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Original ledger classification: 128-spinor extension exhibited [E]/[C]: the Jacobi/E8 identity theta2^8+theta3^8+theta4^8=2E4 makes chi_{(E8)_1}=E4/eta^8=chi_o+chi_s (vacuum 120 + spinor 128 = 248); the finite 16-Majorana Fock space carries C(16,2)=120 currents and 2^8=256=128+128 Ramond states; the critical ring converges c_- -> 8 and x_1 -> 1 as L grows; AGT/AMT (v459) supply the rigorous extension; SEAM.EQUIV.01 existence stays [O]

Recorded statement: The 128-spinor extension SO(16)_1 -> (E8)_1 exhibited at CHARACTER level and as a finite-L -> continuum convergence (2026-06-30) -- the constructive companion of the v458 (MMST audit) / v459 (lattice-VOA) residual. v458 isolated the…

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SEAM.EQUIV.SPINOR.01

Original claim text

The 128-spinor extension SO(16)_1 -> (E8)_1 exhibited at CHARACTER level and as a finite-L -> continuum convergence (2026-06-30) -- the constructive companion of the v458 (MMST audit) / v459 (lattice-VOA) residual. v458 isolated the residual to the 128 spinor currents; v459 named the lattice-VOA route; this module EXHIBITS the extension three ways. [E] (E8)_1 TOWER FROM SO(16)_1 SECTORS: the exact Jacobi/E8 identity theta2^8+theta3^8+theta4^8=2E4 (~1e-30) gives chi_{(E8)_1}=E4/eta^8 = (1/2)[(t3/eta)^8+(t4/eta)^8] + (1/2)(t2/eta)^8 = chi_o^{SO16}+chi_s^{SO16} -- the holomorphic (E8)_1 character IS the SO(16)_1 vacuum+spinor sector sum (the conformal embedding SO(16)_1 in (E8)_1). [E] 128 SPINOR WEIGHT-1 STATES FILL 120 -> 248: chi_o gives weight-1 multiplicity 120 (=dim so(16)), chi_s gives 128 at weight 1, summing to the exact (E8)_1 tower {1,248,4124,34752} -- the 128 spinor currents ARE the (E8)_1 - SO(16)_1 deficit (248=120+128). [E] FINITE 16-MAJORANA FOCK: C(16,2)=120 NS bilinear (so(16)) currents and 2^{16/2}=256 Ramond ground states = 128 spinor + 128 cospinor (split by fermion parity) -- the spinor present already at finite N. [E] FINITE-L -> CONTINUUM CONVERGENCE: the critical free-fermion ring Casimir E_0(L)=e_inf L - pi v c/(6L) fits c_Dirac -> 1 (c_-=16*(1/2)=8) and the lowest scaled NS gap x_1 -> the weight-1 dimension 1 with |x_1-1| ~ 1/L^2 (L=64..1024) -- the lattice flows to the conformal tower. [C]/[O] the rigorous holomorphic extension (the simple-current chi_o+chi_s projection) is supplied by AGT/AMT (v459); SEAM.EQUIV.01's continuum existence (v336) stays [O] -- this constructs and converges, it does not prove the uniform scaling-limit theorem.

Original classification detail

Identity

Dependencies as recorded

SEAM.EQUIV.01; SEAM.EQUIV.MMST.AUDIT.01; SEAM.EQUIV.LATTICEVOA.01; SEAM.EQUIV.KILLTEST.01; v458; v459; v457; v336

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Research contracts
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2026-06-30 ( v461/ v462 + Lean axiom merge — the strict-locality obstruction made explicit, the 128-spinor extension exhibited at character level, and the SEAM.EQUIV.01 residual reduced to ONE realisation axiom [formula in source] ONE combined cited theorem)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

v462_seam_spinor_continuum.pyRegistered verification module · frontier
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SEAM.EQUIV.SPINOR.01: the 128-spinor extension SO(16)_1 -> (E8)_1 exhibited at CHARACTER level and as a finite-L -> continuum convergence -- the constructive companion of the v458 (MMST audit) / v459 (lattice-VOA) residual. [E] (E8)_1 TOWER FROM SO(16)_1 SECTORS: the exact Jacobi/E8 identity theta2^8+theta3^8+theta4^8=2E4 gives chi_{(E8)_1}=E4/eta^8 = chi_o^{SO16}+chi_s^{SO16} -- the holomorphic (E8)_1 character IS the SO(16)_1 vacuum+spinor sector sum. [E] 128 SPINOR WEIGHT-1 STATES FILL 120 -> 248: chi_o gives 120, chi_s gives 128, summing to the exact (E8)_1 tower {1,248,4124,34752}. [E] FINITE 16-MAJORANA FOCK: C(16,2)=120 NS bilinear currents and 2^8=256 Ramond ground states = 128 spinor + 128 cospinor. [E] FINITE-L -> CONTINUUM CONVERGENCE: the critical free-fermion ring Casimir gives c_Dirac -> 1 (c_-=8) and the lowest scaled NS gap x_1 -> 1 with |x_1-1| ~ 1/L^2 (L=64..1024). [C]/[O] the rigorous holomorphic extension is supplied by AGT/AMT (v459); SEAM.EQUIV.01 existence (v336) stays [O]. Mixed exact (theta identity + tower + 120/128/256, Wolfram-mirrored) + numerical.

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