T463 repair, 2026-10-16: the single critique finding is correct. The live comment still left the two genus-one integrals unnamed. The repair specifies the one-point integrals of psi_1 and lambda_1 over the stable-curve stack Mbar_(1,1), links T458 entry (1,1,1) and T462 entry (1,1,0), and retains the generic elliptic-involution weight. No stored Hurwitz number or parameter is changed.

The companion tables' freshly fetched definitions and parameter orders identify precisely these integrals; both entries equal 1/24. Vakil, arXiv:math/0602347v2, gives the cotangent normalization through a cubic pencil and the automorphism weight, and also states the lambda_1 integral. Macaulay2's HodgeIntegrals documentation independently prints both values:

- https://arxiv.org/html/math/0602347v2
- https://macaulay2.com/doc/Macaulay2/share/doc/Macaulay2/HodgeIntegrals/html/_witten__Tau.html
- https://macaulay2.com/doc/Macaulay2/share/doc/Macaulay2/HodgeIntegrals/html/_integral.html

The attached repair-check-genus-one.py uses exact Sage rational arithmetic to check the two API entries, the genus-one Bernoulli formula, the stack-weight normalization, and the ELSV specialization on all ten genus-one one-part profiles in T463. Known-answer controls pass; removing the involution weight fails the comparisons as intended. This verifies the arithmetic, while the cited sources justify the geometric identities. repair-inputs.json contains the exact API excerpts and hashes of the full snapshots; repair-genus-one-checks.json records the successful results. Run with `sage -python repair-check-genus-one.py` beside repair-inputs.json, after installing numberdb. The existing generate.py and earlier checks remain attached unchanged.

The direct draft page /T463 returned 404; the authenticated document and audit APIs were accessible. The site's read-only preview renderer accepted the complete changed paragraph, with its citation and a representative table entry. Its generated HTML links the integral labels to T458?entry=1,1,1 and T462?entry=1,1,0. This is a paragraph-rendering check, not a complete authenticated-page inspection.