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A registered result in its source context

Original ledger classification: Review contract; first slice machine-closed [E]/[PROOF] with honest typing correction (v690); remaining: Jacobian factorization symbolics + writeup.

Recorded statement: Review contract (external review, theorem candidate, registered 2026-08-03): restricting the W(E8) invariant root power sums to the holomorphic mu4 eigenspace V^{1,0} kills exactly the half {2,14,18,30} and keeps {8,12,20,24} = Deg(G31) --…

Statement, assumptions and sources

Paper context: tfpt research contracts

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E8.QUARTIC.HALF.01

Original ledger classification: Review contract; first slice machine-closed [E]/[PROOF] with honest typing correction (v690); remaining: Jacobian factorization symbolics + writeup.

Original claim text

Review contract (external review, theorem candidate, registered 2026-08-03): restricting the W(E8) invariant root power sums to the holomorphic mu4 eigenspace V^{1,0} kills exactly the half {2,14,18,30} and keeps {8,12,20,24} = Deg(G31) -- 'G31 is the holomorphic mu4 shadow of the E8 compiler'. FIRST SLICE EXECUTED by v690 (22/22, QUARTIC-HALF-ALIVE) WITH the honest correction: the vanishing half is TRUE but TRIVIAL (mu4 orbit factor -- holds for all d != 0 mod 4, not degree-list-specific); the substance is F8/F12/F20/F24 as a system of basic G31 invariants (Chevalley cited; the holomorphic restriction generates the FULL G31 ring). REMAINING: the symbolic degree-60 Jacobian factorization (cited standard theorem, named residual) and the paper-level writeup.

Original classification detail

EXECUTED (first slice): v690 proves the vanishing half (trivial, honestly typed) and establishes the basic-invariant substance; remaining: symbolic Jacobian factorization + writeup.

Dependencies as recorded

E8.QUARTICHALF.01; E8.ST31.01

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