{
 "id": "LIB2-052",
 "entry_version": 8,
 "class": "CLAIM",
 "title": "The fixed Peirce sector has the registered unique invariant generator",
 "statement": "Within the registered (1,3) Peirce-sector construction of f4(4), Thalf is, up to scale, the unique G2(2)-invariant generator; the scale is fixed by the normalisation Thalf = Tscalar + ½Toct.",
 "scope": {
  "carrier": "The registered (1,3) Peirce-sector generator",
  "domain": "The internal generator construction.",
  "group": "G2(2)",
  "hypotheses": [
   "The (1,3) sector and the registered Thalf normalization are fixed."
  ],
  "physical_target": null,
  "quantifier": "The registered construction only.",
  "real_form": "f4(4)"
 },
 "source_labels_as_printed": {
  "math_status": "NOT_PRINTED",
  "attachment": "NOT_PRINTED",
  "scorecard_tier_word": null,
  "pdf_page": 153
 },
 "house_tier": null,
 "review_state": "PUBLISHED",
 "scientific_status": "UNDER_REVIEW (house status not yet adjudicated)",
 "evidence_status": [
  {
   "kind": "registry",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Appendix B",
  "section": "§B.5, Structural support (c): generator uniqueness",
  "pdf_page": 159,
  "quote": "Thalf is, up to scale, the unique G2(2) -invariant generator in the (1, 3) Peirce sector of f4(4) ; the scale is the normalisation Thalf = Tscalar + 12 Toct of the item above (Rev32.9)."
 },
 "caution": "Sector-relative uniqueness does not select the sector itself or prove the physical phase attachment.",
 "candidate_ids": [
  "C2-158"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-051"
  },
  {
   "type": "cited_by_section",
   "target": "E-C05.1.claims-used"
  },
  {
   "type": "cited_by_section",
   "target": "E-C05.1.derivation"
  },
  {
   "type": "cited_by_section",
   "target": "E-C05.1.prior-art"
  }
 ],
 "url": "/library-v2/LIB2-052/",
 "content_sha256": "8b9ff2be1bb2157b24b7fa761901c94c33d2b0f1756ed498e3f99ee225d26410",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}