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4556 bytes, as of the version from 2026-10-29 05:38 (current). Recorded here, not run.
# Build evidence for T601
Governing skill manifest:
`agents/runs/20261029T051809Z-build-skills/manifest.json`.
Both valid archived versions were read and hashed; both have SHA-256
`28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
The source snapshot's canonical skill has the same digest. Attached copies
of the manifest and per-version read record are preserved beside the generator.
## Before filling the draft
`dry_run.py` from the source snapshot, invoked through `agents/sage.sh`,
computed all 101 values. The standard exactness and named-ring checks passed;
there were no suspicious decimal values or entry-comment findings. The
longest written fraction is 240 characters, at n=100. The standard block
measurement is 15.173828125 KiB. These measurements support the finite range
chosen in argument-selection.md; no range change was needed.
The attached `checks.py` was run, not just inspected. Its first control counts
all four-step square-lattice walks directly and finds 36 returns among 256
paths; a separate dynamic-programming control gives return counts 1, 4, 36
at times 0, 2, 4. A deliberately false equality and a floating-point value
are rejected by the standard checking helpers.
For every n=0,...,100, the generator's exact QQ recurrence equals a sum using
Python's integer binomial coefficients. Separately, a dynamic program counts
every lattice walk by its current endpoint through 200 steps. It checks the
total count 4^t at every time t and the absence of odd-time returns. Partial
sums of its exact return probabilities agree with all 101 generated values.
The coordinate transformation (x,y) -> (x+y,x-y) proves the connection:
a closed walk of length 2k corresponds to two independent balanced sign
sequences, so its count is binomial(2k,k)^2. The checker does not use that
closed count to generate the walks.
The denominator-cleared three-term recurrence passes for all 99 interior
indices n=1,...,99; all 100 successive increments are positive and the
increments decrease. Every fraction is reduced with positive denominator.
The initial controls are G_0=1, G_1=5/4, G_2=89/64, G_3=381/256.
There is no numerical error or decimal precision claim: all values are exact.
The initial check run took 4.928 seconds after import (numberdb 0.1.10).
The mathematical source checks were section 1 and equation (1.1) of Li,
Liu, Xu and Zhao (arXiv:1309.4564v2), and section 1 and equation (1.1) of
Chen and Choi's public RGMIA manuscript v17a09. They agree on the domain,
indexing, central-binomial formula, and sharpness. The transition from
pointwise |f|<1 to supremum norm <=1 is explained in argument-selection.md.
The recurrence follows by taking the ratio of successive summands; it was
then checked over the whole stored range before inclusion in the document.
## Reproduction and remaining independent review
Download generate.py, checks.py and check.py together. Run
`sage -python checks.py` for the exact checks without API access, and
`sage -python checks.py --stored` to repeat the identities and independent
walk comparison on the database values (a key is needed while private).
Run `sage -python generate.py` for the client's exhaustive verify().
The build handoff retains actual readback and audit results separately.
This is evidence from the builder; a separate critique still has to assess
both the mathematics and argument selection. No draft offer, review or
publication action is performed by the builder.
## Stored values and site audit
The draft was filled once with all 101 exact fractions. With Sage 10.9 and
numberdb 0.1.10, `verify(sample=None)` reports 101/101 matched, zero differing,
zero missing and zero extra. The independent lattice-walk comparison,
closed-binomial sum, recurrence, monotonicity and canonical reduced-fraction
checks all pass on all applicable values read back from T601. The successful
readback run took 4.904 seconds after import; `checks-stored.json` records it.
The site audit returned `findings: []` and `clean: true`.
The first readback run encountered a checker-only Sage initialization error:
`QQ(raw)` attempted to access `sage.rings.real_mpfr`, which was not initialized.
The checker now constructs the rational from parsed Python integers and QQ
arithmetic. The corrected checker ran successfully over the entire stored
range. No number, parameter, formula, or selected index changed. The final
source hashes, including this corrected checker, are recorded by the build
fingerprint; a later independent critique must fingerprint the live files.