup that
hands the §4.3.2.1 `ec_laplace_decode` routine its per-band Q8
`{probability, decay}` pair — not the Laplace decoder itself nor the
2-D `(time, frequency)` predictor that consumes its output. Round 20
landed the CELT pre-band header up to the `intra` flag and noted the
coarse-energy decode as blocked on `e_prob_model`; this round
delivers that table plus the surrounding selector / accessor surface
so the Laplace decoder + predictor can be wired up against it next.

The §4.3.2.1 narrative names three pieces of data the coarse-energy
decoder needs:

1. **`(alpha, beta)` prediction coefficients.** RFC 6716 §4.3.2.1
   p. 108 fixes the intra case at `alpha = 0` and
   `beta = 4915 / 32768` (Q15). The inter case "depend[s] on the
   frame size in use"; numeric values are not in the RFC body.
2. **The `e_prob_model` table** — per
   `(LM, intra, band)` Q8 `{prob, decay}` pair, where
   `LM = log2(frame_size / 120) ∈ {0,1,2,3}` selects the
   120 / 240 / 480 / 960-sample CELT frame sizes,
   `intra ∈ {0,1}` selects inter vs. intra, and `band ∈ 0..21`
   indexes the §4.3 Table 55 MDCT bands. 336 bytes total
   (4 × 2 × 21 × 2).
3. **The `ec_laplace_decode` routine** itself. Out of scope for
   this round.

The module owns:

* `E_PROB_MODEL: [[[u8; 42]; 2]; 4]` — the 336-byte Q8 table,
  laid out exactly as `docs/audio/celt/tables/e_prob_model.csv`
  (one CSV row = one `(LM, mode)` cell with 21 `{prob, decay}`
  pairs).
* `E_PROB_MODEL_LM_COUNT = 4`, `E_PROB_MODEL_MODE_COUNT = 2`,
  `E_PROB_MODEL_BYTES_PER_BAND = 2`,
  `E_PROB_MODEL_BYTES_PER_ROW = 42`,
  `E_PROB_MODEL_TOTAL_BYTES = 336` — shape constants for
  downstream callers.
* `E_PROB_MODEL_MODE_INTER = 0`, `E_PROB_MODEL_MODE_INTRA = 1`  the §4.3.2.1 inner-axis index constants.
* `EnergyPredictionMode::{Inter, Intra}` — typed selector with
  `from_intra_flag(bool)` decode helper and a `table_index()`
  accessor.
* `EProbPair { prob, decay }` — Q8 pair the §4.3.2.1
  `ec_laplace_decode` consumes.
* `e_prob_pair(lm, mode, band) -> Result<EProbPair, EProbModelError>`
  — typed lookup with bounds checks on `lm` and `band`.
* `e_prob_row(lm, mode) -> Result<&'static [u8; 42], EProbModelError>`
  — borrows the full 42-byte row so the band loop can iterate
  without re-indexing.
* `INTRA_PRED_ALPHA_Q15 = 0` / `INTRA_PRED_BETA_Q15 = 4915` /
  `Q15_ONE = 32768` — the §4.3.2.1 intra-case prediction
  coefficients (`4915 / 32768 ≈ 0.15`).

Twenty-two new unit tests (514 lib tests total, up from 492 at
round-28 close) cover: the five shape constants matching the
struct's actual array dimensions; the inner-row length invariant
(42 bytes = 21 bands × 2 bytes) for every `(LM, mode)` cell; the
total-byte invariant summed across all 8 rows; the
`INTRA_PRED_ALPHA_Q15 = 0` / `INTRA_PRED_BETA_Q15 = 4915` /
`Q15_ONE = 32768` constants per RFC 6716 §4.3.2.1 p. 108;
`EnergyPredictionMode::from_intra_flag` truth-table; the
`Inter → 0` / `Intra → 1` `table_index` mapping matching the CSV
layout; seven CSV row spot-checks (CSV rows 0, 1, 3, 4, 6, 7
covering both modes at LM = 0, 1, 2, 3, and bands 0, 5, 10, 20);
the `LmOutOfRange` and `BandOutOfRange` error paths for both
accessors; the full 42-byte row returned by `e_prob_row` (first +
last band positions spot-checked); a total-function sweep over
every `(LM, mode, band)` triple (4 × 2 × 21 = 168 cells); a
`pair_lookup_matches_row_lookup` cross-check that the typed pair
accessor agrees with the raw-row accessor on every cell; and a
sanity property (intra band-0 `prob` < inter band-0 `prob` for
every LM) reflecting the §4.3.2.1 narrative on prediction
effectiveness at band 0.

Provenance: the §4.3.2.1 narrative, the `alpha = 0` /
`beta = 4915 / 32768` intra-case coefficients, the per-`(LM,
intra, band)` table layout, and the Q8 `{prob, decay}` pair
semantics are transcribed from RFC 6716 §4.3.2.1 in
`docs/audio/opus/rfc6716-opus.txt` (pp. 108–109). The 336 Q8 bytes
are reproduced from `docs/audio/celt/tables/e_prob_model.csv` (one
CSV row per `(LM, mode)` cell, 42 bytes each — see the
`e_prob_model.meta` sidecar for the canonical layout). The narrative
`docs/audio/celt/spec/celt-coarse-energy-and-allocation.md` §1.2
cross-references both. The per-LM *inter*-mode `(alpha, beta)` pair
is a §4.3.2.1 docs gap (the RFC says "depend on the frame size in
use" without giving numeric values); deferred until the docs side
delivers the gap fill.

## Round 28 — §4.5.1.4 redundant-CELT-frame decode parameters + cross-lap placement (2026-06-01)

Round 28 lands the §4.5.1.4 *Decoding the Redundancy* fragment
(RFC 6716 §4.5.1.4, pp. 126–127) behind a new
`redundancy_decode_params` module. This is the third §4.5
(mode-switching) fragment after round 26's §4.5.1.1–§4.5.1.3
boundary metadata and round 27's §4.5.2 state-reset decision tree.
Round 26 said *whether* a redundant CELT frame was present and
*where* its bytes sat; round 27 said *which* sub-decoders to reset
across the transition; this round turns the boundary metadata into
the concrete *decode parameters* the §4.3 CELT decoder needs (no
TOC byte; fixed 5 ms duration; inherited channel count; inherited
bandwidth with the MB → WB exception) plus the §4.5.1.4
*cross-lap placement* metadata that tells the caller which 2.5 ms
half of the redundant CELT output feeds the splice with the
SILK/Hybrid signal.

The §4.5.1.4 prose has two normative halves.

**Half 1 — redundant-frame parameters.** *"The redundant frame is
decoded like any other CELT-only frame, with the exception that it
does not contain a TOC byte. The frame size is fixed at 5 ms, the
channel count is set to that of the current frame, and the audio
bandwidth is also set to that of the current frame, with the
exception that for MB SILK frames, it is set to WB."* Four facts:

1. **No TOC byte.** The §3.1 TOC parse is skipped; the §4.3 CELT
   decoder is started directly on the redundant bytes.
2. **Frame size fixed at 5 ms.** Encoded as
   `REDUNDANT_FRAME_TENTHS_MS = 50` in the crate's
   tenths-of-a-millisecond convention.
3. **Channel count inherited** from the carrier Opus frame.
4. **Bandwidth inherited with the MB SILK → WB override**   Hybrid carriers (SWB / FB) and SILK-only NB / WB carriers pass
   through; SILK-only MB carriers bump to WB (the §4.3 CELT layer
   does not support MB).

**Half 2 — cross-lap placement.** *"If the redundancy belongs at
the beginning (in a CELT-only to SILK-only or Hybrid transition),
the final reconstructed output uses the first 2.5 ms of audio
output by the decoder for the redundant frame as is, discarding
the corresponding output from the SILK-only or Hybrid portion of
the frame. The remaining 2.5 ms is cross-lapped with the decoded
SILK/Hybrid signal using the CELT's power-complementary MDCT
window …"* + *"If the redundancy belongs at the end (in a SILK-
only or Hybrid to CELT-only transition), only the second half
(2.5 ms) of the audio output by the decoder for the redundant
frame is used. In that case, the second half of the redundant
frame is cross-lapped with the end of the SILK/Hybrid signal …"*
Two cases:

* `RedundancyPosition::Beginning`  `CrossLapPlacement::FirstHalfAsIs`. Carrier is the post-
  transition SILK/Hybrid frame. The redundant CELT frame's first
  2.5 ms replace the carrier's leading 2.5 ms; the second 2.5 ms
  cross-lap with the SILK/Hybrid signal across the 2.5–5.0 ms
  region of the Opus frame.
* `RedundancyPosition::End`  `CrossLapPlacement::SecondHalfAsIs`. Carrier is the pre-
  transition SILK/Hybrid frame. Only the redundant CELT frame's
  second 2.5 ms are used; that half cross-laps with the trailing
  edge of the SILK/Hybrid signal. The first 2.5 ms are discarded.

The §4.3.7 power-complementary MDCT window that actually performs
the cross-lap mix is part of the §4.3.7 inverse-MDCT stage, which
is gated on the §4.3.2 / §4.3.3 / §4.3.4 chain (all still
deferred). What this round owns is the placement metadata —
WHERE in the carrier's sample buffer the 2.5 ms cross-lap region
sits, and WHICH 2.5 ms half of the redundant CELT output feeds it
— so the §4.3.7 stage, once unblocked, can splice the two streams
directly.

The module owns:

* `REDUNDANT_FRAME_TENTHS_MS = 50` — §4.5.1.4 "fixed at 5 ms"
  duration.
* `REDUNDANT_CROSS_LAP_TENTHS_MS = 25` — half-duration of the
  redundant frame, the cross-lap region size in both cases.
* `RedundantFrameParams { duration_tenths_ms, channels,
  bandwidth, position, size_bytes, cross_lap }` — the §4.5.1.4
  outcome bundled into a single struct.
* `CrossLapPlacement::{FirstHalfAsIs, SecondHalfAsIs}` — half-2
  placement decision, with `from_position` + `uses_first_half` +
  `second_half_is_used_as_is` accessors.
* `apply_mb_to_wb_override(carrier_bandwidth, is_silk_only)`  half-1 bandwidth-override helper exposed for cross-checking.
* `redundant_frame_params(routing, decision) -> Option<...>`  driver entry. Returns `None` for `NotPresent` and `Invalid`
  (the §4.5.1.3 overflow case is "stop and discard" per the RFC
  RECOMMENDATION), otherwise the populated parameters.

Twenty-five new unit tests (492 lib tests total, up from 467 at
round-27 close; 20 integration tests unchanged, grand total 512)
cover: the `REDUNDANT_FRAME_TENTHS_MS = 50` and
`REDUNDANT_CROSS_LAP_TENTHS_MS = 25` constants and their
half-of-frame invariant; `CrossLapPlacement::from_position`
totality; `uses_first_half` accessor truth table; the
"second half is never used as-is" invariant for both placements;
`apply_mb_to_wb_override` firing for SILK-only MB; the override
NOT firing for Hybrid MB (pathological), SILK-only NB / WB / SWB
/ FB pass-through under any carrier mode; `redundant_frame_params`
returning `None` for `NotPresent` and `Invalid`; SILK-only NB +
Beginning ⇒ FirstHalfAsIs with NB pass-through; SILK-only MB +
End ⇒ SecondHalfAsIs with bandwidth bumped to WB; SILK-only WB
pass-through; Hybrid SWB and Hybrid FB pass-through; channel-
count inheritance under five (mode, bandwidth) carriers × both
channel modes; duration always 50 tenths regardless of the
carrier's frame size (4 carrier sizes); `size_bytes` faithful
forwarding under seven sizes; four §4.5.3 Figure 18 cross-checks
("CELT → SILK with Redundancy" / "CELT → Hybrid with Redundancy"
/ "SILK → CELT with Redundancy" / "Hybrid → CELT with Redundancy"
+ a "SILK → SILK with Redundancy MB-carrier" case verifying the
MB → WB bump for both position symbols); a `frame_count_code` /
`Mode` "carrier-only field irrelevance" invariant; and a total-
function sweep over (mode × bandwidth × channels × position) that
verifies the output `bandwidth` is never MB.

