{
  "table": "T575",
  "builder_run": "20261028T074202Z",
  "family": 228,
  "proposal": "Jack polynomials",
  "state": "unpublished draft, not offered by builder",
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  "final_audit": {
    "tid": "T575",
    "title": "Jack polynomials",
    "findings": [],
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    "selection_sha256": "5e28338808e18e90e43477c0b7a9aabfd5f2af62f24c5ec457d1e107f6e3fff8",
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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": [
    "Omit the complete n=4, degree-5 slice after measuring its maximum at 3341 characters; final maximum 1412 characters.",
    "Use the supported wire variable a to denote formal alpha; no numerical alpha selection."
  ],
  "dry_run": {
    "exit_code": 0,
    "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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      "unavailable": "HTTPError"
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