T693 Programs repair, 9 November 2026

The sole optional finding in agents/critiques/T693.md still applied to the
live draft. The Programs example now sets ell = 61 and prints one coefficient
using the existing attached generate.py. Both the old and revised examples
were executed in Sage 10.9 with numberdb 0.1.10. The new result has 521 relative
accuracy bits and contains the 800-bit recomputation (796 accuracy bits).
All 61 existing values were checked at 800 bits against their exact recorded
last-place intervals; order zero remains exact. This check uses the existing
polynomial algorithm, not an independent derivation or a replacement critique.
Arb propagates uncertainty in pi through each polynomial evaluation.

Only Programs changed in the document. The selected orders, mathematical
normalization, values, completeness note and generate.py bytes are unchanged.
No value at order 61 was added. This example illustrates extension, while the
generator's default enumeration remains the full stored prefix 0 through 60.

The campaign fingerprint includes Programs, so a fresh independent critique
is required. The original independent T693-arguments.json was not changed.
The controller should retain this same draft T693. No offer, publication or
human review action was performed.

Reproduce the repair checks by downloading generate.py, repair_check.py,
program-example.py and document-before.json to one directory, then running:

    sage -python repair_check.py

The attached repair-check-results.json contains the successful output.
The first check attempt used a nonexistent RealBall.contains method; the
successful check converts existing rigorous balls to 1000-bit intervals and
compares their endpoints. The failed script and output are retained in the
run artifacts. This was a checker error, not a discrepancy in a table value.

Instruction provenance: agents/runs/20261109T161456Z-repair-skills/manifest.json
Manifest SHA-256: c879ba3e40020535135932a0ac7d93e894d04b267cf416aa702c3c96617ec363
Archived local and live skill SHA-256, each:
886390324dd1971e381a43cf3b46b822ab0bc67d62f31d8481e29ec79556746b
Both archives match the canonical skill in this source snapshot.
The attached instruction-provenance.json records each version separately.