Provenance: every constant, every conditional, the "fixed at
5 ms" duration, the channel-count inheritance, the MB → WB
override, the `Beginning` / `End` placement distinction, and the
2.5 ms cross-lap region size is transcribed from RFC 6716
§4.5.1.4 in `docs/audio/opus/rfc6716-opus.txt` (pp. 126–127). The
non-normative §4.5.3 Figure 18 (p. 129) was used solely as a
cross-check that the four redundancy-bearing transition rows
reproduce the figure's `R` placement; no rule was seeded from
the figure. No external library source was consulted.

## Round 27 — §4.5.2 SILK + CELT state-reset policy across mode transitions (2026-05-31)

Round 27 lands the §4.5.2 *State Reset* decision procedure (RFC 6716
§4.5.2, p. 127) behind a new `mode_transition_reset` module. This is
the second §4.5 (mode-switching) fragment after round 26's §4.5.1
redundancy-flag pipeline, picking up exactly where that round
stopped: §4.5.1 decided *whether* a transition carried a 5 ms
redundant CELT frame; §4.5.2 decides *which sub-decoder needs to be
reset* across the transition and *where* the CELT reset is placed
relative to the redundant frame.

The §4.5.2 prose is four sentences (the only normative content of
the section). The module encodes them as four orthogonal rules:

1. **Rule 1 — SILK reset.** The SILK state is reset before every
   SILK-only or Hybrid frame whose predecessor was CELT-only. The
   bit is independent of redundancy.
2. **Rule 2 — CELT reset (default).** The CELT state is reset
   every time the operating mode changes AND the new mode is Hybrid
   or CELT-only, EXCEPT when the transition uses redundancy.
3. **Rule 3 — SILK/Hybrid → CELT-only with redundancy.** The CELT
   reset moves from "before the new-mode frame" to "before the
   redundant CELT frame embedded in the previous frame's tail" and
   is NOT applied before the following CELT-only frame.
4. **Rule 4 — CELT-only → SILK-only/Hybrid with redundancy.** The
   CELT decoder is NOT reset for decoding the redundant CELT frame.
   Combined with rule 2's "except when … redundancy" exception,
   the CELT decoder is not reset by §4.5.2 policy at all for this
   transition; SILK still resets per rule 1.

The module owns:

* `StateReset { silk: bool, celt: CeltResetPlacement }` — the
  outcome of one transition decision.
* `CeltResetPlacement::{None, BeforeFrame, BeforeRedundantOnly}`
  — three placement outcomes covering the rule-2 default,
  the rule-3 carve-out, and the no-reset cases (same-mode +
  rule 4 + Hybrid → SILK-only).
* `decide_state_resets(prev_mode, next_mode, redundancy)`  entry point. Treats `RedundancyDecision::Invalid` as "no
  usable redundancy" per the §4.5.1.3 RECOMMENDATION to stop
  decoding on overflow.
* `StateReset::{celt_resets, is_noop}` — accessors.

Twenty-seven new unit tests (467 lib tests total, up from 440 at
round-26 close; 20 integration tests unchanged, grand total 487)
cover: the `StateReset::{celt_resets, is_noop}` accessors; rule 1
firing for CELT-only → SILK-only and CELT-only → Hybrid;
rule 1 NOT firing for same-mode and Hybrid → SILK-only; rule 1 NOT
firing whenever `next == CeltOnly`; rule 1's independence from
redundancy state (NotPresent / Present / Invalid all reset SILK
identically); rule 2 firing on every mode-changing transition into
Hybrid or CELT-only without redundancy; rule 2 NOT firing on
Hybrid → SILK-only; rule 2 NOT firing on any same-mode pair under
any redundancy state; the rule-3 carve-out routing SILK-only →
CELT-only and Hybrid → CELT-only with redundancy to
`BeforeRedundantOnly`; rule 3 falling back to the rule-2
`BeforeFrame` default when redundancy is `Invalid`; the rule-4
carve-out suppressing the CELT reset on CELT-only → SILK-only / →
Hybrid with redundancy while leaving the SILK reset (rule 1)
intact; CELT-only → Hybrid WITHOUT redundancy still resetting CELT
under the rule-2 default; the full 3×3 mode-pair × {present,
not_present} cross-product pinned cell by cell; four §4.5.3 Figure
18 cross-checks (SILK → CELT with redundancy / CELT → SILK with
redundancy / CELT → Hybrid with redundancy / Hybrid → WB SILK)
matching the figure's `;` (SILK-only reset) and absent-reset
markers; and a small unit-test on the `redundancy_is_present`
helper that treats `Invalid` as absent.

Provenance: every rule, every cell of the 3×3 × 2-redundancy
transition matrix, the "operating mode changes" predicate, and the
"before the redundant frame vs. before the new-mode frame"
distinction is transcribed from RFC 6716 §4.5.2 in
`docs/audio/opus/rfc6716-opus.txt` (p. 127). The non-normative
§4.5.3 Figure 18 was used solely as a cross-check that the
transcribed rules reproduce the figure's reset markers; no rule
was seeded from the figure. No external library source was
consulted.

## Round 26 — §4.5.1 CELT redundancy / mode-transition side information (2026-05-30)

Round 26 lands the §4.5.1 redundancy-flag pipeline (RFC 6716 §4.5.1
pp. 124–126, Tables 64 and 65) behind a new `celt_redundancy`
module. This is the first §4.5 (mode-switching) fragment, sitting
at the tail of every SILK-only or Hybrid Opus frame to decide
whether an extra 5 ms redundant CELT frame is embedded in the
remaining bytes.

The §4.5.1 procedure is a three-step decision tree:

1. §4.5.1.1 — *redundancy flag*. SILK-only frames signal implicitly
   ("on" iff `remaining_bits >= 17`). Hybrid frames signal explicitly
   via a Table 64 `{4095, 1}/4096` symbol, but only after a stricter
   `remaining_bits >= 37` gate (room for the symbol + a minimum
   2-byte redundant frame).
2. §4.5.1.2 — *redundancy position*. Decoded only when the flag is
   on, using the Table 65 `{1, 1}/2` uniform symbol. Symbol 0 places
   the redundant frame at the END of the Opus frame; symbol 1 at the
   BEGINNING.
3. §4.5.1.3 — *redundancy size*. SILK-only: the remaining whole
   bytes after the §4.5.1.2 read. Hybrid: `2 + dec_uint(256)`. If
   the Hybrid claim exceeds the whole bytes that actually remain
   in the Opus frame, §4.5.1.3 RECOMMENDS the decoder "stop
   decoding and discard the rest of the current Opus frame" — we
   surface that as `RedundancyDecision::Invalid` and let the caller
   pick whether to keep the already-decoded audio (per the §4.5.1.3
   "may keep any audio decoded so far" allowance) or trash it.

The module owns:

* `SILK_ONLY_REDUNDANCY_MIN_REMAINING_BITS = 17`  §4.5.1.1 SILK-only implicit-signal gate.
* `HYBRID_REDUNDANCY_MIN_REMAINING_BITS = 37`  §4.5.1.1 Hybrid explicit-signal gate.
* `REDUNDANCY_FLAG_ICDF = [1, 0]` / `_FTB = 12` — Table 64.
* `REDUNDANCY_POSITION_ICDF = [1, 0]` / `_FTB = 1` — Table 65.
* `HYBRID_REDUNDANCY_SIZE_BASELINE_BYTES = 2` /
  `HYBRID_REDUNDANCY_SIZE_DEC_UINT_FT = 256` — the §4.5.1.3
  Hybrid `size = 2 + dec_uint(256)` formula constants.
* `REDUNDANCY_MIN_SIZE_BYTES = 2` — the §4.5.1.3 invariant lower
  bound on a well-formed redundant CELT frame.
* `RedundancyPosition::{End, Beginning}` — Table 65 symbol →
  placement.
* `RedundancyDecision::{NotPresent, Present { position, size_bytes }, Invalid}`
  — the three legal outcomes per §4.5.1.
* `decode_redundancy(rd, mode, opus_frame_bytes)` — driver entry
  point; CELT-only frames bypass §4.5.1 entirely and return
  `NotPresent` without touching the range decoder.
* `remaining_bits` / `whole_bytes_remaining` — helper accounting
  per §4.1.6 + §4.5.1.3.

The round does NOT decode the redundant CELT frame itself — that
needs the §4.3.2.1 coarse energy (gated on the Laplace decoder +
`e_prob_model`, #936) and the §4.3.3 bit allocator (gated on
`cache_caps50` + `LOG2_FRAC_TABLE`, #943). Round 26 stops at the
boundary metadata — WHERE the redundant CELT bytes start and HOW
MANY of them there are — so the §4.3 decoder, once unblocked, can
slot in directly.

Twelve unit tests cover both the SILK-only implicit-flag boundary
(below 17 bits → not present; full buffer → present), the Hybrid
explicit-flag gate (below 37 bits → not present; full buffer →
flag is read and `tell` advances), the CELT-only bypass invariant,
the Table 64 / Table 65 ICDF derivations, the
`RedundancyPosition::from_symbol` Table 65 mapping, and the
`RedundancyDecision` accessor helpers.

Provenance: every PDF, every byte / bit threshold, every
conditional branch is transcribed from RFC 6716 §4.5.1 in
`docs/audio/opus/rfc6716-opus.txt`. No external library source was
consulted.

## Round 25 — §4.3.4.5 CELT TF-resolution adjustment lookup (2026-05-30)

Round 25 lands the §4.3.4.5 TF (time-frequency) resolution adjustment
machinery (RFC 6716 §4.3.4.5 p. 119–120, Tables 60–63) behind a new
`celt_tf_adjust` module. This is the third CELT-layer fragment after
round 20's Table 56 pre-band header and round 24's Table 55 band
layout, and it sits in the §4.3.4 band loop right after coarse energy
(§4.3.2.1) and bit allocation (§4.3.3) — both still deferred — but
before the §4.3.4.2 PVQ shape decoder reads the band.

Tables 60–63 are the four lookups that turn the `(frame_size,
transient, tf_select, tf_change[b])` tuple into a per-band integer
adjustment `∈ [-3, 3]`. Negative values mean the decoder applies
`|adj|` levels of the Hadamard transform per-vector to increase
temporal resolution; positive values (only reachable on transient
frames per the §4.3.4.5 prose) apply `adj` levels across the
interleaved MDCT vector to increase frequency resolution; zero means
the band's MDCT vector is consumed unchanged.

The module owns:

* `TF_ADJ_NONTRANSIENT_SELECT0` — Table 60 (`[[0,-1],[0,-1],[0,-2],[0,-2]]`).
* `TF_ADJ_NONTRANSIENT_SELECT1` — Table 61 (`[[0,-1],[0,-2],[0,-3],[0,-3]]`).
* `TF_ADJ_TRANSIENT_SELECT0` — Table 62 (`[[0,-1],[1,0],[2,0],[3,0]]`).
* `TF_ADJ_TRANSIENT_SELECT1` — Table 63 (`[[0,-1],[1,-1],[1,-1],[1,-1]]`).
* `celt_tf_adjustment(frame_size, transient, tf_select, tf_change) -> i8`
  — the routed lookup.
* `celt_tf_select_can_affect(frame_size, transient, tf_change_slice)
  -> bool` — the §4.3.1 "tf_select uses a 1/2 probability, but is only
  decoded if it can have an impact on the result knowing the value of
  all per-band tf_change flags" gate. The §4.3.4.5 band loop calls
  this AFTER decoding every per-band `tf_change[b]` to decide whether
  to consume the `tf_select` bit at all. Empty band sets (no coded
  bands) and the universally-redundant 2.5 ms rows ([0, -1] in all
  four tables) return `false`.
* `TfDirection::{Unchanged, IncreaseTime(N), IncreaseFrequency(N)}`
  carrying the Hadamard-transform branch + level count.
* `TfAdjustment` (= `i8`), `TF_ADJUSTMENT_MAX = 3`,
  `TF_ADJUSTMENT_ABS_MAX = 3` named constants pinned to the
  observed max across every documented cell.

