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5578 bytes, as of the version from 2026-10-28 08:03 (current). Recorded here, not run.
{
"table": "T575",
"builder_run": "20261028T074202Z",
"family": 228,
"proposal": "Jack polynomials",
"state": "unpublished draft, not offered by builder",
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"schur_specialization": 34,
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"final_audit": {
"tid": "T575",
"title": "Jack polynomials",
"findings": [],
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"boundary_checks": "J_empty=1 and J_1=sum x_i for n=1..4; one-variable rows of degree 2..5 agree with x1^d product_(j=0)^(d-1)(1+j*a).",
"independent_operator": "D=a*sum_i x_i^2*d_i^2+2*sum_(i<j)(x_i^2*d_i-x_j^2*d_j)/(x_i-x_j). Checked D J_lambda = (a*sum_i lambda_i*(lambda_i-1)+2*sum_i(n-i)*lambda_i) J_lambda exactly, with i starting at 1. Eigenvalues are pairwise distinct over Q(a) within every selected n,weight block.",
"operator_source": "Jiang and Wang, Statistical Properties of Eigenvalues of Laplace-Beltrami Operators, equations (1.1)-(1.3); the checked operator is twice theirs.",
"normalization_sources": [
"Nakajima, section 2(i), Theorem 2.3 and equation (2.4)",
"Stanley (1989), Theorem 1.1, Proposition 1.2 and Proposition 2.2",
"SageMath reference: Jack J, Jack P and c1"
],
"proposal_adjustments": [
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"Use the supported wire variable a to denote formal alpha; no numerical alpha selection."
],
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"exactness": "pass",
"prose": "pass",
"readability_warning": "1412-character maximum is above the usual 1100-1300 guideline. Rationale for retaining the complete four-variable degree-4 slice is in argument-selection.md."
},
"independent_critique": "Pending. This build supplies no acceptance sidecar. The separate critique must validate the range, the documented spelling convention, and every selection-relevant live attachment.",
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