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5724 bytes, as of the version from 2026-11-02 11:01 (current). Recorded here, not run.
# T649 repair evidence
Run: 20261101T112456Z. The repaired object is the existing private draft T649, not a replacement. The two findings in agents/critiques/T649.md were both present in a new authenticated document read and a live Chromium render. The unauthenticated document response says the table does not exist, confirming private visibility before the write. Changes were sent as zeta3 through PUT /api/table/T649; the response records reviewed=false. No offer, publication or review action was performed.
## Governing skill and preserved independent evidence
Manifest: agents/runs/20261101T112456Z-repair-skills/manifest.json. Both archived versions were read and hash-checked; their bytes match the canonical source snapshot.
- Local SHA-256: a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278.
- Live SHA-256: a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278.
The original independent sidecar agents/critiques/T649-arguments.json was not edited or accepted by this repair. Its SHA-256 remains db5ae08078333c64eab385682966b01c2b94456be9307f593e688a3d4c0588b3. This record is repair evidence, not an independent argument-selection verdict.
## Program correction and actual checks
The former example calls value(), whose BY_KEY lookup admits only the generator catalogue. The replacement standalone-program.py accepts a supplied real argument and implements the existing quadratic Jensen integral with the real cube root. It recomputes callable arguments at each precision, avoiding a pre-rounded radical input. Floating quadrature and precision agreement remain heuristic; no interval certification is claimed.
The formula and breakpoint were checked against Samart, arXiv:2301.05390v3, introduction, Lemma 3, equation (2.1), and Proposition 4: https://arxiv.org/html/2301.05390v3 . Substitution y=exp(i*theta/2)*u in the quadratic gives u^2-2*z*u+1=0, where z=(k*exp(i*theta/2)-exp(3*i*theta/2))/2. The roots are exp(plus-or-minus acosh(z)), so the logarithm of the larger modulus is abs(Re(acosh(z))). The interior torus crossing is theta=acos((k-1)/2), with endpoints 0 and pi also included. Adaptive bisection checks estimated quadrature convergence on each subinterval.
The script repair_checks.py was run using agents/sage.sh, with the website's attached generate.py and checks.py as unchanged dependencies. It tested 11 inputs at 140 and 190 working digits: 0, -1, 27, 24, -216, 54, -13500000+1431000*sqrt(89), -8, 1, 8, 125. Minimum observed precision agreement was 136.04143458776056 decimal digits, scaled by max(1,abs(value)). Seven stored entries were compared with their full last-place intervals; the largest midpoint distance was 0.3495686579166958 units in the last place.
The nonzero N(0) control used the independent Hurwitz-zeta expression for L(2,chi_-3); N(27)=3N(0) was also checked. Both controls agreed beyond 191 digits. The four arguments outside the catalogue (-8, 1, 8, 125) were checked against the separate original-cubic Jensen implementation in the existing attached checks.py; minimum agreement was 124.88050653449801 digits. The two exterior cases additionally passed its hypergeometric check. These tests exercise the snippet, not a fresh independent critique of all 36 table values.
Visible code comments were added after the test matrix; the executable AST is identical, recorded in numerical-summary.json. The final standalone-program.py was itself executed with agents/sage.sh and printed exactly the stored 100-digit N(24) string. Both tested source versions and their hashes are retained. Sage 10.9, Python 3.12.3, mpmath 1.4.1; browser Chromium 156.0.8078.4.
## Link correction and audit
Explicit captions replace machine-address text in formula-cm, comment-4 and the zero-entry comment. Fresh reads of T129 and T283 confirmed the target families and T283's entry 3. Link destinations were preserved. The definition, parameter declarations, complete-note, all 36 ordered identities, all numeric strings and all radical labels are unchanged.
A new live render contains 93 math containers, zero MathJax errors and zero page JavaScript errors. All three captions render correctly and the standalone code is present. The final API audit equals the initial audit exactly: its only warning concerns 30 numeric parameters with param-latex. Those are exact radical argument identities expressly permitted by the archived skill; they were retained. No introduced audit finding remains.
## Controller handoff
Fresh independent critique is required on this same T649 draft. Programs and link annotations participate in the version-1 fingerprint even though no selected argument or mathematical definition changed. The old selection hash is 6ea337a5d24b17dcc43402c0584cc9bdfd891b186712a27cbcf6e7e8aaa682d1; the repaired document hash is f9db82a00c69d2a7f0e9ba06ac48404a204e800f3e5abf2e9ec0356403cac79a. Do not update the old sidecar.
Reviewed generator bytes were preserved: generate.py SHA-256 bb666d38c350ff0e622548fcc60de1e587b13ada8559133a37548e1b92d4301f; argument-selection.md SHA-256 ba54c13ab8906d7f82a678f82fe270f6ef19e890b7401c40b105dec5b7db86cf. The generator still has its historical zero-entry caption text; it was not rewritten for presentation-only cleanup. Its enumeration and values remain valid and unchanged.
The work directory is agents/runs/20261101T112456Z-repair-work. It preserves the live documents, printed diff, source downloads, exact test commands/scripts, numerical output, API result, before/after audits, browser output and screenshots. Main document write revision: 6b136bf62c346911d2cec6a025c14dd9d09ae070694581bdab1dffaf5bbed3f8. Subsequent API attachments preserve all prior attachments and revisions.