27 new module tests (428 lib tests total, up from 401 at round-24
close; 20 integration tests unchanged, grand total 448) cover: the
four-row × two-column shape of every table; every cell within the
documented `[-3, 3]` range; every Table 60 / 61 / 62 / 63 cell
hand-pinned to the RFC; the "non-transient `choice = 0` is always 0"
structural invariant on Tables 60 + 61; the "non-transient `choice =
1` is always ≤ 0" pin (stationary content never gains frequency
resolution); the "positive adjustments only on transient frames"
asymmetry, both at the table layer and at `TfDirection`; the
Table 62 `choice = 0` monotone `0, 1, 2, 3` scale across frame
sizes; the universal 2.5 ms row `[0, -1]` across all four tables;
the `TF_ADJUSTMENT_MAX` / `TF_ADJUSTMENT_ABS_MAX` constants matching
the observed max over every cell; the `celt_tf_adjustment` entry
routing each `(transient, tf_select)` corner to the matching table;
`celt_tf_select_can_affect` returning `false` on empty band sets and
on the redundant 2.5 ms rows (both transient and non-transient);
returning `false` on 10 ms non-transient when every band picks
`choice = 0` (Tables 60 and 61 agree on column 0) and `true` as soon
as any band picks `choice = 1`; returning `true` on 20 ms transient
for any non-empty band set (Tables 62 vs 63 disagree on both
columns); `TfDirection::from_adjustment` classifying every cell
correctly with the `levels()` value matching `adj.unsigned_abs()`
over the full `[-3, 3]` range; `IncreaseFrequency` never reachable
on non-transient frames; `IncreaseTime` always reached for
non-transient `choice = 1`.

No external library source was consulted; every cell of every
table, every routing decision, the §4.3.1 `tf_select`
non-redundancy rule, and the §4.3.4.5 "negative = temporal
resolution increased, positive = frequency resolution increased"
classification come directly from RFC 6716 §4.3.1 (p. 109) and
§4.3.4.5 (p. 119–120).

## Round 24 — §4.3 Table 55 CELT MDCT-band layout (2026-05-29)

Round 24 lands the §4.3 CELT MDCT-band layout (RFC 6716 §4.3 p. 103
prose + Table 55 p. 104) behind a new `celt_band_layout` module.
This is the second CELT-layer fragment, after round 20's Table 56
pre-band header, and it sits below every CELT sub-decoder still ahead
(§4.3.2 coarse energy, §4.3.3 bit allocator, §4.3.4 PVQ shape, §4.3.6
denormalisation, §4.3.7 inverse MDCT) — they all iterate band-by-band
and ask "how many MDCT bins in band `b` at this frame size?". The
module owns:

* `CeltFrameSize` — the four CELT frame sizes (2.5 / 5 / 10 / 20 ms)
  as a `repr(u8)` enum whose discriminants double as the Table 55
  "Bins:" column index (`0..=3`), with
  `from_frame_tenths_ms(u32) -> Option<Self>` mapping the §3.1 TOC
  byte's `frame_size_tenths_ms` for CELT-bearing Opus frames and
  returning `None` for 40 / 60 ms SILK-only frames.
* `celt_band_bins_per_channel(band, fs)` — the per-(band, frame-size)
  Table 55 lookup (`1..=176` bins per channel, doubling across the
  four columns), with `band >= CELT_NUM_BANDS` returning `None`.
* `celt_band_start_hz(b)` / `celt_band_stop_hz(b)` — the band-boundary
  frequencies from Table 55 (`0..=20000 Hz` in 200 Hz multiples), with
  `stop(b) == start(b + 1)` and the convention `stop(20) == 20000`.
* `celt_band_at_hz(hz)` — the reverse lookup that turns a frequency
  in Hz into a `Some(band)` (lowest band whose `[start, stop)`
  interval contains `hz`) or `None` at / above 20 kHz, matching the
  CELT-only / Hybrid dispatch convention.
* `celt_first_coded_band(is_hybrid)` / `HYBRID_FIRST_CODED_BAND = 17`
  — the §4.3 "first 17 bands (up to 8 kHz) are not coded" rule for
  Hybrid frames, with CELT-only frames starting at band 0.
* `celt_total_bins_per_channel(fs, is_hybrid)` — the column-sum helper
  that the §4.3.3 bit allocator and §4.3.4 PVQ shape decoder will both
  want before the band loop starts. Pinned: 100 / 200 / 400 / 800 for
  CELT-only at 2.5 / 5 / 10 / 20 ms; 60 / 120 / 240 / 480 for the
  corresponding Hybrid column sums.
* `CELT_NUM_BANDS = 21`, `HYBRID_FIRST_CODED_BAND = 17`,
  `CELT_MAX_BINS_PER_BAND = 176` named constants.

The "Custom" mode of §6.2 (which can use a different number of bands
or different band edges) is explicitly out of scope and is documented
as such in the module preamble; every constructor rejects the
non-standard layouts.

Twenty new module tests (401 lib tests total, up from 381 at round-23
close; 20 integration tests unchanged) cover: the start / stop
boundary of the table (`band 0` starts at 0 Hz, `band 20` stops at
20 000 Hz), gap-free adjacent-band tiling (`stop(b) == start(b + 1)`
for every `b ∈ 0..=19`), positive band widths everywhere, the
power-of-two column-scaling invariant (`column(c) == 1 << c * column(0)`
per band), every cell `∈ [1, 176]` per the §4.3 prose, hand-pinned
spot cells (band 0, 8, 12, 15, 17, 20 across every column) and
hand-pinned band edges (`start(0) = 0`, `stop(16) = 8000` =
`start(17)`, `stop(20) = 20000`), out-of-range index returning `None`,
the `CeltFrameSize::from_frame_tenths_ms` round-trip with explicit
SILK-only rejection (`400` / `600` ms), discriminant-vs-column-index
agreement, the Hybrid-vs-CELT-only first-coded-band split with the
8 kHz boundary pin, the `celt_total_bins_per_channel` column-sum
agreement against an independent `(0..21).sum()` for each mode, the
strict `hybrid_total < celt_only_total` invariant, the four pinned
CELT-only column sums (100 / 200 / 400 / 800) and four pinned Hybrid
column sums (60 / 120 / 240 / 480), the `celt_band_at_hz` round-trip
against the band-edge pair (start, midpoint, and `stop - 1` all land
on the same band), the `>= 20 kHz` rejection of `celt_band_at_hz`,
the `celt_band_at_hz(8000) == 17` pin matching
`HYBRID_FIRST_CODED_BAND`, the multiple-of-200-Hz band-width
invariant with three pinned widths (`200` Hz for band 0, `400` Hz
for band 8, `4400` Hz for band 20), and the
`CELT_MAX_BINS_PER_BAND == max(every cell)` pin.

No external library source was consulted; every cell, every
band-edge frequency, every constant, and the "first 17 bands not
coded in Hybrid mode" rule comes directly from RFC 6716 §4.3 (p. 103
prose + Table 55 p. 104).

## Round 23 — §4.2.7.4 SILK gain dequantization tail (2026-05-29)

Round 23 lands the §4.2.7.4 tail-end mapping from the integer
`log_gain ∈ 0..=63` (decoded since round 5) to the linear Q16
gain `gain_Q16 ∈ [81_920, 1_686_110_208]` consumed by the
§4.2.7.9.1 LTP and §4.2.7.9.2 LPC synthesis filters. A new
`silk_log2lin` module owns:

* `silk_log2lin(in_log_q7)` — the §4.2.7.4 piecewise-linear
  approximation of `2^(inLog_Q7/128)`:
  `(1 << i) + ((-174*f*(128-f) >> 16) + f) * ((1 << i) >> 7)`
  with `i = inLog_Q7 >> 7` and `f = inLog_Q7 & 127`.
* `silk_gains_dequant(log_gain)` — the composed
  `silk_log2lin((0x1D1C71*log_gain >> 16) + 2090)` mapping. Both
  documented endpoints (`81920` at `log_gain = 0` representing
  linear gain 1.25, and `1_686_110_208` at `log_gain = 63`
  representing linear gain ≈ 25 728) are pinned exactly.
* Named constants `SILK_LOG_GAIN_MULTIPLIER = 0x1D1C71`,
  `SILK_LOG_GAIN_BIAS = 2090`, `SILK_GAIN_Q16_MIN = 81_920`,
  `SILK_GAIN_Q16_MAX = 1_686_110_208`.
* `SubframeGains::dequant_q16()` convenience that maps an entire
  decoded frame's `log_gain[]` into a fixed-size `[u32;
  SILK_MAX_SUBFRAMES]` array (trailing unused slots stay zero for
  two-subframe frames).

19 new module tests (381 lib tests total, up from 362; 20
integration tests unchanged): the two §4.2.7.4 endpoints pinned to
the RFC text; strict-monotone-in-`log_gain` property across the
full domain; spec-range invariant across the full sweep;
pure-power-of-two collapse `silk_log2lin(128*i) == 1 << i` for
`i ∈ 0..=30`; an independent i64 oracle of the §4.2.7.4 formula
matched bit-for-bit by the production i32 implementation across
the entire `i ∈ 0..=30 × f ∈ 0..=127` Q7 domain plus the
log-gain dequant sub-domain; pinned endpoint algebra
(`log_gain = 63 → in_log_q7 = 30*128 + 83 = 3923`); the halfway
pin `silk_log2lin(7*128 | 64) = 181` matching the true `2^7.5 ≈
181.019`; the `SubframeGains::dequant_q16` trailing-slot zeroing
and per-subframe agreement properties.

## Round 22 — §3.4 R1..R7 malformed-input rejection audit (2026-05-27)

Round 22 lands a dedicated integration-level malformed-input audit
(`tests/malformed_input.rs`, 20 tests) that pins the §3.4
requirements R1..R7 rejection behaviour to a per-requirement set of
property-style sweeps. This is the audit-grade evidence — for both
fuzz tooling and a future Auditor pass — that the §3.2 frame-packing
parser rejects every concrete malformed shape RFC 6716 §3.4
enumerates, and that the §4.2.3 / §4.2.4 SILK header decoder is
panic-free on any truncation of a previously-valid bitstream.

Coverage:

* **R1** — empty-packet rejection (`OpusPacket::parse(&[]) =>
  EmptyPacket`).
* **R2** — implicit frame length capped at `MAX_FRAME_BYTES = 1275`:
  code 0 with 1276 B body rejects; 1275 B accepts (boundary); code 1
  with 2552 B body (two 1276 B halves) rejects; 2550 B accepts; code
  3 VBR boundary at 1275 B accepts.
* **R3** — code-1 packets with odd body length (i.e. even `N`)
  rejected, sweeping body_len ∈ 0..=8.
* **R4** — code-2 packets across three failure shapes: missing
  length byte, missing second length byte for first ∈ 252..=255, and
  declared length > remaining; plus the §3.2.1 DTX boundary where
  declared length equals remaining (second frame is zero-length).
* **R5** — code-3 `M=0` rejected; `M ∈ 1..=48` with zero R/M
  accepted; `M > 48` rejected by the high-bit constraint
  (`MAX_FRAMES_PER_PACKET = 48`).
* **R6** — code-3 CBR where R is not a multiple of M (R=7, M=3)
  rejected; R=6, M=3 (R/M=2) accepted (boundary).
* **R7** — code-3 VBR declared lengths overrunning remaining
  rejected; declared=5, M=2 with 15 body bytes accepted (boundary,
  final frame = 10 B).
* **§3.2.5 padding chain** — missing padding-length byte rejected;
  padding > remaining rejected; unterminated 255-chain rejected.
* **TOC determinism** — every `u8` parses to a self-consistent TOC
  byte; `frame_size_tenths_ms` is always in `{25, 50, 100, 200, 400,
  600}` (Table 2).
* **§4.2.3 / §4.2.4 truncation safety** — for every
  `(num_silk_frames, stereo) ∈ {1, 2, 3} × {false, true}`,
  truncating a 32-byte buffer to every prefix length 1..=32 never
  panics; the returned `SilkHeaderBits` always has zero high-order
  bits beyond `num_silk_frames`. The §4.1.4 RangeDecoder
  zero-extension rule makes this provably safe — the test pins the
  contract.
* **§4.2.4 PDF bounds**`decode_per_frame_lbrr` always returns a
  value in `{1..=2^N - 1}` for any input, never `0`, by way of the
  §4.1.3.3 leading-zero offset.
* **Mono-only safety**`SilkHeaderBits::decode(..., stereo=false)`
  never emits `Some(side)` or a non-zero `side` LBRR bitmap (swept
  across all 256 byte-0 starts × 3 frame counts).
* **Slice lifetimes** — frames returned by a successful parse all
  point inside the input buffer's bounds.
* **Pathological short-packet sweep** — every `(c, body_len)` shape
  from 0..=12 bytes × five different filler patterns runs without
  panicking.

