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4897 bytes, as of the version from 2026-10-28 11:14 (current). Recorded here, not run.
# Numerical build evidence for T579
The governing instructions are the coordinated copies in
`agents/runs/20261028T110020Z-build-skills/manifest.json`.
Both the local and live skill SHA-256 hashes are
`e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
Build run: `20261028T110020Z`. This is builder evidence; an independent critique
is still required, and this file does not attest to that critique.
All 22 polynomials were computed in SageMath 10.9 over ZZ[t]. There are no
floating-point coefficients, numerical error estimates or precision cutoffs.
Exact integers are retained; a nominal 100-digit decimal representation would
weaken the values. The stored variable is t, with the EPW grading.
The generator groups uniform flats by cardinality and braid flats by integer
partition block sizes. Multiplicities use integer arithmetic with an asserted
zero remainder on division. Named matroids use actual flat intervals, with
Möbius functions computed by incidence recursion. No cache uses only a rank,
characteristic polynomial or Tutte polynomial as an isomorphism identifier.
Every recurrence call checks the full polynomial identity, not only the
coefficients from which its low-degree answer was recovered.
The separate checks.py computes the same outputs via the palindromicity of
Z_M(t) from Proudfoot–Xu–Young, Proposition 2.3, Corollary 2.5 and Remark 2.6.
It shares no characteristic-polynomial or Möbius arithmetic with generate.py.
Uniform and braid cases are expanded into full Sage flat lattices. Each named
case independently tests every ground-set subset for flatness by rank changes.
It performs the Z recursion on actual upper intervals, including nonsimple
contractions. This is an alternative calculation sharing the documented Sage
input matroids, not a second independently developed matroid package.
Four controls run first: the rank-four Boolean matroid has polynomial 1,
U(3,4) has 1+2t, M(K_4) has 1+t, and Fano has 1. They pass both the independent
calculation and the general generator. A deliberately changed quadratic
coefficient is rejected. All 22 independent comparisons agree exactly.
The constant term, degree bound, coefficient nonnegativity, and hyperplane
count minus rank-one-flat count formula for the linear coefficient pass on
all 22 objects. EPW Appendix A.1 gives 12 uniform comparisons with corank
1,2,3 and ranks 5 through 8; Appendix A.2 gives all three braid comparisons.
All 15 published polynomials match coefficient for coefficient.
The initial independent computations finished in about 14 seconds, including
approximately 12 seconds for M(K_8). Named examples have flat counts by rank:
- R10: 1,10,45,75,30,1.
- TicTacToe: 1,9,36,84,94,1.
- K5dual: 1,10,45,105,115,37,1.
The existing agents/table-build/dry_run.py passes with 22 exact entries and
no prose or disguised-exactness complaints. The maximum written value is
31 characters; U(8,11) is the first maximizer. The measured flat-record block
is approximately 1.3 KB (approximately 1.4 KB when the dry-run key includes
`matroid=`). Length does not justify a larger argument selection by itself.
Reproduction after downloading all five attachments:
```
sage -python checks.py
sage -python generate.py
```
The second command reads the table and compares every entry. For a private
draft, set NUMBERDB_API_KEY; for independent checks on the stored entries use
`sage -python checks.py --stored`. The builder also executes the Programs
snippet and checks its two sample calls and complete enumeration. The saved
run logs, JSON results, source downloads and post-fill checks are preserved in
`agents/runs/20261028T110020Z-build-work/` in the campaign artifact archive.
Sources checked:
- EPW, arXiv:1412.7408v3, Theorem 2.2, Propositions 2.11–2.12, sections
2.4–2.5, Appendix A.1–A.2. Downloaded PDF SHA-256:
`ad7944144ea5eb2a7a105b446634654669466ab8ed098742d35f13ba583bf755`.
- PXY, arXiv:1706.05575, Definition 2.1, Proposition 2.3, Corollary 2.5,
Remark 2.6. Downloaded PDF SHA-256:
`7ef3101be848eb1d3098ebd4389c0547f0f2754db76060481f167b0913b8e09a`.
- SageMath catalogue and database_matroids documentation for Uniform,
CompleteGraphic, R10, TicTacToe and K5dual; source hashes are recorded in
sources.json in the run evidence directory.
No arithmetic disagreement was encountered. An initial local checker run
accidentally entered its optional draft-read branch because the environment
variable held the string `0`; the branch now requires the literal `1`.
That attempt made no write and did not affect the mathematical checks.
Post-fill verification: all 22 values read back from T579 agree with the
independent Z-symmetry computation; constant terms, degree bounds and linear
coefficients pass again. Generator.verify(sample=None) reports 22/22 matched,
zero differing, zero missing and zero extra. The site audit has no findings.