Premises · PRM-024
Route B golden-unit restriction (positive algebraic integers in Q(√5), abc = 1)
What this surface is. A register of the premises this programme has DECLARED — postulates, adopted premises, measured inputs, conventions, loaded correspondences, fences and open requirements. Every statement is quoted from its source — verbatim from the sealed text, or transcribed by the house from the TeX where the extraction was damaged, as each page's statement-quality row says — and carries that source's locator. No premise on this page has been adjudicated by the house, and none is defended here. A premise is what an argument RESTS ON, not what it establishes.
As printed
Let Jvac = diag(a, b, c) with a, b, c > 0 algebraic integers in ℚ(√5) and abc = 1.
Register corrected (R81, D20, S327j). The PI ruled a correction to this row. Until then it read: statement “Let Jvac = diag(a, b, c) with a, b, c > 0 algebraic integers in Q( 5) and abc = 1.”. Paper 2:521-527 restates the restriction without "positive"; App E:117 controls. Nothing is overwritten (R29): the earlier row is kept in the register’s history.
Provenance
| kind | ADOPTED_PREMISE |
|---|---|
| source | the sealed suite, PDF p.171 (search that part for “===== PDF PAGE 171 /”) · the sealed PDF |
| basis | Rev33.1_S369 · PDF sha b64ddcd9e16a6dcd… |
| statement quality | HOUSE_TRANSCRIBED — transcribed by the house from the TeX at the locator, not the PDF’s extraction text (R81) |
| review state | DRAFTED — not adjudicated by the house |
| first seen | S312 · 2026-09-06T21:57Z |
Claims declared to rest on this premise (2)
| record | title | why the house declared it |
|---|---|---|
| LIB2-001 | Route-B admissible-gap classification | Proposed by the drafting lane (A1634): The gap-pair classification uses exponent triples obtained from this positive golden-unit domain. Its zero-sum exponent condition comes from abc=1; the field restriction supplies the unit-power reduction. — House reading: House read App E:117–124: the classification is stated for positive golden-field units with abc = 1 (the premise's exact domain); the unit-power reduction a = φ^n uses it. The premise is a hypothesis of the result. |
| LIB2-020 | Route B selects the positive golden-unit triple under DET-7 | Route B instead restricts to positive golden units in Q(sqrt 5) with abc = 1 (H0 is bundled into PRM-024/r1). Route A uses no number-field restriction (the record says so in its own domain field). The two are separate sufficient hypothesis sets: conjoining them would narrow the domain needlessly and misstate which conditions each route needs, and no combination licenses dropping both distinguishing assumptions. [R129 D-5, S340: "unioning the two bundles would assert a theorem domain neither route proves" re-worded per A1704 F2b] |
Claims reaching it transitively (2)
LIB2-001, LIB2-020
Premise note
Where the suite invokes this premise, in what role, and what rests on it: the premise note (drafted by the ChatGPT drafting lane, verified by the house, R76/R78/R81).
Generated from library_v2.jsonl + PRM_REGISTER_S312.jsonl. Declared volatile fields (R36): BUILD_STAMP.
BUILD_STAMP S371a · 2026-09-26 22:53Z · cut 9dcc6ce9a8ee3e02