{
  "tid": "T200",
  "before_count": 8,
  "after_count": 49,
  "baseline_revision": "eb4365b54aeeb95f88424a61a52fc9e3fd255a48b9cc97895420028d51ae3fd5",
  "baseline_stale": false,
  "selection": {
    "complete_note": "it retains all earlier anchors and includes $W_0(-ne^{-n})$ for $2\\leq n\\leq12$ and $n=7/2,9/2$; the hypergraph lower-branch arguments for $3\\leq k\\leq13$; the exploratory inverse inputs $1/2,1,2,\\ldots,8$ on $W_0$ and $-1/m$ for $3\\leq m\\leq8$ on both real branches",
    "comment": "The spectral family uses the nonzero maximum of $x^n/(e^x-1)$, whose location is $n+W_0(-ne^{-n})$; the linear-frequency and linear-wavelength cases are $n=3,5$, and the half-integer cases occur in CITE{WienPeaks}. The integer prefix through $12$ is a bounded reference extension, not a claim that each exponent has a separate standard physical convention. For $k$-uniform hypergraphs set $u=k-1$; differentiating the minimisation in CITE{CoreGeometry}, equation (1), gives $e^\\lambda-1=u\\lambda$, hence $\\lambda=-W_{-1}(-e^{-1/u}/u)-1/u$. This Lambert form is our derivation. The cutoff $k=13$ is practical. The positive and negative simple-input slices are exploratory references for small-coefficient inverse equations; no individual application is asserted for each. Only $0,e,-1/e$ are used as exact inverse anchors; identities giving arbitrary rational outputs are not added.",
    "sources": [
      "https://dlmf.nist.gov/4.13",
      "https://doi.org/10.1590/S1806-11172011000300008",
      "https://www.cs.toronto.edu/~molloy/webpapers/xorrsarevised.pdf"
    ],
    "families": [
      "intrinsic origin, omega and branch-point anchors",
      "spectral maxima, including documented half-integer dispersion exponents",
      "integer hypergraph edge sizes",
      "bounded exploratory positive inverse and two-real-branch negative inputs"
    ]
  },
  "policy_sha256": "e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c",
  "sources_preserved": {
    "checks-evidence.json": "68ce5495cde421b9a27b8a958a252edf1c95942d4ec20201a439a9404fd650f6",
    "generate.py": "ce93a54b012afa70a349be9ebb0667d1555a10c3406a14ce0b86c78d82670590",
    "relevance-audit.json": "2b69c67621182835997058b7631e9266ba45bc227bbb005e8a8971574c8ac47a",
    "republish.py": "20d5d23f80895adc6629e61126d165364199b100a5956d234b152de8e34af0b3",
    "t200_checks.py": "f4f4a683036f83697884200b6ad868cdb8657eb23e1a28f1aa71c12742f550ae",
    "t200_values.py": "2542ab30a43387b72858c715a0e36d1a9f32637f22507fcf7afe3bafbb15e290"
  },
  "new_generator_provenance": "Extends the attached certified elementary/delay approach; all retained strings remain unchanged and are recomputed, new values are separately checked.",
  "removed_entries": [],
  "assistance": "codex-cli selected families, implemented generator and performed numerical checks"
}