{
  "source_repository_path": "shifted-even-beta/review/independent-audit-2026-11-06.txt",
  "text": "INDEPENDENT AUDIT REPORT FOR THE V2 ARGUMENT\nReceived 6 November 2026\n\nAuditor identity/model and a separate audit date were not supplied.\nThe report below is reproduced from the user with line wrapping and\nlocal-file references normalized. Section and line references refer to\nthe audited plain-text proof, whose full hash and scope are recorded in\nindependent-audit-2026-11-06.json. They are not references to the PDF.\n\n--- Begin supplied report ---\n\nI found no substantive gap in the general proof, and independently\nreproduced all the recorded exact certificates. Theorems A and B pass\nthis audit.\n\nI did not run or import the supplied checkers. I inspected their source\nto identify the advertised coverage, then derived fresh calculations\nfrom the mathematical definitions.\n\nThe general argument checks out:\n\n• Gram construction: the differentiated kernel, clockwise-contour sign,\n  cancellation at the central zero, and positive weight are consistent.\n  The largest-distance pole establishes kernel independence, so the seed\n  matrix is nonsingular. §2, proof.txt:151.\n\n• Denominator clearing: the grouped cancellation works for rational grid\n  points, including primes dividing the grid denominator. It establishes\n  the required exponent δₙᵃ⁺ᵏ. §3, proof.txt:265.\n\n• Decay: the Stirling estimate remains valid as t/n→0; the Cauchy circles\n  are safe; the separate tail estimate handles unbounded t/n. The\n  stationary-point calculation and criterion U<1 are correct.\n  §4, proof.txt:315.\n\n• Prime dilation and elimination: the two Wilson signs cancel, the\n  surviving constant acquires exactly χ(p), and the exponent is correctly\n  τ=a-E+k. The nonzero last Vandermonde minor preserves the seed after\n  eliminating any B-1 possible irrational values. The resulting integer\n  contradiction is valid. §5, proof.txt:384.\n\nThe independent finite calculations reproduced:\n\n• All 8,909 recorded structural checks, with every category count\n  matching—including all 49 Gram entries, 4,516 grouped-integrality\n  checks, 404 selected-pole congruences, and 19 constant congruences.\n• All 21 endpoint certificates, using exact rational enclosures for\n  logarithms.\n• All six uniform parameter records, the uniform inequalities, and all\n  seven integer-r exclusions.\n\nFor independence, I reconstructed kernels by rational interpolation\nfrom direct kernel evaluations, extracted pole coefficients using a\nlogarithmic-derivative Taylor recurrence, and evaluated Gram integrals\nthrough a separate moment recurrence.\n\nThe tightest listed endpoint certificate also passes:\nB=10, m=3, a=8382, U≈0.991303468061.\nI separately reproduced the numerical limiting endpoint multiplier\n18.5722528999226532907….\n\nFor human readability, I recommend adding a worked B=2,m=1 Gram example\nand spelling out the coefficient scaling between (5.2) and (5.3).\nThese are exposition improvements; I found no mathematical repair\nnecessary.\n\nThe audited proof has SHA-256 beginning 603211b50609dc4a.\n\n--- End supplied report ---\n\nThe two exposition recommendations are incorporated in the subsequent\nv2 manuscript. The worked example has an additional exact self-check,\nrecorded in checks/worked_example.json. This is not an extension of the\nindependent audit. The report is a mathematical audit, not formal\nverification or a certification of priority. The typeset assembly and\nits review are recorded separately in review/assembly-review.json.\n"
}