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Original ledger classification: the chiral c=8 content is (E8)_1 (248 currents, 1 primary) via the exact character + mu4/GSO promotion [E]

Recorded statement: S3 closure stack (2026-06-23): the chiral c=8 content of the seam is the SPECIFIC net (E8)_1, not just 'some c=8' -- shown by the exact affine character q-series and the mu4/GSO promotion SO(16)_1 -> (E8)_1 (the genus-0 character…

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SEAM.S3.E8CHARACTER.01

Original ledger classification: the chiral c=8 content is (E8)_1 (248 currents, 1 primary) via the exact character + mu4/GSO promotion [E]

Original claim text

S3 closure stack (2026-06-23): the chiral c=8 content of the seam is the SPECIFIC net (E8)_1, not just 'some c=8' -- shown by the exact affine character q-series and the mu4/GSO promotion SO(16)_1 -> (E8)_1 (the genus-0 character discriminator that pins the target of the scaling limit). [E] chi = E4/eta^8 = q^{-1/3}(1+248q+4124q^2+...): eta^8=q^{1/3}prod(1-q^n)^8 gives the prefactor q^{-c/24}=q^{-1/3} => c=8; the level-1 coefficient 248=dim E8 (one primary = the vacuum module), computed exactly from E4*prod(1-q^n)^{-8}. [E] the promotion: 248=240+8=(E8 roots)+(Cartan rank), 240=dim S^+*g_car*N_fam=16*5*3 (carrier trace); equivalently 248=120+128=dim SO(16)+spinor(128) -- the order-4 mu4 clock condenses the SO(16)_1 vacuum+spinor into the single (E8)_1 module. [E] discriminator: (E8)_1 has 1 primary and 248 level-1 currents vs SO(16)_1 4 primaries and 120. [O] the continuum existence (v336); the mu4 projection = the seam one-sidedness (S3).

Original classification detail

[E] the exact character q-series (c=8, 248, 4124) + the integer promotion identities (248=240+8=120+128, 240=16*5*3) + the 1-vs-4 primary discriminator; [O] the continuum existence (v336) + the mu4 projection = S3. Pins the target net (E8)_1; does NOT close SEAM.EQUIV.01.

Dependencies as recorded

SEAM.EQUIV.01; v336; v351; v83; v1

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Registered verification modules

  • v377_seam_s3_e8character.pyRegistered verification module · core
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    S3 closure stack: the chiral c=8 content is the SPECIFIC net (E8)_1, via the exact affine character q-series + the mu4/GSO promotion. [E] chi = E4/eta^8 = q^{-1/3}(1+248q+4124q^2+...): leading -c/24=-1/3 => c=8; level-1 = 248 = dim E8 (one primary). [E] mu4/GSO promotion SO(16)_1 -> (E8)_1: 248=240+8=(E8 roots)+(Cartan), 240=dim S^+*g_car*N_fam=16*5*3; 248=120+128=dim SO(16)+spinor. [E] discriminator: (E8)_1 has 1 primary/248 currents vs SO(16)_1 4 primaries/120. [O] continuum existence (v336); mu4 projection = seam one-sidedness (S3). Pins the target net; does NOT close SEAM.EQUIV.01.

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