{
 "id": "LIB2-087",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "Schur block structure does not force a zero triplet eigenvalue",
 "statement": "Schur symmetry supplies singlet–triplet block separation and scalar action λI on each irreducible triplet block, but does not force λ = 0.",
 "scope": {
  "carrier": "The representation-level Coleman–Weinberg Hessian at the registered vacuum",
  "domain": "The distinction between a permitted scalar block and a numerically vanishing eigenvalue.",
  "group": "The source’s G2 representation decomposition",
  "hypotheses": [
   "Use the invariant block decomposition described in Appendix A §A.7.5."
  ],
  "physical_target": null,
  "quantifier": "What follows from the stated representation symmetry alone.",
  "real_form": null
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 146
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "analytic",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Appendix A",
  "section": "§A.7.5, Rev32.1 Schur correction",
  "pdf_page": 151,
  "quote": "Schur’s lemma ensures the block structure at the algebraic representation level — no singlet–triplet mixing, and scalar action λI on each irreducible triplet block; it does not by itself force λ = 0"
 },
 "caution": "This correction neither reproduces the separate numerical zeros nor provides an all-orders protection theorem.",
 "candidate_ids": [
  "C2-114"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [],
 "url": "/library-v2/LIB2-087/",
 "content_sha256": "bae9a64d75a3e506d792063cb269fbcc83de16a2005980ea8284e03ca9fde6fb",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}