Total test count: 362 lib tests + 20 integration tests = 382 tests
(was 362 lib + 0 integration after round 21).

The audit caught one real shape that would otherwise have been
unspecified in the test suite: `M ∈ 49..=63` (reachable from the
6-bit `M` field but disallowed by R5's "120 ms / 2.5 ms = 48" cap)
must be rejected — the existing parser already does so via
`MAX_FRAMES_PER_PACKET`, but the test now pins the behaviour
explicitly.

## Round 21 — §3.1 / §4.2 framing dispatch (2026-05-27)

Round 21 lands the framing dispatch (`framing` module:
`OpusFrameRouting` / `OperatingMode` / `SilkBandwidth`) — the single
pure-function lookup that turns an `OpusTocByte` into the
per-Opus-frame routing decision a §4 decoder needs *before* it
touches the range coder. This codifies the SILK / Hybrid / CELT-only
dispatch logic, the §4.2 "Hybrid → SILK runs in WB regardless of TOC
bandwidth" pin, the §4.2.2 SILK-frame count per channel (1 for
10/20 ms, 2 for 40 ms, 3 for 60 ms), the §4.2.4 per-frame LBRR-flag
presence gate (duration > 20 ms), and the channel-count multiplier
for stereo — fields that were previously open-coded by every caller
that constructed a SILK or CELT context.

Concretely, `OpusFrameRouting::from_toc` is the dispatch entry point.
For a 60 ms stereo SILK-only WB frame (config 11, s=1) it produces:
`operating_mode = SilkOnly`, `silk_bandwidth = Some(Wb)`,
`silk_frames_per_channel = Some(3)`, `channel_count() = 2`,
`total_silk_frames() = 6`, `has_per_frame_lbrr_bits() = true`. For a
20 ms stereo Hybrid SWB frame (config 13, s=1) it produces:
`operating_mode = Hybrid`, `silk_bandwidth = Some(Wb)` (the §4.2 pin
even though the TOC bandwidth is `Swb`), `silk_frames_per_channel =
Some(1)`, `total_silk_frames() = 2`, `has_per_frame_lbrr_bits() =
false`. For a 5 ms mono CELT-only NB frame (config 17, s=0):
`operating_mode = CeltOnly`, `silk_bandwidth = None`,
`silk_frames_per_channel = None`, `total_silk_frames() = 0`,
`has_per_frame_lbrr_bits() = false`.

Thirteen new unit tests cover the SILK-only Table 2 row-by-row
expectations (12 cells × `(toc_bandwidth, frame_size, silk_bandwidth,
silk_frames_per_channel)`), the Hybrid WB-pin (4 Hybrid configs × the
SWB→WB / FB→WB downgrade), CELT-only frames sweep across mono / stereo
(16 × 2 configs), the §4.2.4 per-frame LBRR gate against every Table 2
cell (32 configs), the `total_silk_frames` formula across all 32 ×
{mono, stereo}, a 60 ms stereo SILK-only worked example, the `c`-bit
independence of the routing (the §3.2 frame-count code never affects
the §4 dispatch), the channel-mapping pass-through for CELT-only, the
`OperatingMode::from(Mode)` bijection, the `SilkBandwidth::to_bandwidth`
lift, and the `silk_layer ⇔ silk_bandwidth.is_some() ⇔
silk_frames_per_channel.is_some()` invariants across the entire Table 2
grid.

Total test count: 362 lib tests (was 349 after round 20).

## Round 20 — first CELT-layer fragment (2026-05-26)

Round 20 lands the §4.3 / Table 56 pre-band header symbols every
CELT-bearing Opus frame opens with, behind a new `celt_header`
module exposing `CeltHeaderPrefix` / `CeltPostFilter`. These are
the only Table-56 entries that fit between the SILK pipeline now
wired up and the two known-blocked CELT sub-pieces (§4.3.2.1
coarse energy, gated on the Laplace decoder + `e_prob_model`
table; §4.3.3 bit allocation, gated on `cache_caps50` +
`LOG2_FRAC_TABLE`). The per-band `tf_change` flags (§4.3.1) live
in the band loop after coarse energy per Table 56, so they're
deferred as well.

The decode order encoded by `CeltHeaderPrefix::decode` mirrors
Table 56: `silence` via the 2-entry `{32767, 1}/32768` iCDF
(short-circuits the rest of the prefix when set); `post-filter`
via `dec_bit_logp(1)` (logp=1, PDF `{1, 1}/2`); if post-filter is
enabled, the §4.3.7.1 four-parameter group — `octave` via
`dec_uint(6)` (uniform on `0..=5`), `fine_pitch` via
`dec_bits(4 + octave)` (at most 9 raw bits), the §4.3.7.1 pitch
period reconstruction `T = (16 << octave) + fine_pitch - 1`
(global bounds `15..=1022`; per-octave lower bounds
`{15, 31, 63, 127, 255, 511}` and per-octave upper bounds
`{30, 62, 126, 254, 510, 1022}`), `gain_index` via `dec_bits(3)`
(downstream gain `G = 3 * (gain_index + 1) / 32`), and `tapset`
via the §4.3.7.1 `{2, 1, 1}/4` iCDF — and finally `transient`
(§4.3.1) and `intra` (§4.3.2.1), both as `dec_bit_logp(3)` (PDF
`{7, 1}/8`).

Ten new unit tests cover the iCDF transcription self-checks
(silence PDF sums to 32768, tapset PDF sums to 4, both iCDF
arrays terminate at zero and decrease monotonically), the pitch
period formula at the global minimum (15), the global maximum
(1022), the lower bound of each octave (`fine_pitch = 0`), and
the upper bound of each octave (`fine_pitch = (1 << (4+k)) - 1`),
an all-zero buffer where every most-likely-symbol branch fires
(no silence / no post-filter / no transient / no intra), an
all-ones buffer where every produced field still stays in its
declared range, a `tell()`-advance proof, a 256-buffer
fuzz-style range sweep over the post-filter fields, and the
silence-shortcut post-condition.

Total test count: 349 lib tests across SILK + CELT-header (was
339 after round 19).

The §4.3.4 PVQ shape decoder, §4.3.5 anti-collapse, §4.3.6
denormalization, and the §4.3.7 inverse MDCT plus its
post-filter application all remain ahead, sitting behind the
two §4.3.2.1 / §4.3.3 blockers above.

The prior implementation was retired under the workspace clean-room
policy: provenance for several core modules could not be defended
against the "no external library source as reference" rule that
governs every crate in this workspace. Per workspace policy, the only
acceptable response is a full clean-room re-implementation against the
Opus standards documents and black-box validator binaries.

Round 1 (2026-05-20) landed the RFC 6716 §3.1 packet TOC byte parser:
the 32-config × stereo-flag × frame-count-code triple plus the
implied `(min, max)` frame-count range. Five unit tests sweep Table 2,
Table 3, Table 4 and the R1 empty-packet rejection.

Round 2 (2026-05-21) lands the RFC 6716 §3.2 frame-packing parser
behind a new `OpusPacket::parse` entry point:

* **Code 0** (§3.2.2) — one frame, the remaining `N - 1` bytes.
* **Code 1** (§3.2.3) — two equal-size frames; rejects odd `(N - 1)`
  per requirement R3.
* **Code 2** (§3.2.4) — two frames with a one- or two-byte §3.2.1
  length prefix for the first; rejects R4 violations
  (length-exceeds-remaining, length-byte missing, etc.).
* **Code 3** (§3.2.5) — signalled frame count `M ∈ 1..=48` (R5) in
  the frame-count byte, optional Opus padding (with the §3.2.5
  "value 255 chains another length byte" extension), then either CBR
  (every frame is `R / M` bytes; R6 enforces `R % M == 0`) or VBR
  (`M − 1` §3.2.1 length sequences with the final frame implicit;
  R7 enforces no length overrun).

The §3.2.1 helper decodes the one- and two-byte length sequence
(`0`, `1..=251`, `252..=255 → (second*4 + first)`) and treats length
zero as a valid DTX / lost-frame marker (zero-byte slice in the
returned list).

`OpusPacket::frames()` returns `&[&[u8]]` borrowed from the input
buffer; the slices are ready to feed into the SILK / CELT decoders
once those land. Padding length is exposed separately so the caller
can sanity-check against the §3.2.5 budget.

Twenty-seven new unit tests cover each `c` code (round-trip plus
under-length and over-length rejections), the §3.2.1 length encoding
end-to-end (including the 252/255 extension boundaries), the
padding-chain 255-extension behaviour, the R5 cap at 48 frames, and
the R6/R7 boundary conditions.

Round 3 (2026-05-21) lands the RFC 6716 §4.1 range decoder behind a
new `RangeDecoder` API. This is the shared entropy primitive that
every SILK and CELT symbol passes through. The implementation covers:

* §4.1.1 initialization (`b0 >> 1` into `val`, leftover bit into the
  renorm buffer, immediate renormalization to the `rng > 2^23`
  invariant).
* §4.1.2 generic symbol decode (`ec_decode` / `ec_dec_update`) and
  §4.1.2.1 renormalization (MSB-first byte intake with the
  zero-extension past end-of-frame).
* §4.1.3.1 `decode_bin` for power-of-two `ft`.
* §4.1.3.2 `dec_bit_logp` for `2^-logp` binary symbols.
* §4.1.3.3 `dec_icdf` for inverse-CDF table decoding.
* §4.1.4 `dec_bits` for raw bits packed LSB-first from the end of
  the frame, with §4.1.4 zero-extension.
* §4.1.5 `dec_uint` covering both the small (`ftb <= 8`) range-coded
  branch and the large (`ftb > 8`) range-plus-raw-bits branch, with
  the §4.1.5 corrupt-frame error-flag latch.
* §4.1.6.1 `tell()` and §4.1.6.2 `tell_frac()` accounting, satisfying
  the `tell() == ceil(tell_frac() / 8.0)` identity.

The sibling `oxideav-celt` crate carries an independent clean-room
copy of the same primitive — both crates own their own copy until a
shared low-level primitives crate is introduced.

Nineteen new unit tests cover: initialization on empty + non-empty
buffers, `dec_bit_logp` bias under extreme inputs, raw-bit LSB-first
ordering, zero-extension past EOF, `dec_uint` degenerate (`ft=0`,
`ft=1`) and both ftb regimes, `decode_bin` matching the generic
`decode(1<<ftb)` path bit-for-bit, `dec_icdf` agreement with
`dec_bit_logp` on binary distributions plus uniform and
single-symbol coverage, `tell()` and `tell_frac()` monotonicity, the
§4.1.6.1 ceiling identity, and the `dec_bits` zero-width and
over-large-width guards.

Round 4 (2026-05-21) lands the SILK per-frame header decoder for
RFC 6716 §4.2.7.1 through §4.2.7.5.1 behind a new `SilkFrameHeader`
type. The caller passes a `SilkFrameHeaderConfig` describing whether
the current SILK frame is mid- or side-channel of a stereo Opus
frame, the side-channel-required flag (driving §4.2.7.2), the frame
kind (regular-inactive / regular-active / LBRR), and the SILK-layer
bandwidth (NB / MB / WB). `decode` returns:

* `stereo_pred: Option<StereoPredictionWeights>` per §4.2.7.1 — the
  three sub-symbols (Table 6 stage-1 25-cell PDF, two stage-2 3-cell
  PDFs, two stage-3 5-cell PDFs) composed via the §4.2.7.1 formula
  into `(w0_Q13, w1_Q13)` against Table 7 (16-entry Q13 weight
  table).
* `mid_only_flag: Option<bool>` per §4.2.7.2 (Table 8 PDF
  `{192, 64}/256`).
* `frame_type: u8``0..=5` per §4.2.7.3 (Table 9 inactive / active
  PDFs; active rows are transcribed as 4-entry iCDFs with a +2
  caller offset since the §4.1.3.3 primitive cannot model
  leading-zero-mass cells).
* `signal_type: SignalType`, `qoff_type: QuantizationOffsetType`
  decoded from `frame_type` via Table 10.
* `lsf_stage1: u8``0..32` per §4.2.7.5.1 with PDF chosen from
  Table 14 by `(bandwidth, signal_type)`.

