Struct FittedAtom 

pub struct FittedAtom {
    pub name: String,
    pub topology: AtomTopology,
    pub frame: Array2<f64>,
    pub ard_variances: Option<Array1<f64>>,
    pub lowering_error: f64,
    pub chart_canonicalized: bool,
    pub inner_fit: Option<AtomInnerFit>,
}

One fitted atom as the certificate sees it.

frame is the fitted decoder frame whose columns the isometry generators rotate: an (output_dim, latent_dim) matrix whose column a is the fitted image of latent axis a in output space (e.g. the decoder Jacobian columns at the atom’s centroid, or the leading decoder directions). The isometry generators of Isom(M_k) act on these columns; the certificate lifts that action to a tangent direction on the flattened decoder frame.

Fields

name: String

topology: AtomTopology

frame: Array2<f64>

(output_dim, latent_dim) fitted decoder frame.

ard_variances: Option<Array1<f64>>

ARD prior variances (one per latent axis of this atom), used to detect equal-ARD eigenspaces inside which a rotation is unpinned by the prior. None ⇒ no ARD prior on this atom (every within-frame rotation is then a candidate generator, pinned-or-not decided solely by the data + the isometry penalty).

lowering_error: f64

Lowering-error scale (#995), in [0, 1]: the mass-weighted relative dispersion of the atom’s per-row decoder tangents around the mean frame the certificate compresses them into, Σ_n a_n Σ_ax ‖t_ax(n) − frame[:,ax]‖² / Σ_n a_n Σ_ax ‖t_ax(n)‖².

0 ⇒ the frame represents every row exactly (hand-built fixtures, flat decoders) and the certificate’s verdicts within this atom are at full resolution. Values toward 1 ⇒ a curved decoder whose tangent field disperses strongly (e.g. a full circle, whose tangents average to ≈ 0): the mean-frame lowering then cannot distinguish gauge motion from genuine curvature, so the verdict tolerance for generators touching this atom is calibrated up to this scale — the certificate refuses to claim a pin it cannot resolve, the same honesty contract as the diffeomorphism-unpinned escalation.

chart_canonicalized: bool

#1019 stage 1: true when the atom’s d = 1 latent chart was pinned post-fit to its arc-length (unit-speed) canonical representative. #1019 stage 2: true as well when a d = 2 torus atom’s chart was pinned post-fit to the minimum-isometry-defect flow representative, in which case the residual chart freedom is Isom(T², flat) = U(1)² ⋊ D₄. The certificate then records that this atom’s continuous chart (reparameterization) freedom is pinned by canonicalization — a provenance distinct from curvature/penalty pinning (VerdictProvenance::PinnedByCanonicalization) — and that the residual chart freedom is the finite isometry group of the reference manifold for d = 1 charts: rotation + reflection (O(2)) on the circle, reflection + translation on the interval.

inner_fit: Option<AtomInnerFit>

Per-atom inner-decoder-smooth byproducts harvested at fit time, the single source the post-PIRLS atom inference reports (AtomFunctionalReport #1097, AtomSmoothSignificance #1103) consume in dictionary_report.

The certificate path that builds FittedSaeManifold does so without a fit harness in scope, so it leaves this None; callers that own the fitted term attach it through FittedAtom::with_inner_fit (the term builder fills it from the live per-atom basis, decoder, assignment mass, and smoothness Gram). When None, both reports below are None: the genuine prerequisite — the post-fit inner-smooth design, penalized Hessian, and row scores — is simply not present on a bare certificate-only FittedSaeManifold.

Implementations

impl FittedAtom

pub fn with_inner_fit(self, inner_fit: AtomInnerFit) -> Self

Attach the inner-decoder-smooth byproducts harvested at fit time. The term builder calls this so dictionary_report can produce the three post-PIRLS atom inference reports.

Trait Implementations

impl Clone for FittedAtom

fn clone(&self) -> FittedAtom

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for FittedAtom

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.