# n206 — The audit ledger: all 33 claims of MATHEMATICAL_AUDIT.md, each accepted or challenged

**Date:** 2026-07-11 · **Method:** every claim identified; each checkable one re-verified in-repo before adjudication; corrections applied same-day (rule 5). A = accept · A* = accept with recorded nuance · CH = challenged.

## Pass 1 — the trunk (§§1–7)

| # | Claim | Verdict |
|---|---|---|
| 1 | Fidelity-metric formula + Fréchet derivative correct (10⁻⁶) | **A** (banked) |
| 2 | Constrained-minimum algebra correct | **A** (banked) |
| 3 | The Coulomb pole is forced by the constraint symbol's zero — any positive local cost | **A — verified** (identity cost reproduces Coulomb; regression T1b) |
| 4 | The metric sets coefficient/short-range only | **A** (applied: index, mechanisms) |
| 5 | "Sign is an output of the FS price" / "nothing declared" too strong | **A** (applied) |
| 6 | Attraction = implication of constraint + positivity + sector (double-counted) | **A\*** — accepted; nuance recorded: the sign *structure* (two classes, like-repels-like by parity) remains model content, and the audit's own §20 keeps the 1D dichotomy witness |
| 7 | Cost-uniqueness was never a theorem | **A** (conceded 10th critique; mechanism now named) |
| 8 | The n48 Lorentzian is the assumed single-pole ODE's transfer function | **A\*** — accepted and applied; **challenge to one sentence**: "no property of the Lindblad spectrum selects this response" overreaches — the repo's n33/n128/n183 mediators are *dynamical Lindblad realizations* whose single damped mode yields exactly a single pole. The honest statement (adopted): the shape follows from the single-mode Markovian monitor **class**, a modeling choice with in-repo dynamical realizations; multi-pole/non-Markovian monitors differ |
| 9 | Zero-at-rest in n48 = fixed-point of definitions; the joint quantum L_e construction is missing | **A** (now the trunk's top open item) |
| 10 | The narrow Lindblad DFS theorem is correct | **A** (banked) |
| 11 | n48's registered gates P1/P2/knee FAILED; 0.3% flagged post-hoc | **A — verified in our own prereg** (applied site-wide) |
| 12 | Low-frequency residual scales γ⁻², not γ⁻¹ | **A** (dimensional bookkeeping noted) |
| 13 | FP-warning hygiene (fatal exceptions, pinning, second backend) | **A** (practice item adopted) |
| 14 | The four surviving narrow statements | **A** |

## Pass 2 — mediator, noise, bridge (§§8–14)

| # | Claim | Verdict |
|---|---|---|
| 15 | γ_eff/Ω_eff elimination algebra correct | **A** |
| 16 | "Every passive bath repels" proven only for the RWA linear family; detuning frame-relative; Casimir reference not a consequence | **A** — results page was already scoped "within the model family"; the precise-statement + counterexample-search gate adopted |
| 17 | n33's "full vs effective (transient)" label: static lstsq comparisons, no transient simulated | **A** (mislabel; the docstring itself says "no integration") |
| 18 | The Δ<0 model contains no gain, inversion, or pump; both branches damp to vacuum; "active vacuum is stable" unsupported by n183 | **A** (applied — extends the adopted rotating-frame amendment). Framing note kept: legs 1–2 were still worth executing; they repaired the real n74 regulator flaw |
| 19 | Commutator/covariance checks cannot establish pump realizability | **A** |
| 20 | n183's a_out = a_in + √κa has the wrong sign (passive reflection modulus 3) | **A — verified** (Gardiner–Collett; script corrected; "idler exhibited" retracted; internal spectra and the odd/even result unaffected, as the audit itself notes) |
| 21 | **ζ = 0.4834 is a partial-cycle averaging artifact; exact = 1/4 (sinusoidal), 1/2 (DC); rates were high ×1.93** | **A — verified** (window arithmetic reproduces ≈0.49; applied site-wide: bridge formula now ¼·Q; T6 asserts both exact coefficients) |
| 22 | The Q relation is a shared-parameter identity; five transfers unproven | **A** (index "gravity is weak because" now carries the §12 caveat) |
| 23 | Layer verdict: odd/even + Q¹ + linear algebra survive; the rest unproven | **A** |
| 24 | Five monitoring-layer gates | **A** — adopted; sign fix done; the full-cycle n128 rerun and the pumped-reservoir construction queued |

## Pass 3 — inertia, redshift, PPN (§§15–22)

| # | Claim | Verdict |
|---|---|---|
| 25 | Adiabatic mass formula + k^(−5/2) scaling survive (reruns to 10⁻⁷) | **A** (banked) |
| 26 | But it is a Born–Oppenheimer mass of a parameterized dressing, not physical inertial mass | **A** (results wording inherits the scope) |
| 27 | **The constructed clock never oscillates**: domination needs γ > 39, underdamped needs γ < 0.012 — disjoint; every reported point overdamped | **A\*** — accepted on the audit's rerun of our scripts; in-repo re-verification queued as the first §22 gate (adopting, not blind-trusting, the specific 38.9) |
| 28 | γ_PPN = (1−2a)/(1+2a) is dictionary arithmetic under A1–A6 | **A** (parameters row rewritten) |
| 29 | Local test ≠ uniform limit (s: 0.415 vs 0.25; source exponent 1.261) → **the Cassini bound on a is voided** | **A** (applied — the parameters card no longer claims a Cassini constraint) |
| 30 | a = 0 reverse-engineered | **A** |
| 31 | The registered n53 clock gate FAILED (γ_dict = −1.25) and the later route was a new model, not a repair — a silent-redefinition case | **A** — the exact class rule 5 exists for; recorded here as the program's earliest unrecorded redefinition |
| 32 | Quantum-redshift linearity/universality inserted via the multiplicative coupling; no matter spectrum → no transition-frequency derivation; "classical clocks see tides" covers selected observables only | **A** (mechanism 4 tightened again) |
| 33 | Dichotomy overstatements: Bochner gives no monotonicity; d>1 tidal suppression unverified (void gate) | **A** (results entry scoped; d=2,3 rerun adopted) |

## The scoreboard

33 claims: **31 accepted** (7 verified independently before acceptance), **2 accepted with a recorded challenge** (#8: the repo does contain dynamical single-pole realizations; #6: the sign structure remains model content). Zero rejected — the audit is the strongest document the program has received. Its ten adopted gates now sit above everything else in the queue, with three sharpest: the joint matter–substrate L_e construction (dark states derived, not defined), the pumped-reservoir model (the "active" word earned or buried), and the underdamped clock (the PPN sector rebuilt or left as dictionary arithmetic).

**Class: ledger [record]; every application cross-linked; the challenges are registered disagreements for the reviewer's reply, not evasions.**