Seventeen new unit tests cover PDF→iCDF transcription self-checks
(Tables 6 / 8 / 9 / 14 each sum to 256), the Table 7 weight-table
symmetry (`w[15-k] == -w[k]`), the Table 10 frame-type → signal /
qoff mapping, end-to-end decode against the range coder for the
mono-inactive, mono-active, stereo-mid (with both stereo prediction
weights and mid-only flag), stereo-side, and LBRR configurations,
plus a random-buffer sweep of the stereo-prediction decoder to
confirm `wi*` clamping keeps the Table 7 lookup in-bounds.

Round 5 (2026-05-22) lands the SILK subframe quantization-gain
decoder for RFC 6716 §4.2.7.4 behind a new `SubframeGains` /
`SubframeGainsConfig` API. The caller passes the signal type
(`SignalType` from the §4.2.7.3 frame-type symbol), the subframe
count (2 for 10 ms SILK frames, 4 for 20 ms / Hybrid), whether the
first subframe is independently coded per the §4.2.7.4 enumeration
("first SILK frame of its type for this channel in the current Opus
frame, OR previous SILK frame of the same type was not coded"), and
the previous SILK frame's last-subframe `log_gain` if available.
`decode` returns:

* An array of up to 4 `SubframeGain { log_gain: u8 }` values in
  `0..=63`.
* The independent path decodes the 3-bit MSB from one of three
  signal-type-conditioned PDFs (Table 11: Inactive `{32, 112, 68,
  29, 12, 1, 1, 1}/256`; Unvoiced `{2, 17, 45, 60, 62, 47, 19,
  4}/256`; Voiced `{1, 3, 26, 71, 94, 50, 9, 2}/256`), then a
  uniform 3-bit LSB from Table 12 `{32, …, 32}/256`. The two are
  joined into `gain_index = (msb << 3) | lsb` and clamped with
  `log_gain = max(gain_index, previous_log_gain - 16)` (the clamp
  is skipped after a decoder reset / on a side channel whose
  predecessor was not coded — caller passes `None`).
* The delta path decodes a 41-symbol `delta_gain_index` from Table
  13 `{6, 5, 11, 31, 132, 21, 8, 4, 3, 2, 2, 2, 1, 1, …, 1}/256`
  then folds it into the previous coded gain via
  `log_gain = clamp(0, max(2*delta - 16, prev + delta - 4), 63)`.

The §4.2.7.4 tail-end `silk_log2lin` conversion to `gain_Q16` lives
in the excitation stage and is intentionally left to a later round.

Twenty new unit tests cover PDF→iCDF transcription self-checks
(Tables 11 / 12 / 13 each sum to 256), the four signal-type → iCDF
routings, the §4.2.7.4 clamp behaviour (no prev / low prev no-op /
high prev raises floor / sub-16 prev saturates at 0), the delta
path's dual-max + clamp formula reproduced against an independent
range-decoder pass, end-to-end decode for mono-inactive 4-subframe,
mono-unvoiced 2-subframe with prev, mono-voiced 4-subframe with
prev (asserting the clamp floor), the rejection of a
"first-subframe delta without prev" / non-{2,4} num_subframes
malformed input, and a four-subframe chain-consistency check that
re-derives the gain chain from the raw PDF reads.

Round 6 (2026-05-22) lands the SILK Normalized LSF Stage-2 decoder
for RFC 6716 §4.2.7.5.2 behind a new `LsfStage2` API. The caller
passes the SILK-layer bandwidth (NB / MB / WB) and the stage-1 index
`I1 ∈ 0..32` (returned by the §4.2.7.5.1 decoder). `decode` returns:

* `i2: &[i8]` of length `d_LPC` (10 for NB / MB, 16 for WB) — the
  signed stage-2 residual indices `I2[k] ∈ [-10, 10]`. Each
  coefficient reads one symbol from one of the 16 Table 15 (NB / MB
  `a..h`) or Table 16 (WB `i..p`) PDFs, indexed by
  Table 17 / Table 18 against `(I1, k)`. The raw symbol `0..=8` is
  shifted by `-4`; if the resulting `|idx| == 4`, a second symbol
  is drawn from the Table 19 extension PDF (7-cell
  `{156, 60, 24, 9, 4, 2, 1}/256`) and added to the magnitude with
  the same sign.
* `res_q10: &[i32]` of length `d_LPC` — the Q10 stage-2 residual
  after the §4.2.7.5.2 backwards-prediction inverse. The recursion
  runs `k = d_LPC-1` down to `0` per
  `res_Q10[k] = (k+1 < d_LPC ? (res_Q10[k+1]*pred_Q8[k])>>8 : 0)
  + ((((I2[k]<<10) - sign(I2[k])*102) * qstep) >> 16)`. `qstep` is
  `11796` (Q16, ≈0.18) for NB / MB and `9830` (≈0.15) for WB. The
  Q8 prediction weight `pred_Q8[k]` is one of A/B (NB/MB) or C/D
  (WB) from Table 20, selected per-coefficient by Table 21 / 22.

The RFC's Table 17 row label at `I1 = 6` is mistyped as "g" in the
source PDF; the row's cells (`a c c c c c c c c b`) are valid
codebook letters and the table is transcribed with the I1 row-label
restored. A unit test pins the exact row contents.

Thirty new unit tests cover the 16 Table 15 / Table 16 PDF→iCDF
transcriptions (each sums to 256 with monotone-decreasing iCDFs),
the Table 19 extension PDF, the four Table 17 / 18 / 21 / 22 table
row-widths and value ranges, the `pred_weight` A↔B and C↔D
resolution, end-to-end decode for NB/MB/WB at several `I1` values
(asserting every `i2[k] ∈ [-10, 10]`), rejection of `I1 ≥ 32` /
SWB / FB, the `res_Q10[]` formula re-derivation against the decoded
`i2[]` for both NB/MB and WB, a sweep of all 32 `I1` values across
{NB, MB, WB}, and a `tell()` monotonicity check.

Round 7 (2026-05-22) lifts `res_Q10[]` to the final normalized LSF
vector `NLSF_Q15[]` per RFC 6716 §4.2.7.5.3 behind a new
`NlsfReconstructed::from_stage1_and_stage2(bandwidth, lsf_stage1,
&stage2)` API. Three steps run inline:

* **Table 23 / 24 stage-1 codebook lookup.** 32 × 10 NB/MB and
  32 × 16 WB rows of `cb1_Q8[]` are transcribed verbatim. The
  `(bandwidth, I1) → cb1_Q8[..d_LPC]` mapping is the `cb1_q8()`
  helper.
* **IHMW weights `w_Q9[k]`.** Closed-form derivation from
  `cb1_Q8[]` with boundary `cb1_Q8[-1] = 0` /
  `cb1_Q8[d_LPC] = 256`:
  `w2_Q18[k] = (1024 / d_left + 1024 / d_right) << 16`
  (integer division), reduced through `i = ilog(w2_Q18)`,
  `f = (w2_Q18 >> (i-8)) & 127`,
  `y = ((i & 1) ? 32768 : 46214) >> ((32-i) >> 1)`,
  `w_Q9[k] = y + ((213 * f * y) >> 16)`. The spec asserts the
  resulting 13-bit weights tabulate to `1819..=5227` — a property
  the test sweep verifies across all 32 × {NB, MB, WB} codebook
  rows.
* **Final reconstruction.**
  `NLSF_Q15[k] = clamp(0, (cb1_Q8[k]<<7)
                       + (res_Q10[k]<<14) / w_Q9[k], 32767)`
  with integer division. Each `NLSF_Q15[k]` is held as `i16` in
  `[0, 32767]`.

26 new unit tests (144 lib tests total in the crate, up from 118 at
round-6 close) cover Table 23 / 24 transcription (strict monotone +
row widths + spot-checks of rows 0 and 31), the `cb1_q8()` routing
table (Nb/Mb → 23, Wb → 24, plus Swb/Fb and out-of-range I1
rejection), `ilog()` against the seven RFC §1.1.10 examples,
concrete hand-computed IHMW matches (NB I1=0 k=0 → 2897; WB I1=0
k=0 → 3657), the IHMW 13-bit-range assertion across every cell,
the zero-residual identity `NLSF_Q15[k] == cb1_Q8[k] << 7`, and
all-`I1` round-trips on a synthetic range-decoder buffer for NB /
MB / WB confirming the final `NLSF_Q15[]` exactly matches the
formula re-applied to `res_Q10[k]` and `w_Q9[k]`.

Round 8 (2026-05-23) stabilizes the reconstructed `NLSF_Q15[]` per
RFC 6716 §4.2.7.5.4 behind a new
`NlsfStabilized::from_reconstructed(bandwidth, &recon)` API, ensuring
consecutive coefficients stay at least the Table 25 minimum spacing
apart (the 0.01-percentile spacing of the SILK training set). The
boundary conventions are `NLSF_Q15[-1] = 0` and `NLSF_Q15[d_LPC] =
32768`; Table 25's `NDeltaMin_Q15[]` carries `d_LPC + 1` entries (one
trailing entry for the spacing against the implicit upper edge).

* **Up to 20 distortion-minimizing passes.** Each pass scans
  `i ∈ 0..=d_LPC` for the smallest `NLSF_Q15[i] - NLSF_Q15[i-1] -
  NDeltaMin_Q15[i]` (ties to lower `i`). If non-negative, the
  coefficients already satisfy every constraint and the procedure
  stops. Otherwise: `i == 0` sets `NLSF_Q15[0] = NDeltaMin_Q15[0]`;
  `i == d_LPC` sets `NLSF_Q15[d_LPC-1] = 32768 - NDeltaMin_Q15[d_LPC]`;
  any interior `i` re-centres the pair via the `min_center` /
  `max_center` running-sum band and the
  `center_freq = clamp(min_center, (NLSF[i-1]+NLSF[i]+1)>>1,
  max_center)` midpoint, then writes
  `NLSF_Q15[i-1] = center_freq - (NDeltaMin_Q15[i]>>1)` and
  `NLSF_Q15[i] = NLSF_Q15[i-1] + NDeltaMin_Q15[i]`.
* **Fallback (once, after the 20th pass).** Sort ascending, then a
  forward `max(NLSF[k], NLSF[k-1] + NDeltaMin[k])` sweep and a
  backward `min(NLSF[k], NLSF[k+1] - NDeltaMin[k+1])` sweep that
  mechanically guarantee the spacing. Per the **RFC 8251 §7**
  erratum the forward sweep's addition is performed with 16-bit
  saturating addition (`silk_ADD_SAT16`) so an adversarial input near
  `i16::MAX` cannot wrap around into a negative value.

19 new unit tests cover Table 25 lengths and spot-checks (NB/MB index
0 = 250 / index 10 = 461; WB index 0 = 100 / index 2 = 40 / index 16
= 347), the SWB/FB column rejection, `add_sat16` saturation, an
"already-stable input is left untouched" identity for NB and WB, the
two boundary branches (first coefficient pushed up to `NDeltaMin[0]`,
last coefficient pulled down to `32768 - NDeltaMin[d_LPC]`), an
interior re-centring with hand-computed exact `NLSF_Q15[i-1]` /
`NLSF_Q15[i]` values, the fallback path on a fully reversed input,
all-zero and all-32767 inputs spread to valid spacing, the RFC 8251
no-wrap guard near `i16::MAX`, an all-`I1` × {NB, MB, WB} end-to-end
sweep wired through the §4.2.7.5.2 / §4.2.7.5.3 decoders (asserting
the spacing post-condition, the `[0, 32767]` bound, and strict
monotonicity), length-matches-bandwidth checks, and the SWB/FB +
length-mismatch rejections.

Round 9 (2026-05-24) lands the SILK Normalized LSF interpolation for
RFC 6716 §4.2.7.5.5 behind a new `LsfInterpolated` /
`LsfInterpContext` API. For a 20 ms SILK frame the first half (the
first two subframes) may use NLSF coefficients interpolated between
the most recent coded frame's vector `n0_Q15[]` and the current
stabilized vector `n2_Q15[]`. `decode` takes the range decoder, the
§4.2.7.5.4 `NlsfStabilized` (`n2`), the prior frame's `n0_Q15[]`
(or `None`), and an `LsfInterpContext`:

* **`TwentyMs`** — decode the Q2 factor `w_Q2 ∈ 0..=4` from the
  Table 26 PDF (`{13, 22, 29, 11, 181}/256`, iCDF `[243, 221, 192,
  181, 0]`) and compute
  `n1_Q15[k] = n0_Q15[k] + (w_Q2*(n2_Q15[k] - n0_Q15[k]) >> 2)`.
* **`TwentyMsAfterResetOrUncoded`** — the factor is still decoded
  (the range coder must stay in sync) but its value is discarded and
  `4` is substituted, so `n1_Q15[] == n2_Q15[]` (no interpolation).
  This is also the behaviour whenever `n0_Q15[]` is `None`
  (no prior-frame history).
* **`TenMs`** — the factor is not present in the bitstream; nothing is
  decoded and there is no first-half vector.

