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6412 bytes, as of the version from 2026-10-28 10:24 (current). Recorded here, not run.
# T578 build evidence
T578, Macdonald polynomials, was created as an empty private draft and filled
once with 14 exact integral-form polynomials. The final audit is clean.
It has not been offered, reviewed or published by this build.
## Governing instructions
The source and live skill archives were read before computation and agree.
The authoritative run manifest is
`/home/ubuntu/numberdb-campaign-20261026-hundred/repo-balanced-coverage/agents/runs/20261028T101159Z-build-skills/manifest.json`.
Both archived skill files have SHA-256
`e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
`skill-manifest.json` is an attached copy; `skill-evidence.json` records the
original path. This build did not combine different policy versions.
## Corpus and convention checks
`corpus-screen.json` records `already_here`, `already_asked`, six text
searches, the existing tags, and three exact polynomial `api/lookup` calls.
The polynomial queries returned no matches. The Macdonald matches were
Macdonald–Kostka coefficients (T260), Hall–Littlewood P (T261), and an unrelated
Bessel function name. The closed family issue #140 did not contain a J table;
its text is in `family-140.txt`. T260's definition explicitly concerns Schur
coefficients of modified H-tilde. This table stores expanded symmetric J.
The actual returned slugs were used for all corpus links. No new tag was made.
The normalization, scalar product, arm/leg coordinates, partition order and
alphabet conventions were fixed in `definition.md` before computation. The
family issue #228 specified J; there was no unresolved normalization choice.
Haiman Section 2 supplies triangularity (2.9), the integral form (2.16), and
the finite-variable difference-operator derivation on p. 8. Sage's J()
documentation specifies the integral form and determinantal implementation.
Downloaded sources and their SHA-256 records are in `sources.json`.
## Generation and measurement
All Sage work ran through `agents/sage.sh`, in its isolated computation
environment. Versions: SageMath 10.9, numberdb 0.1.10. No decimal approximation
is involved: coefficients are exact Sage integers. Gram–Schmidt operates over
QQ(q,t), and the completed expansion must coerce to ZZ[x1,...,xn,q,t].
`measure-proposal.log` and `proposal-values.json` retain the 26 polynomials
measured across n=2,3,4 and degrees 2,3,4, including every rejected slice.
`argument-selection.md` explains the decision to keep complete slices
(n=2,d=2..4), (n=3,d=2..3), and (n=4,d=2). The selected table has 14 entries,
with a maximum of six polynomial variables and longest value 1916 characters.
The diagnostic serialized block is 8.474 KiB. The script's advisory warning
at 1300 characters was considered explicitly, not ignored or treated as a hard
mathematical cutoff. The 1906- and 1916-character slices retain useful shape
and alphabet breadth; the excluded slices reach 7185 and 4198 characters.
## Checks actually run
`preflight.py` invokes the repository's unmodified `dry_run.main`, then the
attached `checks.py`. `preflight.log` and `preflight-result.json` record:
- Exactness, named ring imports and no approximate values disguised as exact.
- All 14 identities enumerated independently with Sage's Partitions routine,
in the intended order, against the generator's default enumeration.
- All 14 coefficients/expansions agree exactly with Sage's independent
Macdonald J implementation (determinantal formulas).
- All 14 satisfy the q-difference eigenidentity after multiplication by the
Vandermonde, checked as a zero polynomial. This computation does not use
the generator's scalar-product, inclusion–exclusion or Gram–Schmidt code.
- Controls first: D(1), D(p1), the Schur linear polynomial and e2 give their
known answers. A deliberately incorrect quadratic fails the eigenidentity.
- All 14 satisfy alphabet homogeneity, permutation symmetry, dominance
support and the integral leading coefficient.
- All 14 q=t specializations match independent alternant Schur polynomials
and the corresponding stored T122 values.
- All 14 q=0 specializations match stored T261 values multiplied by the
Hall–Littlewood normalization b_lambda(t).
- All 14 pass alphabet stability, including the zero case for full length.
- The four retained column shapes satisfy the elementary-polynomial formula.
- Omitted degree-0 and degree-1 formulas are checked for n=1..4; one-variable
row formulas are checked for degrees 1..4.
- The Programs snippet was executed successfully (`program.log`).
The two archived corpus documents used for comparison are attached as
`T122.json` and `T261.json`. Their SHA-256 values are bound by the fingerprint.
## Stored values and audit
`readback.py` calls `MacdonaldPolynomials().verify(sample=None)` against the
authenticated draft, then runs every check on the actual stored polynomials.
`readback.log` records 14/14 matched, zero differing, zero missing and zero
extra. All independent tests passed again (`readback-result.json`). The
stored document and entries are preserved as separate JSON artifacts.
The first audit found only a missing package-installation command in the
generator docstring. Adding `sage -pip install numberdb` repaired it without
changing any computation. `audit-first.json` preserves the finding;
`audit-final.json` is `clean: true` with an empty findings list. The final
source attachment, including that documentation correction, is fingerprinted.
`publication-check.json` confirms that an unauthenticated API request cannot
read the draft. No offer, publish or human-review endpoint was called.
## Fingerprint and remaining independent work
`selection-fingerprint.json` was produced by the repository command
`agents/argument_review.py fingerprint`, not by an invented hash algorithm.
It binds the live selection and the attached generator, checks, check helper,
argument-selection justification, skill manifest and corpus snapshots.
Selection SHA-256:
`88c6cda3ad8c16d702446212300e4a42c6e3e228b50edfb0a1a6343650ebba06`.
This is build evidence, not the required independent critique. The critic must
independently assess both the exact polynomials and the argument selection,
including the deliberate 1916-character upper extent. It must obtain current
fingerprints and write its own -arguments.json with its own reviewer_run.
The build has not authored or accepted such a sidecar.