Expositions · C03.1 · Registrar

C03.1 · Prior art

Section of C03.1 — From Jordan boundary to Freudenthal bulk and exceptional representation. Section object E-C03.1.prior-art · kind PRIOR_ART · 5 record uses, all UNREVIEWED — no lane has read this section · attestation inherited from the article (R69).

← What this does not show · Sources/receipt →

4 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.

ResultStatusCitation / locator
F1STANDARDFreudenthal construction from a cubic Jordan algebra, with its alternating form and quartic. | [K04] §3.1, Definition 17 and Proposition 18.
F2STANDARDA coordinate half in a vector space plus its dual is Lagrangian. | [A07] §1; the full split-Albert coordinate calculation below.
F3PROGRAMMERegistration of the mass-coordinate half as the particular Jordan boundary. | LIB2-011, Appendix X p.348.
F4PROGRAMMEThe frozen exceptional matrices and the full polarized-cubic solder/local polarization. | LIB2-006, LIB2-012, LIB2-013. Original arrays are [NOT VERIFIED] here.
F5STANDARDThe positive solution of a matrix congruence equation is a geometric mean. | [LL] Definition 3.2 and Riccati characterization.
F6PROGRAMMEClosure of the registered dressing, conditional on the supplied Cartan-pair realization. | LIB2-197, Paper 1 §9 p.29; the group-theoretic implication is proved below, its frozen realization is not rerun.
F7STANDARDHamiltonian transverse derivative and grading consequences of the explicit Freudenthal quartic. | [K04] §3.1 quartic; [A07] §2; exact coefficient test below.
F8UNRESOLVEDThe actual frozen-frame identification, transported positive polarization and microscopic Hamiltonian attachment. | Missing named tensors/maps; see holds.

| Result | Classification | Predicate and exact scope | Source | |---|---|---|---| | F1 | STANDARD | Freudenthal construction from a cubic Jordan algebra, with its alternating form and quartic. | [K04] §3.1, Definition 17 and Proposition 18. | | F2 | STANDARD | A coordinate half in a vector space plus its dual is Lagrangian. | [A07] §1; the full split-Albert coordinate calculation below. | | F3 | PROGRAMME | Registration of the mass-coordinate half as the particular Jordan boundary. | LIB2-011, Appendix X p.348. | | F4 | PROGRAMME | The frozen exceptional matrices and the full polarized-cubic solder/local polarization. | LIB2-006, LIB2-012, LIB2-013. Original arrays are [NOT VERIFIED] here. | | F5 | STANDARD | The positive solution of a matrix congruence equation is a geometric mean. | [LL] Definition 3.2 and Riccati characterization. | | F6 | PROGRAMME | Closure of the registered dressing, conditional on the supplied Cartan-pair realization. | LIB2-197, Paper 1 §9 p.29; the group-theoretic implication is proved below, its frozen realization is not rerun. | | F7 | STANDARD | Hamiltonian transverse derivative and grading consequences of the explicit Freudenthal quartic. | [K04] §3.1 quartic; [A07] §2; exact coefficient test below. | | F8 | UNRESOLVED | The actual frozen-frame identification, transported positive polarization and microscopic Hamiltonian attachment. | Missing named tensors/maps; see holds. |

Registrar records this section cites

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).

← What this does not show · Sources/receipt →

Receipt, script and stdout: on the article page. Registrar master sha256 01d1a5873ede42f5b2c5f4fdcee3a4a74c09a14b99a0deea86a60ebd9c821033 · BUILD_STAMP S371a · 2026-09-26 22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02