Expositions · C03.2 · Registrar
C03.2 · Prior art
Section of C03.2 — Scalar complements, Lie-triple tests and carrier geometry. Section object E-C03.2.prior-art · kind PRIOR_ART · 4 record uses, all UNREVIEWED — no lane has read this section · attestation inherited from the article (R69).
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2 standard · 3 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 |
|---|---|---|
| S1 | STANDARD | The Lie-triple criterion relates a tangent subspace to a totally geodesic symmetric-space submanifold. | [TL] Theorem 3.3; its ambient Cartan realization must be specified. |
| S2 | PROGRAMME | The identity-anchored scalar complement in the chosen exceptional representation. | LIB2-007; Paper 4 §4.2, p.69. |
| S3 | PROGRAMME | Failure of the registered Jordan-visible plane and closure of its registered complement. | LIB2-008 and LIB2-009; Appendix F §5.3, p.181. |
| S4 | PROGRAMME | Identification of the algebra generated by that particular complementary plane. | LIB2-010; Appendix F p.181, with local geometry qualified at Paper 4 p.69. |
| S5 | STANDARD | Dimension, rank, centre and Cartan character alone need not determine a semisimple real Lie algebra. | [MW] §2 for split D4; [BM] §5.3 and Appendix B for split G2; the explicit comparison below. |
| S6 | UNRESOLVED | An exact independent certificate for the programme’s frozen planes and their embedding. | The exact projectors, brackets and identification map are absent. This is not an unresolved classification of abstract split D4. |
| Result | Classification | Predicate and exact scope | Source | |---|---|---|---| | S1 | STANDARD | The Lie-triple criterion relates a tangent subspace to a totally geodesic symmetric-space submanifold. | [TL] Theorem 3.3; its ambient Cartan realization must be specified. | | S2 | PROGRAMME | The identity-anchored scalar complement in the chosen exceptional representation. | LIB2-007; Paper 4 §4.2, p.69. | | S3 | PROGRAMME | Failure of the registered Jordan-visible plane and closure of its registered complement. | LIB2-008 and LIB2-009; Appendix F §5.3, p.181. | | S4 | PROGRAMME | Identification of the algebra generated by that particular complementary plane. | LIB2-010; Appendix F p.181, with local geometry qualified at Paper 4 p.69. | | S5 | STANDARD | Dimension, rank, centre and Cartan character alone need not determine a semisimple real Lie algebra. | [MW] §2 for split D4; [BM] §5.3 and Appendix B for split G2; the explicit comparison below. | | S6 | UNRESOLVED | An exact independent certificate for the programme’s frozen planes and their embedding. | The exact projectors, brackets and identification map are absent. This is not an unresolved classification of abstract split D4. |
Registrar records this section cites
- LIB2-007 · 1 use · role UNREVIEWED · legacy citation role compare
- LIB2-008 · 1 use · role UNREVIEWED · legacy citation role compare
- LIB2-009 · 1 use · role UNREVIEWED · legacy citation role compare
- LIB2-010 · 1 use · role UNREVIEWED · legacy citation role compare
Registrar records are IN REVIEW and noindex; a use's role here is the Registrar's not-read state until two non-drafting lanes read it (R67 §3).
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Receipt, script and stdout: on the article page. Registrar master sha256 01d1a5873ede42f5b2c5f4fdcee3a4a74c09a14b99a0deea86a60ebd9c821033 · BUILD_STAMP S371a · 2026-09-26 22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02