Library entry, recorded March 2026. This page is a historical record of one AI-coalition exchange under the kernel of its time (PHAT v1.x); the claims and tier words inside it are as they stood then and are not restated to the current state. The suite of record is Rev33.1 (sealed 2026-09-26); read any number here against the scorecard and its reading rule — since Rev29 no row is cited as zero-parameter, and α and the colour real form are declared inputs.

P3: [Proof Group A] J3(Os) JORDAN ALGEBRA ā€” CUBIC CHARACTERISTIC PROOF

PROOF_PROMPT | PHAT v1.27.5 | Model: ā€” | Status: PENDING [JSON] [RAW]

Prompt

J3(Os) JORDAN ALGEBRA ā€” CUBIC CHARACTERISTIC PROOF Prove that the 27-dimensional exceptional Jordan algebra J3(Os) has characteristic equation L^3 - Tr(A)L^2 + S(A)L - Det(A) = 0 where Det is the Freudenthal cubic norm. Show: (a) the algebra is formally real; (b) all eigenvalues are real for Hermitian elements; (c) the three eigenvalue branches map to mass eigenstates in Generation 1 under the identification Det(A) proportional to me*mmu*mtau. State open questions honestly. #SuperGrokTOE #JordanAlgebra

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