CLAIMS — the ledger

Every claim this run touched, whether the run generated it or the repository already carried it. A claim with no disposition is an unfinished claim, not a true one.

Disposition vocabulary

"The director thinks this is correct" is not a disposition and may not be used.

Ledger

Each entry: ID → origin → generating context → dependencies → evidence → counterexample attempts → controls → replications → knownness → formal status → objections → confidence → disposition.

(entries are appended by the run; see docs/25-the-director-run.md for the narrative and GRAVEYARD.md for what died)

Repository claims put on trial

C-RIG-01 — "A nonzero proven_sign is a proof." (zeta/rigor.py) origin: repository, standing · attacked by: skeptic (ball arithmetic), then reproduced by the director · evidence against: np.float32(21.02203941345215) → proven_sign = −1, true Z = +2.56e-7, enclosure 3.6e-46 wide excluding the truth, both backends · controls: 46 well-typed abscissae × 3 precisions × 2 backends showed 0 violations, so the hole is exactly the input path · replication: director, independently · knownness: n/a (implementation) · formal status: n/a · confidence: certain · disposition: REJECTED as stated; repaired, and the repaired contract is pinned by a regression test.

C-RIG-02 — "sign is 1/−1 proven, 0 undecided, never guessed." evidence against: an unproven Fejér cutoff leaves the unproven-steps list non-empty while sign is read off an enclosure that assumes the very step that failed · disposition: REJECTED as stated; sign is now gated on the same flag that gates positivity_proven, pinned by a regression test.

C-RIG-03 — "Two independent implementations must produce overlapping enclosures." · evidence: the two backends share _exact, the contour and subdivision policy, the grid policy, and the final interval summation of S(T)/N(T); C-RIG-01 is a live demonstration that a shared-input fault is invisible to the check · disposition: INCONCLUSIVE → narrowed. The check is real for the ζ and log Γ evaluators and does not cover the pipeline; the claim is now stated at that scope.

C-LI-01 — "The Sturm branch is exact: the polynomial converts to ℚ[X] without error." · evidence against: X² − 2X + (1+10⁻⁴⁵) returns hyperbolic=True, n_real_exact=1, agree=True at dps 15 and 20 · disposition: REJECTED; repaired (Sturm now runs on the input coefficients) and pinned by the pre-existing near-miss control, which now discriminates.

C-DET-01 — "online_list_is_complete checks the cached list against an independent count." · evidence against: the reference is the same technique on a grid 1.4×–1.8× coarser than the one that produced the list · found independently by two investigators · disposition: REJECTED; a genuinely independent strip-count route added, and the cheap route now reports independent: False in data.

C-DET-02 — "The detector quantifies the violation (1.3e-14)." · evidence against: end-to-end through the module's own pipeline the recovery error is 92.8 % · disposition: REJECTED as a headline; true only when the ordinate is supplied independently, which is now stated where the claim is made.

C-LI-02 — "li_positivity_scan reports whether λ_n is positive." · evidence against: on method="zeros" the column is structurally True for every n · disposition: REJECTED for that route (a control with no power); can_report_negative now says so in data.

C-SHIFT-01 — "Any coefficient functional is blind to the position of the critical line by construction." (docs/24 §6, hunts/README.md, localpos.py docstring and provenance_report(), CORRECTIONS.md §4) · attacked by: an explorer, then a skeptic tasked with destroying the explorer, then a prior-art search · evidence against: mis-cited (docs/18 §6 says ordinate); premise false (a_n ↦ n^δ a_n); universal refuted in-tree by criteria.py face 1 (Titchmarsh 14.25(B)/(C)) · disposition: REJECTED.

C-SHIFT-02 — c_p(ζ(·−δ)) = 2x/(1+x), x = p^{δ−½}; c_p ≤ d exactly when δ ≤ ½. · replication: recomputed by a second investigator from definitions, not importing the first's code; agreement to 1e-15 · knownness: this is the Selberg-class Euler-product axiom's θ < ½ (Conrey–Ghosh 1992) and the Jacquet–Shalika bound, stated as sharp by Sarnak · disposition: KNOWN. Correct, useful in-tree, not new.

C-SHIFT-03 — "θ(f) = abscissa of the partial sums of the coefficients of 1/f equals sup Re(zeros of f), for general f." (produced by this run) · attacked by: skeptic and knownness independently, with different counterexamples (1/(1−2·2^{-s}); exp(2^{-s})) · disposition: REJECTED — false as an equality. The ζ case (Titchmarsh 14.25) is what survives, and it needs analytic continuation plus a vertical growth bound on 1/f.

C-LOCPOS-01 — "gate reports PASS/FAIL, with the truncation bound cleared before a FAIL is spoken." · evidence against: at p = 2, δ = 0.49 the reported "bound" 2.52 understates the actual error 15.0 by 6×; the gate returns FAIL with named witness primes on δ ∈ [0.4877, 0.5] where every place satisfies the bound, and PASS above δ = 1 where c_p = +∞ · disposition: REJECTED; repaired to three regimes (summable / boundary / divergent) with the hunt's recorded verdicts unchanged.

C-WEIL-01 — W(h) ≈ 8.86e-18 for the near-tight Gaussian, enclosure ~1e-51 wide. · replication: blind — statement only, package forbidden — reproduced to 43 digits with an independently built Arb enclosure of radius 1.600e-51 · controls: prime tail beyond n_max = 2·10⁵ bounded by 3.0e-79, so the value is converged and not a truncation residue; agreement with an independently computed zero-side sum improves with precision as a real quantity must · disposition: RIGOROUSLY COMPUTED, and now independently replicated.

C-LEAN-01 — lean/ builds with zero sorrys. · replication: elan and Mathlib installed from nothing on a cold machine; 8715 jobs; every sorry string is prose about the rule · disposition: FORMALLY VERIFIED (as a build claim).

C-R3-01 — "The centre needs nExp raised, and that trade is the one genuinely unresolved thing in rung 3." (HANDOFF.md) · evidence against: the box width is bit-identical under nExp ∈ {16,20,24,28}; the floor is the κ enclosure's 6e-7 width; and the centre could not have passed at any parameters because normBound counts the inflation radius twice where the plan budgeted it once (2r_c = 7.47e-4 > ε′ = 5e-4) · disposition: REJECTED; the corrected diagnosis and a configuration with ≥1.1× margins are in docs/25 §4.3.

C-R3-02 — A plan with ≥10 % headroom exists at ~130k terms and unchanged literal sizes. · evidence: mirror measurements, margins 1.164 (centre), 1.139 (big box), ≥10× (grid cell) · caveats: 26/104 grid sites, 11/110 big boxes all on one edge, one re-planned box · disposition: EMPIRICALLY SUPPORTED, pending the low-σ edge measurement named in docs/25 §7.