Triadic (higher-order) blind spot in pairwise Neff/k_eff — synergy channel to strengthen L-01 mitigation

[emooreatx]

Summary

The operative Neff/k_eff in RATCHET is a pairwise (second-order) correlation diagnostic, and it returns its maximally-safe value on a deception structured in the third order — a parity/GHZ-type forbidden joint combination across ≥3 constraint axes, with every pair individually in-distribution. Such a deception posts pairwise correlation ρ̄ ≈ 0 → k_eff = k (maximum effective dimension) → the codimension/collapse model predicts a false all-clear, while the attack carries up to ~1 bit of genuine multi-information the pairwise detector cannot see (~100% hidden).

This is a sharpening of the already-CRITICAL L-01 / I-01 class (KNOWN_LIMITATIONS.md), not a falsified guarantee. Two things are new: (1) the pairwise detector reads maximally safe — a manufactured false all-clear, not mere non-detection; (2) the fix is tractable because the robust higher-order object is bounded-arity (~3-body), so a small fixed interaction order suffices (not 2ⁿ).

Scope — what is and isn't affected

• Affected (semantic layer): the geometric/codimension diagnostic V ~ exp(−λ·k_eff) and the eigenvalue-Neff — experiments/exp1_multimodel_neff/phase1_aggregate.py:204-262 (Pearson corrcoef eigenspectrum), ratchet/engines/geometric.py:161-194 (scalar-ρ Kish k_eff), ratchet/engines/correlation_tensor.py:248-262 (participation ratio).
• NOT affected (floors, orthogonal to correlation): the deception-cost complexity floor T_D/T_H = Ω(2^m) (SAT/ETH, m = world-model size — ratchet/engines/complexity.py), and the CEG cryptographic-attestation floor (Ed25519/PBFT — ratchet/federation/).

Evidence the Third is already computed and then discarded

ratchet/engines/correlation_tensor.py (added for reviewer concern 2.3) already has compute_triplet_correlations (lines 397-459) + a HigherOrderCorrelations dataclass — but compute_k_eff (line 248) and effective_dimension (line 168) ignore them and return the pairwise participation ratio. The existing L-01 mitigation ratchet/detection/compositional.py (MIAmplificationDetector) uses a pairwise MI baseline (lines 71-78) and a naive fixed-20-bin histogram MI (line 448) with no bias correction and no null control — exactly the finite-sample false-positive failure mode.

Proposed fix — a synergy channel alongside (never folded into) the pairwise Neff

1. correlation_tensor.py: upgrade compute_triplet_correlations from co-skewness to bias-corrected multi-information / O-information to bounded order (~3, optionally 4). Surface as a distinct field/verdict on ExtendedCorrelationModel. Do not feed it into compute_k_eff — the pairwise number must stay honest.
2. Dual null (mandatory): a shuffle-null (per-axis permutation, for estimator bias) and a shot-noise-matched null (matched to marginals + pairwise structure + sampling/discreteness). Without the shot-matched null the estimator produces finite-sample false positives — this exact failure sank an independent measurement in the sister repo. If a rank/copula transform is used, replace argsort∘argsort tie-breaking with random tie-breaking (it manufactured 37–63% of the fake signal there).
3. detection/compositional.py: replace the pairwise MI baseline + histogram estimator with an O-information/total-correlation estimator over the constraint axes themselves, same dual null. Directly strengthens the L-01 mitigation against the marginal-preserving/parity case it currently cannot see.
4. Conscience/roadmap slot (already designated): AGENT_FSDs/CONSCIENCE_V3.md §10 and AGENT_FSDs/PROOF_OF_BENEFIT_FEDERATION.md §2.5 already specify "Recursive Interaction Information across K orthogonal axes" as cracking L-01 — specified but unimplemented. Wire the estimator here.
5. Adversarial test (currently missing): RATCHET has no clean adversarial-Neff spec (fiction/ADVERSARIAL_ANALYSIS.md is quarantined synthetic). Add one — or a phase in experiments/exp1_multimodel_neff/ — that injects a GHZ/parity-coordinated constraint set (every pair in-distribution) and confirms: (i) pairwise Neff reads ≈ n, (ii) the synergy channel fires, (iii) the shot-noise-matched null suppresses the finite-sample false positive.

Honest bottom line

Real-and-fixable, semantic-layer only. The deception-resistance floor (complexity + crypto) is untouched; the correlation diagnostic has a documented-class hole that becomes a false all-clear on a triadic attack. Most of the machinery already exists; bounded-arity keeps the fix tractable. One caveat surfaced by the audit: the in-repo attestation is stubbed (attestation_level constant 0, "failed in this release" — real CEG lives in CIRISConstitution), so within RATCHET's runnable demo the semantic leg carries more weight than the architecture intends.

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Filed from the coherence-ratchet "Third" analysis (2026-07-20). Mechanized reference: Core/TriadicChannel.lean, local_op_does_not_increase_TC — triadic coordination is un-forgeable by local operations, so a positive synergy reading is provably real coordination, not estimator noise.

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