Module fri 

FRI low-degree-test soundness.

Conjectured regime: random-words bound, [2025/2010] §1.5. Legacy regime: historical pre-random-words ethSTARK query estimate, [2021/582]. Proven regime: round-by-round, [2024/1553] Theorems 2 & 3, with the DKT26 Johnson line-MCA commit bound ([2026/2056] Theorem 5.12 and Appendix B.1–B.2, extended to powers batching through the order-zero case of §7.2, Equation (88)). Its characteristic-free transfer is Lemma 5.3, not the positive-order powers-batching corollary in that section.

Correspondence with crate::assumption::SecurityAssumption:

• proven_error_udr is the FRI counterpart of UniqueDecoding (with FRI-specific α = (1 + ρ⁺)/2 incorporating OOD expansion).
• proven_error_ldr_m / best_ldr_m is the FRI counterpart of JohnsonBound, but searches m ∈ [3, LDR_M_CAP] rather than fixing m = 10 as WHIR does.
• CapacityBound is not currently supported by FRI’s commit-phase analysis.

Structs

FriRegime

Security-relevant mirror of p3_fri::FriParameters.

Functions

best_ldr_m

Search m ∈ [3, min(compute_upper_m, LDR_M_CAP)] for the value maximising LDR security; returns (best_m, ldt_error_at_best_m).

commit_phase_error_ldr_m

FRI commit-phase per-round error in LDR with explicit proximity parameter m. DKT26 Theorem 5.12 and Appendix B.1–B.2 give the Johnson-regime line-MCA count C = 8·n·(m + 1/2)^3/(3·rho_minus); multiplying by folding − 1 accounts for the polynomial-curve degree of a folding round. We also retain the independent n/|F| bound from [2024/1553] and take the minimum of their security bits. Round-by- round soundness is dominated by round 0 (largest n), so we use n = lde_domain_size for every round. For positive-degree codes at m >= 3, MCA gives fewer security bits and determines this minimum. Reconstruction can instead cap the separate constant-code bound.

commit_phase_error_udr

FRI commit-phase per-round error in UDR.

conjectured_commit_phase_error

FRI commit-phase per-round error in the conjectured regime.

conjectured_error

Conjectured low-degree-test soundness (random-words, [2025/2010] §1.5).

ldr_candidates

Every admissible m ∈ [3, min(compute_upper_m, LDR_M_CAP)] with the LDT-only error attained there, in increasing order of m.

legacy_conjectured_error

Historical FRI query-error estimate (ethSTARK 2021/582 §5.10.1, pre-random-words).

proven_error_ldr_m

Proven LDT-only error in the LDR regime with explicit m.

proven_error_udr

Proven LDT-only error in the UDR regime. Combines commit-phase and query-phase contributions; AIR/DEEP terms compose at the protocol call site (e.g. crate::stark::proven_security).

query_phase_error

FRI query-phase error: ε ≤ αᵏ, contributing query_pow − k·log2(α) bits.