A registered result in its source context
Original ledger classification: (E8)_1 character/sector kill-test [E]/[X]: chi=E4/eta^8={1,248,4124,34752}; the discriminators 248=120+128 (weight-1) and |det Cartan E8|=1 vs |det D8|=4 (sectors) -- a measured 120 or 4 sectors would FALSIFY (E8)_1, the data give 248/1 (PASSED); SEAM.EQUIV.01 stays [O]
Recorded statement: An explicit (E8)_1-vs-SO(16)_1 character/sector kill-test for the seam edge (2026-06-30, G7 of the post-F next steps) -- a FALSIFIABLE consistency test of the (E8)_1 identification of SEAM.EQUIV.01. [E] (E8)_1 CHARACTER TOWER:…
Statement, assumptions and sources
Paper context: Research contracts
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SEAM.EQUIV.KILLTEST.01
Original ledger classification: (E8)_1 character/sector kill-test [E]/[X]: chi=E4/eta^8={1,248,4124,34752}; the discriminators 248=120+128 (weight-1) and |det Cartan E8|=1 vs |det D8|=4 (sectors) -- a measured 120 or 4 sectors would FALSIFY (E8)_1, the data give 248/1 (PASSED); SEAM.EQUIV.01 stays [O]
Original claim text
An explicit (E8)_1-vs-SO(16)_1 character/sector kill-test for the seam edge (2026-06-30, G7 of the post-F next steps) -- a FALSIFIABLE consistency test of the (E8)_1 identification of SEAM.EQUIV.01. [E] (E8)_1 CHARACTER TOWER: chi=E4/eta^8=q^{-1/3}(1+248q+4124q^2+34752q^3+...) the exact conformal-tower degeneracies (E4*prod(1-q^n)^{-8}, Wolfram-mirrored). [E] CURRENT-COUNT DISCRIMINATOR: the weight-1 multiplicity is 248=dim E8=120(SO16)+128(spinor), NOT the 120 of the free SO(16)_1. [E] SECTOR-COUNT DISCRIMINATOR: (E8)_1 is INVERTIBLE |det Cartan E8|=1 (one primary) vs SO(16)_1=D8 |det Cartan D8|=4 (four sectors). [X] KILL CRITERION: a measured weight-1 count of 120, OR a sector count of 4, OR a tower coefficient != {1,248,4124,...} would FALSIFY (E8)_1; current data give 248/1/{1,248,4124}, so PASSED. [C]/[O] the (E8)_1 identification survives the kill-test; SEAM.EQUIV.01's continuum EXISTENCE (v336) stays [O].
Original classification detail
Identity
Dependencies as recorded
SEAM.EQUIV.01; SEAM.EQUIV.E8.MODULAR.01; SEAM.S3.E8CHARACTER.01; SEAM.S3.MODULAR.01; v156; v281; v452; v336
Open the original ledger source, row 519Location recorded in the ledger
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- Research contracts
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- 2026-06-30 ( v454– v459 + Lean + Wolfram — the post-F ``G-block'': the lattice Sugawara current algebra, a uniform-in- [formula in source] Tomita–Takesaki tower, chirality forced by [formula in source] , an [formula in source] character kill test, the exact MMST citation audit and the complementary lattice-VOA route)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
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- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
- Front matter / supportResearch contracts
- Research Contract 1 — [formula in source]tfpt research contracts
Registered verification modules
- v457_seam_character_killtest.pyRegistered verification module · frontier
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SEAM.EQUIV.KILLTEST.01 [X]: an explicit (E8)_1-vs-SO(16)_1 character/sector kill-test for the seam edge -- a FALSIFIABLE test of the (E8)_1 identification (G7). [E] (E8)_1 CHARACTER TOWER: chi=E4/eta^8=q^{-1/3}(1+248q+4124q^2+34752q^3+...) -- exact (E8)_1 tower degeneracies. [E] CURRENT-COUNT DISCRIMINATOR: weight-1 multiplicity=248=dim E8=120(SO16)+128(spinor) -- not the free 120. [E] SECTOR-COUNT DISCRIMINATOR: |det Cartan E8|=1 (invertible) vs |det Cartan D8|=4. [X] KILL CRITERION: 120 (not 248), OR 4 sectors (not 1), OR a wrong tower coeff would FALSIFY (E8)_1; data give 248/1/{1,248,4124}, PASSED. [C]/[O] SEAM.EQUIV.01 existence stays [O]. Exact (Wolfram-mirrored) + det cross-check.
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