{
 "id": "LIB2-309",
 "entry_version": 7,
 "class": "OPEN",
 "title": "Derive one source law for the real ladder step and compact phase",
 "statement": "Can one source law fix both a real ladder step and a nonzero commuting compact phase without choosing the angle after comparison?",
 "scope": {
  "carrier": "The real ladder scaling and a commuting compact datum",
  "domain": "The unselected joint scaling/phase law on the registered carriers, not an abstract existence claim for compact subalgebras.",
  "group": null,
  "hypotheses": [],
  "physical_target": null,
  "quantifier": null,
  "real_form": null
 },
 "source_labels_as_printed": {
  "math_status": null,
  "attachment": null,
  "scorecard_tier_word": null,
  "pdf_page": null
 },
 "house_tier": null,
 "review_state": "IN_REVIEW",
 "scientific_status": "OPEN",
 "evidence_status": [
  {
   "kind": "registry",
   "availability": "shipped"
  }
 ],
 "primary_source": {
  "component": "Appendix N",
  "section": "Part N.E, Typed missing complex-ratio operator",
  "pdf_page": 270,
  "quote": "The missing object is typed: QL = SL eαJL with (JL |E )2 = −IE and [JL |E , SL |E ] = 0 on the ladder two-plane E, with E and its orientation named by the registering datum (as the antecedent D1247 states the target “on the ladder 2-plane”), and one source law fixing both the real rung step and a nonzero α; installing JL , choosing the angle, or selecting after comparison does not qualify."
 },
 "caution": "Compact subalgebra existence and a shared spectral number do not supply a selected phase-bearing ladder operator.",
 "candidate_ids": [
  "C2-104"
 ],
 "basis": {
  "pdf_sha256_prefix": "b64ddcd9e16a6dcd",
  "release": "Rev33.1_S369"
 },
 "relationships": [
  {
   "type": "related_to",
   "target": "LIB2-015"
  },
  {
   "type": "related_to",
   "target": "LIB2-101"
  },
  {
   "type": "related_to",
   "target": "LIB2-102"
  },
  {
   "type": "related_to",
   "target": "LIB2-103"
  }
 ],
 "url": "/library-v2/LIB2-309/",
 "content_sha256": "6770e7674e88db3e39f87cf0f21d9d5f4f7e5ae2eca50125edcd3936d8c41efe",
 "build_stamp": "BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02"
}