The result exposes the decoded `w_q2()` (`None` for 10 ms) and the
first-half `n1_q15()` (`None` for 10 ms). The second half of a 20 ms
frame and the whole of a 10 ms frame always use `n2_Q15[]` directly —
that is the caller's responsibility.

Ten new unit tests cover the Table 26 PDF→iCDF transcription
(sum-to-256 and monotone-decreasing self-checks), the 10 ms
no-read / no-first-half path (range coder untouched), the
end-to-end 20 ms interpolation against an independent formula
re-derivation, the `w_Q2 == 0 → n0` and `w_Q2 == 4 → n2` algebraic
identities, the reset/uncoded context decoding-then-forcing-4
behaviour (with a `tell()` parity check against the normal context),
the no-history `n0 = None` forced-`n2` path, the `n0`-length-mismatch
rejection, and a sweep asserting every interpolated value stays in
`[0, 32767]` across {NB, MB, WB} × all 32 `I1` × `w_Q2 ∈ 0..=4`.

Round 10 (2026-05-24) lands the SILK Normalized LSF → LPC core
conversion for RFC 6716 §4.2.7.5.6 behind a new `LpcQ17` API. Given a
stabilized / interpolated `nlsf_q15[]` (the §4.2.7.5.4 / §4.2.7.5.5
output) and the SILK-layer bandwidth (NB / MB / WB), the three-step
`silk_NLSF2A` procedure runs:

* **`silk_NLSF2A_cos` (Table 27 + Table 28).** The 129-entry Q12
  cosine table (`cos_Q12[0]=4096`, `cos_Q12[64]=0`,
  `cos_Q12[128]=-4096`, anti-symmetric about i=64) is transcribed
  verbatim. Each coefficient splits into top-7-bits `i = nlsf >> 8`
  and next-8-bits `f = nlsf & 255`; the §4.2.7.5.6 piecewise-linear
  interpolation `c_Q17[ordering[k]] = (cos_Q12[i]*256 +
  (cos_Q12[i+1]-cos_Q12[i])*f + 4) >> 3` populates the re-ordered Q17
  cosine vector. Table 27's `ordering[]` is `[0,9,6,3,4,5,8,1,2,7]`
  for NB/MB and `[0,15,8,7,4,11,12,3,2,13,10,5,6,9,14,1]` for WB.
* **`silk_NLSF2A_find_poly` recurrence.** Two rolling-row passes on
  the even-indexed (P) and odd-indexed (Q) `c_Q17[]` cells run
  `p[k][j] = p[k-1][j] + p[k-1][j-2] - ((c*p[k-1][j-1] + 32768)>>16)`
  with the §4.2.7.5.6 boundary conditions `p[k][j<0] = 0` and
  `p[k][k+2] = p[k][k]`. Intermediates are computed in i64 to absorb
  the spec's noted "up to 48 bits of intermediate precision".
* **`silk_NLSF2A` last-row assembly.** The final P / Q rows are
  folded into the 32-bit Q17 LPC coefficients via the §4.2.7.5.6
  sum / difference pair `a32_Q17[k] = -((q_diff) + (p_sum))` and
  `a32_Q17[d_LPC-k-1] = (q_diff) - (p_sum)`, where
  `q_diff = q[d2-1][k+1] - q[d2-1][k]` and
  `p_sum = p[d2-1][k+1] + p[d2-1][k]`.

The §4.2.7.5.7 range-limiting bandwidth-expansion loop (shrinks
`a32_Q17[]` to fit Q12) and the §4.2.7.5.8 prediction-gain stability
check (chirps until `silk_LPC_inverse_pred_gain_QA` passes) are both
deferred to subsequent rounds.

22 new unit tests (195 lib tests total in the crate, up from 173 at
round-9 close) cover Table 27 row-widths + permutation-of-`0..d_LPC`
self-checks + bandwidth routing (SWB / FB rejected), Table 28 length
+ three anchor cells + strict-monotone-decreasing pairwise check +
the anti-symmetric-about-64 invariant + Q12-range bound + four row
spot-checks, `nlsf_to_c_q17` at the table anchor points (`f == 0`
round-trip against `cos_Q12[8*k]`) and at the linear-interpolation
midpoint (`f == 128` matching the `16*(a+b)` algebraic identity),
SWB / FB and length-mismatch rejection, the production
`LpcQ17::from_nlsf` agreeing bit-for-bit with an independent
2D-matrix spec-transcription oracle on synthetic ascending NLSF
vectors for both NB and WB, the same production / oracle agreement
across the full §4.2.7.5.2 → §4.2.7.5.3 → §4.2.7.5.4 pipeline ×
all 32 `I1` × {NB, MB, WB}, and a no-panic sweep over three buffers
× all 32 `I1` × {NB, MB, WB}.

Round 11 (2026-05-24) lands the SILK LPC range-limiting bandwidth
expansion for RFC 6716 §4.2.7.5.7 behind a new `LpcQ17::range_limited`
method. Given the raw §4.2.7.5.6 `a32_Q17[]` (which is too large to fit
a signed 16-bit value), the procedure shrinks the coefficients so they
fit Q12:

* **Up to 10 rounds of `silk_bwexpander_32` chirping.** Each round finds
  the index `k` with the largest `abs(a32_Q17[k])` (ties to the lowest
  `k`), computes `maxabs_Q12 = min((maxabs_Q17 + 16) >> 5, 163838)`, and
  stops once `maxabs_Q12 <= 32767`. Otherwise it derives the chirp factor
  `sc_Q16[0] = 65470 - ((maxabs_Q12 - 32767) << 14) /
  ((maxabs_Q12 * (k+1)) >> 2)` (integer division) and runs the recurrence
  `a32_Q17[k] = (a32_Q17[k]*sc_Q16[k]) >> 16`,
  `sc_Q16[k+1] = (sc_Q16[0]*sc_Q16[k] + 32768) >> 16`. The first multiply
  runs in i64 ("up to 48 bits of precision"); the second is unsigned per
  the §4.2.7.5.7 note to avoid 32-bit overflow.
* **Post-loop Q12 saturation.** If `maxabs_Q12` is still greater than
  32767 after the 10th round, each coefficient is saturated in the Q12
  domain and converted back to Q17:
  `a32_Q17[k] = clamp(-32768, (a32_Q17[k] + 16) >> 5, 32767) << 5`. In
  practice the adaptive chirp converges every realistic input within 10
  rounds, so this branch is the spec-documented belt-and-suspenders step.

The output is held in the Q17 domain (the §4.2.7.5.8 prediction-gain
limiting that follows consumes Q17 coefficients), so it shares the
`LpcQ17` representation. `maxabs_Q17` is taken via `i32::unsigned_abs()`
so an `i32::MIN` coefficient cannot panic.

Six new unit tests (201 lib tests total in the crate, up from 195 at
round-10 close) cover the small-coefficient pass-through, production /
independent-i128-oracle agreement on synthetic overflow vectors and on
the 163838-cap extreme, the Q12-fit post-condition, the `i32::MIN`
no-panic edge, the post-loop saturation formula pinned in isolation, and
a real §4.2.7.5.2 → §4.2.7.5.7 pipeline sweep across all 32 `I1` values
× {NB, MB, WB}.

Round 12 (2026-05-24) lands the SILK LPC prediction-gain limiting for
RFC 6716 §4.2.7.5.8 behind a new `LpcQ17::prediction_gain_limited` method
returning a new `LpcQ12` type. Even after the §4.2.7.5.7 range-limiting,
the filter may have so much prediction gain that it is unstable; this
stage drives up to 16 rounds of bandwidth expansion off the
`silk_LPC_inverse_pred_gain_QA` stability test rather than the coefficient
magnitude:

* **`silk_LPC_inverse_pred_gain_QA` stability test (`is_lpc_stable`).**
  Each round converts to the real Q12 coefficients `a32_Q12[n] =
  (a32_Q17[n] + 16) >> 5` and runs the DC-response check (`DC_resp =
  Σ a32_Q12[n] > 4096` ⇒ unstable) followed by a fixed-point Levinson
  recurrence on the Q24-widened coefficients (`inv_gain_Q30[d_LPC] =
  1<<30`, `a32_Q24[d_LPC-1][n] = a32_Q12[n] << 12`). For `k` from
  `d_LPC-1` down to `0` it rejects on `abs(a32_Q24[k][k]) > 16773022`
  (≈ 0.99975 in Q24) or `inv_gain_Q30[k] < 107374` (≈ 1/10000 in Q30),
  and otherwise (for `k > 0`) computes row `k-1` via the spec's
  `b1 = ilog(div_Q30)` / `inv_Qb2` / `err_Q29` / `gain_Qb1` / `num_Q24` /
  `a32_Q24[k-1][n]` formulas. Every spec-flagged ">32-bit" multiply runs
  in i64.
* **Stability-driven chirp loop.** If stable, the Q12 coefficients are
  returned; otherwise a chirp round with `sc_Q16[0] = 65536 - (2<<i)` is
  applied via the same `silk_bwexpander_32` as §4.2.7.5.7. On round 15
  `sc_Q16[0]` is `0`, zeroing every coefficient so an all-zero (trivially
  stable) filter is the worst-case outcome.

`LpcQ12` exposes `a_q12()`, `len()`, `is_empty()`, and `rounds()` (chirp
rounds run before stability).

Nine new unit tests (210 lib tests total in the crate, up from 201 at
round-11 close) cover `is_lpc_stable` agreement with an independent
2D-matrix spec oracle on hand-built filters, the all-zero stable case,
DC-response rejection, a round-0 pass-through on a typical decoded NLSF
vector, deliberately-unstable inputs always converging to a stable filter
within ≤ 16 rounds, the forced round-15 zeroing, the signed-16-bit Q12
fit, a real §4.2.7.5.2 → … → §4.2.7.5.8 pipeline sweep across all 32 `I1`
× {NB, MB, WB} on three buffers, and the `ilog64` §1.1.10 boundaries.

Round 13 (2026-05-24) lands the SILK Long-Term Prediction parameters
for RFC 6716 §4.2.7.6 behind a new `LtpParameters` / `LtpConfig` API.
The caller passes the SILK-layer bandwidth (NB / MB / WB), the signal
type from §4.2.7.3, the subframe count (2 for 10 ms; 4 for 20 ms /
Hybrid), a `LagCoding` enum selecting absolute vs relative primary-lag
coding (with the prior frame's unclamped primary lag for the latter),
and a boolean for whether the §4.2.7.6.3 LTP scaling field is present.
`decode` returns:

* **§4.2.7.6.1 pitch lags.** Non-voiced frames consume no bits.
  Voiced frames decode the primary lag either as
  `lag = lag_high * lag_scale + lag_low + lag_min` (absolute path:
  Table 29 32-entry high-part PDF + Table 30 bandwidth-conditioned
  low-part PDF + scale `{4, 6, 8}` for `{NB, MB, WB}` + `lag_min`
  `{16, 24, 32}` + `lag_max` `{144, 216, 288}`), or as
  `lag = previous_lag + (delta_lag_index - 9)` (relative path:
  Table 31 21-entry delta PDF, with a decoded delta of 0 falling back
  to the absolute-coding sub-path that reads the high + low parts).
  The pitch-contour VQ index follows from one of the four Table 32
  PDFs picked by `(bandwidth, num_subframes)`, then the per-subframe
  lag is `pitch_lags[k] = clamp(lag_min, lag + lag_cb[contour_index][k],
  lag_max)` with the offsets from Tables 33 (NB 10 ms, 3 entries × 2),
  34 (NB 20 ms, 11 × 4), 35 (MB/WB 10 ms, 12 × 2) and 36 (MB/WB
  20 ms, 34 × 4). The primary lag itself is held unclamped per the
  §4.2.7.6.1 note so the next frame's relative coding remains
  consistent.
* **§4.2.7.6.2 LTP filter coefficients.** A 3-entry periodicity
  index (Table 37 PDF `{77, 80, 99}/256`) gates one of three filter
  codebooks; each subframe then decodes a filter index from the
  periodicity-conditioned PDF in Table 38 (codebook sizes 8 / 16 /
  32) into a 5-tap signed Q7 filter from Tables 39 (periodicity 0),
  40 (periodicity 1) or 41 (periodicity 2).
* **§4.2.7.6.3 LTP scaling.** When `ltp_scaling_present` is true, a
  3-entry index from the Table 42 PDF `{128, 64, 64}/256` selects a
  Q14 scale factor from `{15565, 12288, 8192}` (≈ 0.95 / 0.75 / 0.5).
  When absent the default `15565` is used and no bits are consumed.
  Non-voiced frames also use the default.

