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3238 bytes, as of the version from 2026-10-25 06:26 (current). Recorded here, not run.
# T475 repair evidence, 2026-10-25
The live API document was fetched again before repair. All three findings in
the separate critique still applied. Six numbers and their uncertainties,
parameter order, title and coverage were preserved.
1. The computational provenance supports `assumed-bound`, with the assumptions
stated explicitly. The O(2) source uses the outer hull of excluded points
near the sampled boundary, and assumes this contains the physical solution
([section 4.2, equations (40)-(42)](https://arxiv.org/pdf/1912.03324)). The O(3)
source uses the same construction ([section 4.1, equations (21)-(23)](https://arxiv.org/pdf/2011.14647)).
Appendix B of each paper specifies finite precision, conformal-block
approximation settings and finite spin sets. This repair adopts the quoted
conditional bounds; it does not certify the bootstrap optimization.
2. The two-point relation was moved to Formulas. Internal O(N) invariance gives
the Kronecker tensor, and the scalar scaling dimension gives the power
2 Delta_phi. The identity 1+eta = 2 Delta_phi was checked in Sage.
3. Griffiths now names the Rushbrooke and Widom relations. With each relation
written as its left side minus its right side, Sage verifies
Griffiths = Rushbrooke - Widom as a polynomial identity.
`repair_checks.py` independently parses the six parenthetical uncertainties
from the source equations and compares exact rational endpoints against the
API values. All six match. It verifies the two identities described here,
all five displayed scaling identities as rational functions, and 108 exact
substitution equalities across the corners, edge midpoints and centre of
each class's dimension rectangle. Known-answer parsing controls pass. The
corrected generator's `verify(sample=None)` reports six matches with no
missing, extra or differing entries. These are transcription and algebra
checks, not a new bootstrap or Monte Carlo computation.
Run the supplemental checks with SageMath and the NumberDB Python package:
```
sage -python repair_checks.py --stored < key-file
```
The key must be authorized to read the private draft. Alternatively pass an
API document JSON filename to check a saved snapshot. The run used Sage 10.9.
The generator and source notes now use the same `assumed-bound` classification.
The full private page returned HTTP 404. Five read-only previews of the edited
sections and their context were rendered by the deployed site, then inspected
in Chromium using the site's MathJax: 116 math containers, no math errors,
page-script errors or parsing alerts. The formulas, remaining exponent comment
and new rigour paragraph were also read in screenshots. This checks edited
sections, not the full authenticated page layout.
The pre-repair audit's two structural warnings describe the class and operator
parameters as possible separate tables. The class indexes the O(N) family;
the operator selects a component of its spectrum. Both axes index the object
whose scaling dimension is stored. The definition states this interpretation,
and the value header is Delta_O, so neither warning justifies splitting.
No publication, offering for review or human review action is part of this repair.