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A registered result in its source context

Original ledger classification: Lattice/rep theory [E]

Recorded statement: E8 HULL FORBIDS THE 126 (2026-06-17): the E8 audit hull supplies exactly {1,10,16,45} for SO(10) -- turning the scalaron-match '16-Higgs over 126-Higgs' selection into an algebraic statement. The carrier D5(+)A3 = SO(10)xSU(4) is a rank-8…

Statement, assumptions and sources

Paper context: tfpt anschluss zellen seam 2026-09-14

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PS.E8BRANCH.01

Original ledger classification: Lattice/rep theory [E]

Original claim text

E8 HULL FORBIDS THE 126 (2026-06-17): the E8 audit hull supplies exactly {1,10,16,45} for SO(10) -- turning the scalaron-match '16-Higgs over 126-Higgs' selection into an algebraic statement. The carrier D5(+)A3 = SO(10)xSU(4) is a rank-8 subalgebra of E8 via SO(16); the adjoint 248 branches as (45,1)+(1,15)+(10,6)+(16,4)+(16bar,4bar) = 45+15+60+64+64 = 248 (SO(16) split: 120 adjoint + 128 spinor = spinor_SO10 (x) spinor_SO6). (1) [E] ranks 5+3=8=rank E8. (2) [E] dims sum to 248. (3) [E] the SO(10) reps in the hull are exactly {1,10,16,45}; the 126 (dim 126) is ABSENT -> the renormalisable 126_H is algebraically forbidden if fields are E8-hull reps, and 10+16+45 is E8-supplied, not fitted. (4) [E] MULTIPLICITY CAVEAT: only ONE (45,1) and ONE (1,15) in the 248 -> the minimal E8-allowed content (one 45) is proton-MARGINAL, a sharp falsifiable constraint. (5) [O] the field-content principle ('TFPT fields are E8-hull reps') + the NCG inner-fluctuation complement (v250).

Original classification detail

[E] E8->SO(10)xSU(4) branching: SO(10) content {1,10,16,45}, 126 absent (126_H forbidden), only one 45/15 (proton-marginal); [O] the field-content principle

Dependencies as recorded

E8.GLU.01; QFT4D.MATTER.01

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Registered verification modules

  • v247_e8_branching_no126.pyRegistered verification module · registry
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    PS.E8BRANCH.01 — the E8 audit hull forbids the 126 and supplies exactly {1,10,16,45} for SO(10). Carrier D5⊕A3 = SO(10)×SU(4) ⊂ E8 (via SO(16)); 248 = (45,1)+(1,15)+(10,6)+(16,4)+(16bar,4bar) = 248. [E] ranks 5+3=8; [E] dims=248 (SO(16): 120 adj + 128 spinor); [E] SO(10) content {1,10,16,45}, the 126 ABSENT → 126_H algebraically forbidden, 10+16+45 E8-supplied not fitted; [E] CAVEAT only one 45/one 15 → proton-marginal; [O] the field-content principle + NCG complement (v250). Makes the scalaron-match 16-over-126 selection algebraic.

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