The §4.2.7.9 LTP synthesis filter that consumes these parameters is
intentionally left to a later round — this module only produces the
decoded parameter set.

Nineteen new unit tests (229 lib tests total in the crate, up from 210
at round-12 close) cover the PDF → iCDF transcriptions for Tables 29 /
30 (per-bandwidth) / 31 / 32 (all four PDFs) / 37 / 38 (all three
codebooks) / 42 (each sums to 256, strictly monotone-decreasing iCDF,
terminator 0), Table 30 scale + min-lag + max-lag values, the
contour-codebook size-matches-PDF self-checks plus index-0 (all-zero
offset) and several interior-row spot-checks against the spec
(`CONTOUR_NB_20MS[1] == [2,1,0,-1]`, `CONTOUR_MBWB_20MS[33] == [-9,-3,
3,9]`, `CONTOUR_MBWB_10MS[11] == [-3,3]`), the LTP-filter-codebook
sizes (8 / 16 / 32) and four boundary-row spot-checks against Tables
39–41 (`P0[0]=[4,6,24,7,5]`, `P0[7]=[16,14,38,-3,33]`,
`P1[15]=[3,-1,21,16,41]`, `P2[31]=[2,0,9,10,88]`), the no-bits-consumed
property for non-voiced frames (both Inactive and Unvoiced signal
types), the malformed-config rejections (non-2-non-4 subframe count;
SWB / FB bandwidth), the in-range + formula-match property for absolute
coding across {NB, MB, WB} × {2, 4} subframes (independent re-derivation
of the production decode), the relative-coding non-zero-delta path
(`primary = previous_lag + (delta - 9)`), the relative-coding zero-delta
fallback into the absolute sub-path, the LTP-scaling-present path's
output landing in `{15565, 12288, 8192}`, the LTP-scaling-absent path
consuming strictly fewer bits than the present path, and a sweep
across {NB, MB, WB} × {2, 4} subframes × {absent, present} scaling ×
{Absolute, Relative} coding × three buffers that asserts no panics, the
`[lag_min, lag_max]` clamp post-condition, and the periodicity ≤ 2
invariant.

Round 14 (2026-05-25) lands the SILK Linear Congruential Generator
seed for RFC 6716 §4.2.7.7 behind a new `decode_lcg_seed` helper, plus
the full SILK excitation decoder for §4.2.7.8 behind a new
`Excitation` / `ExcitationConfig` API. The LCG seed reads a single
symbol from the uniform 4-entry Table 43 PDF (`{64, 64, 64, 64}/256`),
yielding a value in `0..=3` that initialises the pseudorandom sign
generator used by §4.2.7.8.6 reconstruction.

The §4.2.7.8 excitation decodes in six substeps:

* **§4.2.7.8.1 Rate level.** A single symbol per SILK frame drawn from
  one of two Table 45 PDFs selected by `(signal_type)`  `{15, 51, 12, 46, 45, 13, 33, 27, 14}/256` for Inactive/Unvoiced and
  `{33, 30, 36, 17, 34, 49, 18, 21, 18}/256` for Voiced. The decoded
  value `0..=8` indexes the per-block pulse-count PDF table.
* **§4.2.7.8.2 Pulses per shell block.** Table 44 routes
  `(bandwidth, frame_size)` to the shell-block count (5, 8, 10, 10,
  15, 20 for the six (NB/MB/WB × 10ms/20ms) cells). For each block,
  read from the rate-level-`r` PDF in Table 46. The special value 17
  flags "extra LSB present" — re-read from rate level 9; if the result
  is 17 again, re-read from level 9; on the tenth consecutive 17,
  switch to rate level 10, whose cell-17 probability is exactly zero
  (capping extra LSBs at 10 per block per the §4.2.7.8.2 note).
* **§4.2.7.8.3 Pulse locations.** A recursive-partition decoder runs
  per block with pulse count > 0: at each level the partition halves
  (16 → 8 → 4 → 2 → 1) and the left-half pulse count is decoded from
  the Table 47 / 48 / 49 / 50 split PDF (one PDF per `(partition_size,
  pulse_count)` cell). When the partition collapses to a single
  sample, the remaining pulse count is the sample's magnitude.
* **§4.2.7.8.4 LSB decoding.** For each block with `lsbs > 0`, read
  one binary symbol from the Table 51 PDF (`{136, 120}/256`) for every
  coefficient (even those with zero pulses) for `lsbs` iterations
  MSB-first, doubling the running magnitude and adding each bit.
* **§4.2.7.8.5 Sign decoding.** For every coefficient with magnitude
  > 0, read one binary symbol from the Table 52 PDF chosen by
  `(signal_type, qoff_type, min(pulses_in_block, 6))`. A 0 means
  negate; a 1 means keep positive. The pulse count for sign-PDF
  selection is the initial pre-LSB count.
* **§4.2.7.8.6 Reconstruction.** For each sample:
  `e_Q23[i] = (e_raw[i] << 8) - sign(e_raw[i])*20 + offset_Q23` with
  `offset_Q23` per Table 53 (`{Inactive,Unvoiced}/Low=25,
  /High=60; Voiced/Low=8, /High=25`), then a 32-bit LCG step
  `seed = (196314165*seed + 907633515) & 0xFFFFFFFF`. If the LCG MSB
  (`seed & 0x80000000`) is set, `e_Q23[i]` is negated. Finally
  `seed = (seed + e_raw[i]) & 0xFFFFFFFF` feeds the next sample.

Thirty new unit tests (259 lib tests total in the crate, up from 229
at round-13 close) cover the Table 43 LCG-seed iCDF transcription and
the 0..=3 + bits-consumed properties; Table 44 (all six valid
(bandwidth × frame_size) cells plus SWB/FB rejection); the two Table
45 rate-level PDFs; all eleven Table 46 pulse-count PDFs (sums to 256,
iCDF transcription, plus the L10 cell-17 = 0 boundary that caps the
LSB-chain depth); one spot-check per Table 47/48/49/50 (1- and ≥7-
pulse cells); Table 51 LSB PDF; six Table 52 sign PDFs across each
`(signal_type, qoff_type)` quadrant plus the "6 or more" saturation;
all six Table 53 quantization offsets; the LCG recurrence first few
steps pinned algebraically; `Excitation::decode` rejections (invalid
LCG seed, SWB/FB bandwidth); correct sample count per (bandwidth ×
frame_size); the §4.2.7.8 "fits in 24 bits including sign" invariant
across three buffers × all (NB/MB/WB × 10/20ms) cells with high
quantization offset; per-block pulse-count ≤ 16 and LSB-count ≤ 10
invariants; a hand-pinned reconstruction of an isolated mag=5, sign=-1
sample producing ±1235 (depending on LCG flip); the zero-magnitude
sample identity `|e_Q23[i]| == offset_Q23` after the LCG step; bit-
exact reproducibility across two decoder passes of the same buffer +
config; LCG-seed divergence (different seed = different output); and a
sweep across three buffers × {NB, MB, WB} × {10, 20 ms} × 3 signal
types × 2 qoff types × 4 seeds asserting no panics.

Total crate test count: 277 (5 TOC + 27 frame-packing + 19 range
decoder + 17 SILK header + 20 subframe gains + 30 LSF stage-2 +
26 LSF reconstruction + 19 LSF stabilization + 10 LSF interpolation
+ 22 LSF → LPC core + 6 LPC range-limiting + 9 LPC prediction-gain
limiting + 19 LTP parameters + 4 LCG seed + 26 excitation + 18 LPC
synthesis).

Round 14 stops after the §4.2.7.8 excitation — the SILK frame header,
the gains, the full LSF → LPC pipeline, the long-term-prediction
parameters, the LCG seed and the full excitation reconstruction are
all decoded.

Round 15 (2026-05-25) lands the §4.2.7.9.2 SILK LPC synthesis filter
behind a new `lpc_synthesis_subframe` / `lpc_synthesis_frame` /
`LpcSynthState` API. The per-subframe short-term predictor combines
the §4.2.7.4 Q16 gain, the §4.2.7.9.1 residual `res[i]`, and the
§4.2.7.5.8 stabilised Q12 filter `a_Q12[k]` into

```
                                  d_LPC-1
                 gain_Q16[s]         __              a_Q12[k]
        lpc[i] = ----------- * res[i] + \  lpc[i-k-1] * --------
                   65536.0              /_               4096.0
                                        k=0
        out[i] = clamp(-1.0, lpc[i], 1.0)
```

The `d_LPC` unclamped `lpc[i]` history is carried across subframes via
the stateful `LpcSynthState` (cleared to zero on a decoder reset per
RFC 6716 §4.5.2 or after an uncoded regular SILK frame). The
§4.2.7.9.2 wording "the decoder saves the unclamped values lpc[i] to
feed into the LPC filter for the next subframe, but saves the clamped
values out[i] for rewhitening in voiced frames" is honoured exactly:
state holds the unclamped values; the rendered output is the clamped
vector. d_LPC routing follows §4.2.7.5 — 10 for NB / MB, 16 for WB
(SWB / FB rejected at the SILK layer). The §4.2.7.9 preamble licenses
a floating-point implementation here ("the remainder of the
reconstruction process for the frame does not need to be bit-exact"),
so the accumulator runs in `f32`.

Eighteen new unit tests (277 lib tests total in the crate, up from 259
at round-14 close) cover `subframe_samples` routing including SWB / FB
rejection; `LpcSynthState` d_LPC routing + zero initialisation + reset
to zero; the three input-validation rejections (`res` / `out_clamped`
length mismatch + `a_q12` length mismatch); the algebraic identities
(`a_Q12 = 0 → lpc = gain * res`; zero residual with zero history → zero
output regardless of a_Q12 / gain); a hand-pinned NB unity-gain
single-tap impulse response (constant 1.0); a hand-pinned WB half-gain
single-tap impulse response (geometric series `0.5^(i+1)` matched to
1e-9 precision); a hand-traced two-tap NB filter with non-trivial
`res[]` producing the exact sequence `[1.0, 2.5, 4.5, 2.875, 2.5625]`
plus the per-sample clamp; the cross-subframe history carry-over (an
impulse in subframe 0 keeps the unit-feedback filter emitting 1.0 in
subframe 1); decoder-reset path zeroes history; out ∈ `[-1.0, 1.0]`
under deliberately over-driven inputs; the unclamped-history-vs-clamped-
output distinction; `lpc_synthesis_frame` agreement with an explicit
per-subframe loop including state, plus its length-mismatch rejection;
and a no-panic sweep over {NB, MB, WB} × {10 ms, 20 ms} asserting the
clamp post-condition and the d_LPC history length.

The §4.2.7.9.1 LTP synthesis filter that produces `res[i]` for voiced
frames is now wired up — see round 16 below. The CELT band machinery
and the §5 encoder pipeline are still ahead; the higher-level encode /
decode entry points still return `Error::NotImplemented`.

Round 16 (2026-05-25) lands the §4.2.7.9.1 SILK LTP synthesis filter
behind a new `ltp_synthesis_subframe` / `ltp_synth_commit_subframe` /
`LtpSynthState` API. Two regimes per the spec:

* **Unvoiced** (`signal_type != Voiced`). The LPC residual is just a
  normalised copy of the §4.2.7.8 excitation:
  `res[i] = e_Q23[i] / 2^23`.
* **Voiced**. The 5-tap Q7 LTP convolution is applied:
  `res[i] = e_Q23[i]/2^23 + Σ_{k=0..4} res[i - pitch_lag + 2 - k] *
  b_Q7[k] / 128`. The "prior res[]" values it reads come from
  rewhitening the prior-subframe outputs through the current
  subframe's LPC coefficients (because the coefficients may have
  changed between subframes):

  * **Region A** (out[] rewhiten, indices
    `(j - pitch_lag - 2) <= i < out_end`):
    `res[i] = 4 * LTP_scale_Q14 / gain_Q16 *
    clamp(out[i] - Σ out[i-k-1] * a_Q12[k]/4096, -1, 1)`.
  * **Region B** (lpc[] rewhiten, indices `out_end <= i < j`):
    `res[i] = 65536 / gain_Q16 *
    (lpc[i] - Σ lpc[i-k-1] * a_Q12[k]/4096)`.

