Expositions · C04.1 · Registrar
C04.1 · Prior art
Section of C04.1 — Golden-field selectors and the admissible-gap proof. Section object E-C04.1.prior-art · kind PRIOR_ART · 6 record uses, all UNREVIEWED — no lane has read this section · attestation inherited from the article (R69).
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2 standard · 5 programme · 1 unresolved. Standard results are known mathematics, executed here as exposition; the citation is given. Nothing on this page is claimed as new.
| Result | Status | Citation / locator |
|---|---|---|
| V1 | STANDARD | The integer ring and unit group of the real quadratic golden field. | [KC] Theorem 1.1 and §2 Table 1, d=5. |
| V2 | PROGRAMME | DET-7 as an imposed selector premise. | LIB2-018; Appendix E §3 p.164. |
| V3 | PROGRAMME | The field-free inverse-spectrum selector. | LIB2-019; Appendix E §3 p.164. |
| V4 | PROGRAMME | The golden-field selector and its admissible-gap classification. | LIB2-001 and LIB2-020; Appendix E §4 p.165. |
| V5 | PROGRAMME | The source-specific rejection of spread monotonicity. | Appendix E p.165 and the exact control below. |
| V6 | STANDARD | An invariant function is constant on group orbits; at a stationary point its Hessian annihilates orbit directions. | Elementary differentiation of invariance; [TL] Cartan/symmetric-space framework. |
| V7 | PROGRAMME | Application of the orbit obstruction and the norm-only action restriction to the declared Jordan selector. | LIB2-041 and LIB2-042; Appendix E p.167. |
| V8 | UNRESOLVED | The stronger variational theorem alluded to by the source pointer and the physical selection of premises. | Appendix E p.172 names s1085 without its full stronger statement; no physical selector is supplied. |
| Result | Classification | Predicate and exact scope | Source | |---|---|---|---| | V1 | STANDARD | The integer ring and unit group of the real quadratic golden field. | [KC] Theorem 1.1 and §2 Table 1, d=5. | | V2 | PROGRAMME | DET-7 as an imposed selector premise. | LIB2-018; Appendix E §3 p.164. | | V3 | PROGRAMME | The field-free inverse-spectrum selector. | LIB2-019; Appendix E §3 p.164. | | V4 | PROGRAMME | The golden-field selector and its admissible-gap classification. | LIB2-001 and LIB2-020; Appendix E §4 p.165. | | V5 | PROGRAMME | The source-specific rejection of spread monotonicity. | Appendix E p.165 and the exact control below. | | V6 | STANDARD | An invariant function is constant on group orbits; at a stationary point its Hessian annihilates orbit directions. | Elementary differentiation of invariance; [TL] Cartan/symmetric-space framework. | | V7 | PROGRAMME | Application of the orbit obstruction and the norm-only action restriction to the declared Jordan selector. | LIB2-041 and LIB2-042; Appendix E p.167. | | V8 | UNRESOLVED | The stronger variational theorem alluded to by the source pointer and the physical selection of premises. | Appendix E p.172 names s1085 without its full stronger statement; no physical selector is supplied. |
Registrar records this section cites
- LIB2-001 · 1 use · role UNREVIEWED · legacy citation role compare
- LIB2-018 · 1 use · role UNREVIEWED · legacy citation role compare
- LIB2-019 · 1 use · role UNREVIEWED · legacy citation role compare
- LIB2-020 · 1 use · role UNREVIEWED · legacy citation role compare
- LIB2-041 · 1 use · role UNREVIEWED · legacy citation role compare
- LIB2-042 · 1 use · role UNREVIEWED · legacy citation role compare
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