`out_end` and the effective `LTP_scale_Q14` follow the §4.2.7.9.1
LSF-interpolation-split branch. For the third or fourth subframe of a
20 ms SILK frame that used a `w_Q2 < 4` LSF interpolation, `out_end =
j - (s-2) * n` and `LTP_scale_Q14 = 16384`; otherwise `out_end = j -
s*n` and the §4.2.7.6.3 decoded scaling factor is used directly.

`LtpSynthState` carries the spec-stated buffer sizes — 306 samples of
`out[]` (WB max pitch 288 + d_LPC 16 + 2) and 256 samples of `lpc[]`
(3 prior WB subframes 240 + d_LPC 16) — across subframes and across
SILK frame boundaries; `reset()` clears both for the §4.5.2
decoder-reset / uncoded-side-channel-frame paths, and `start_frame()`
resets only the in-frame subframe counter without touching the
cross-frame histories. The companion `ltp_synth_commit_subframe`
pushes the §4.2.7.9.2 outputs back into the state once the LPC
synthesis filter has run.

Twenty-one new unit tests (298 lib tests total, up from 277 at
round-15 close): the constant table matches the §4.2.7.9.1 buffer-size
paragraph (`LTP_OUT_HISTORY_MAX == 306`, `LTP_LPC_HISTORY_MAX == 256`,
`LTP_SCALE_FRESH_Q14 == 16384`); `LtpSynthState::new` d_LPC routing
(NB/MB = 10, WB = 16; SWB/FB rejected); zero-initialised and
reset-zeroed histories + subframe-index; `start_frame()` preserves
histories but clears the index; `push_subframe` keeps the most-recent
samples at the tail and shifts older samples down; the unvoiced
`res[i] = e_Q23[i]/2^23` identity (Wb 80-sample sweep); the Inactive
signal type is treated as unvoiced; the four input-validation
rejections (mismatched `e_q23` / `res_out` / `a_q12` lengths;
mismatched state-vs-cfg bandwidth; out-of-range subframe index;
non-positive pitch lag for voiced); the zero-history /
zero-excitation / zero-b voiced-decode identity (output is zero); the
voiced `b == 0` identity (LTP convolution drops out, residual is
`e_Q23/2^23` regardless of prior history); the voiced `b_Q7[0] = 64`
pitch-lookback algebra (rewhitening of an injected out[] sample
matches `0.5 * 4*LTP_scale_Q14/gain_Q16 * out[j-14]`); the voiced
`b_Q7[2] = 64` region-B (lpc[]) rewhiten algebra; the
LSF-interpolation-split branch override at `subframe_index = 2` with
`lsf_interp_used = true` (effective scale becomes
`4*16384/65536 = 1.0` exactly); voiced-decode determinism (same
inputs → same outputs); and a no-panic finite-output sweep across 3
buffers × {NB, MB, WB} × {10 ms, 20 ms} × 4 subframes with histories
committed back into state via `ltp_synth_commit_subframe`.

Round 17 (2026-05-25) lands the §4.2.8 SILK stereo unmixing
(`silk_stereo_MS_to_LR`) behind a new `stereo_ms_to_lr` /
`StereoUnmixState` / `StereoWeightsQ13` / `StereoFrame` API
(`silk_stereo` module). After both stereo channels finish §4.2.7.9
reconstruction, the mid/side `out[]` signals are converted to
left/right. The side channel is predicted from a low-passed mid term
`p0 = (mid[i-2] + 2*mid[i-1] + mid[i]) / 4` and the unfiltered,
one-sample-delayed mid (`mid[i-1]`), using the §4.2.7.1 Q13 weights:

```text
 left[i] = clamp(-1.0, (1 + w1)*mid[i-1] + side[i-1] + w0*p0, 1.0)
right[i] = clamp(-1.0, (1 - w1)*mid[i-1] - side[i-1] - w0*p0, 1.0)
```

The first `n1` samples (64 NB / 96 MB / 128 WB ≈ 8 ms) interpolate the
weights linearly from the previous frame's `(prev_w0_Q13, prev_w1_Q13)`
to the current frame's `(w0_Q13, w1_Q13)`; the rest of the frame uses
the current weights (`min(i, n1)` clamps the ramp). An uncoded side
channel (§4.2.7.2) is treated as all-zero. The two trailing mid
samples, one trailing side sample, and the previous-frame weights are
carried across the frame boundary by `StereoUnmixState`, cleared to
zero on a decoder reset (`StereoUnmixState::reset`) per the §4.2.8
closing paragraph. Per the §4.2.7.9 "does not need to be bit-exact"
preamble, the stage runs in `f32`.

Nine new unit tests (307 lib tests total, up from 298 at round-16
close): the `interp_phase_samples` table (64/96/128; SWB/FB rejected);
fresh/reset state zeroing; empty-mid and mismatched-side-length
rejection; the zero-weight no-side collapse to delayed mono
(`L = R = mid[i-1]`); a hand-computed constant-weight mid/side
reconstruction (coded side, fresh history); phase-1 ramp endpoints
(effective `w1` at samples 1, `n1`, and the steady region); mid-history
carry across two frames; side-history carry across two frames; and
output clamping under oversized weights.

Round 18 (2026-05-26) lands the RFC 6716 §4.2.3 SILK packet-level
header bits and the §4.2.4 per-frame LBRR flags behind a new
`SilkHeaderBits` / `SilkChannelHeader` / `PerFrameLbrr` API
(`silk_header` module). The decoder reads, in §4.2.2 Figures 15/16
order:

* For each channel (mono: 1; stereo: 2), `N` uniform-binary VAD bits
  followed by a single global LBRR flag — all via
  `RangeDecoder::dec_bit_logp(1)`. `N = silk_frame_count(frame_size)`
  per §4.2.2 (1 for 10/20 ms Opus frames, 2 for 40 ms, 3 for 60 ms).
* For Opus frames longer than 20 ms (`N >= 2`), one §4.2.4 per-frame
  LBRR symbol per channel whose global LBRR flag is set. The Table 4
  PDFs are `{0, 53, 53, 150}/256` (40 ms) and
  `{0, 41, 20, 29, 41, 15, 28, 82}/256` (60 ms). Both have a leading
  zero entry: per §4.1.3.3 the iCDF drops that entry
  (`PER_FRAME_LBRR_{40MS,60MS}_ICDF`) and the helper adds an offset of
  1, producing a 2- or 3-bit bitmap with at least one bit set, packed
  LSB-to-MSB so bit `i` is the LBRR flag for SILK frame `i`.

For 10/20 ms Opus frames the per-frame LBRR bitmap mirrors the global
LBRR flag without consuming any extra bits — per §4.2.4 "the global
LBRR flag in the header bits is already sufficient to indicate the
presence of that single LBRR frame".

The output records each channel's VAD bitmap, the global LBRR flag,
and a fully-expanded `PerFrameLbrr { mid, side }` bitmap consumed by
the (forthcoming) §4.2.5 LBRR / §4.2.6 regular SILK loop.

Fourteen new unit tests (321 lib tests total, up from 307 at round-17
close): the Table 4 PDF/iCDF transcription self-checks (40 ms and
60 ms, including strictly-decreasing + terminator-zero invariants);
the `per_frame_lbrr_pdf` dispatch fallback; the `silk_frame_count`
§4.2.2 dispatch including the CELT-only 2.5/5 ms `None` arm; a 10 ms
mono decode that consumes exactly 2 bits; a 60 ms stereo decode that
populates all 3-bit VAD + LBRR bitmaps within range; rejection of
`num_silk_frames ∉ {1, 2, 3}`; the §4.2.3-implied per-frame LBRR
mirror on 10 ms with the global flag set (verifying no extra symbol
is consumed); the §4.2.4 skip path on 60 ms when both global LBRR
flags are unset (verifying exactly 8 bits are consumed); the VAD /
LBRR bitmap accessors for present-side and missing-side cases; and
exhaustive 40 ms / 60 ms `decode_per_frame_lbrr` symbol-range sweeps
plus a 60 ms full-coverage sweep over `{1..=7}`.

Round 19 (2026-05-26) lands the RFC 6716 §4.2.9 SILK resampler delay
budget and the internal-vs-output sample-rate accounting behind a new
`silk_resampler` module:

* **Table 54 — normative delay allocation per SILK audio bandwidth.**
  NB = 0.538 ms, MB = 0.692 ms, WB = 0.706 ms. The §4.2.9 resampler
  itself is explicitly non-normative ("a decoder can use any method it
  wants to perform the resampling"), but the delay budget is normative
  so the encoder can apply a matching pre-delay to the MDCT layer and
  keep SILK and CELT aligned across a §4.5 mode switch. `silk_resampler_delay_ms`
  returns the bandwidth's delay in milliseconds; `silk_resampler_delay_samples_at`
  scales it to a sample count at any output rate (round half away from
  zero — §4.2.9 itself notes "it may not be possible to achieve exactly
  these delays while using a whole number of input or output samples").
  SWB and FB return `None`: they never reach the §4.2.9 SILK resampler.
* **Internal SILK sample rate per bandwidth.** NB = 8 kHz, MB = 12 kHz,
  WB = 16 kHz (implied by the §4.2.1 / §4.2.7.x decode pipeline; the
  resampler bridges this to the application's chosen output rate).
  `silk_internal_rate_hz` and `silk_frame_samples_internal` cover the
  pre-resampler sample-count accounting (NB 20 ms = 160; MB 20 ms =
  240; WB 20 ms = 320).
* **§4.2.9 supported output rates.** 8 / 12 / 16 / 24 / 48 kHz, the
  five rates "the reference implementation is able to resample to …
  within or near this delay constraint". Exposed as
  `SUPPORTED_OUTPUT_RATES_HZ` + `is_supported_output_rate`;
  `REFERENCE_RATE_HZ` (= 48 kHz) marks the rate Table 54 anchors
  against and the rate CELT operates at.
* **Per-frame output sample count.** `silk_frame_samples_at_output`
  returns the post-resampler sample count for one SILK frame at any
  output rate (e.g. 480 samples at 48 kHz for any bandwidth × 10 ms;
  960 for 20 ms). Sized so a caller can allocate the output buffer
  without knowing the resampler kernel.

Eighteen new unit tests (339 lib tests total, up from 321 at round-18
close): Table 54 transcription self-checks and the SWB/FB exclusion;
the strict NB < MB < WB monotonicity §4.2.9 explicitly motivates; the
Table 54 expansion to 48 kHz samples (NB = 26, MB = 33, WB = 34) plus
internal-rate samples and 24 kHz intermediate-rate samples; SWB / FB /
zero-rate rejections on the delay-samples helper; the five §4.2.9
supported output rates plus a sweep of unsupported rates (11.025 /
22.05 / 32 / 44.1 / 96 kHz); the SILK internal rate per bandwidth and
its membership in the §4.2.9 supported-output set; canonical
per-frame sample counts at internal + output rates plus rejection of
non-SILK durations (25 / 50 / 400 / 600 / 1234 tenths-ms); and a
cross-check that the Table 54 delay is strictly less than one 10 ms
SILK frame at every supported output rate × every SILK bandwidth.

## Planned clean-room sources

The clean-room rebuild will consult only:

* RFC 6716 — Definition of the Opus Audio Codec.
* RFC 8251 — Updates to the Opus Audio Codec.
* RFC 7587 — RTP Payload Format for the Opus Speech and Audio Codec.
* RFC 7845 — Ogg Encapsulation for the Opus Audio Codec.
* Black-box invocations of `opusdec` / `opusenc` (the binaries — not
  their source) as opaque validators.

No external library source — neither the Opus reference encoder /
decoder nor any third-party Opus implementation — is permitted as a
reference under the workspace clean-room policy.

## License

MIT. See `LICENSE`.