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Original ledger classification: Numerical (finite MTC) [E]/[C]

Recorded statement: SPIN-STATISTICS + MODULAR (S,T) DATA (2026-06-17): the exchange statistics, modular S/T matrices, Verlinde fusion and Gauss-Milgram central charge of the carrier MTC -- the statistics+kinematics layer on top of v241. Same abelian MTC: Z4 x…

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DHR.MODULAR.01

Original ledger classification: Numerical (finite MTC) [E]/[C]

Original claim text

SPIN-STATISTICS + MODULAR (S,T) DATA (2026-06-17): the exchange statistics, modular S/T matrices, Verlinde fusion and Gauss-Milgram central charge of the carrier MTC -- the statistics+kinematics layer on top of v241. Same abelian MTC: Z4 x Z4, q(x,y)=(5x^2+3y^2)/8 mod 1 (the Lean glue form FORM.GLUE.01), B(a,b)=q(a+b)-q(a)-q(b), theta(a)=e^{2 pi i q(a)}. (1) [E] spin-statistics: T=diag(theta_a) splits the 16 anyons into 6 BOSONS (theta=1, the condensable/isotropic set), 2 FERMIONS (theta=-1) = {(0,2),(2,0)}, and 8 genuine anyons. (2) [E] modular S_ab=(1/sqrt 16) e^{-2 pi i B(a,b)} is unitary, symmetric, S^2=C (charge conjugation, C_ab=delta(b,-a)), S^4=I. (3) [E] Verlinde N_ab^c = sum_x S_ax S_bx conj(S_cx)/S_0x = delta(c,a+b) -- the fusion ring is RECOVERED from the modular data, not posited. (4) [E] Gauss-Milgram (1/sqrt 16) sum_a theta_a = e^{2 pi i c/8} with c=8=g_car+N_fam -- the anyon data already encodes the chiral central charge of the (E8)_1 net (v156/v175); statistics and c=8 are one fact. (5) [C] the boson/fermion split is the kinematic skeleton of the matter content; mapping sectors to physical fermion multiplets is the interpretation

Original classification detail

[E] T=diag(theta) spin-statistics (6 bosons, 2 fermions, 8 anyons); modular S unitary/symmetric, S^2=C, S^4=I; Verlinde reproduces the group-law fusion; Gauss-Milgram gives c=8=g_car+N_fam. [C] the boson/fermion-to-field map is the interpretation

Dependencies as recorded

DHR.SECTORS.01; GATE.HOLO.02

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  • v242_spin_statistics_modular.pyRegistered verification module · registry
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    DHR.MODULAR.01 — spin-statistics and the modular (S,T) data of the carrier MTC: statistics + the fusion ring recovered from modular data + the anyon central charge c=8. Same MTC as v241 (Z4×Z4, q=(5x²+3y²)/8, θ=e^{2πi q}). [E] spin-statistics: T=diag(θ_a) → 6 bosons (θ=1), 2 fermions (θ=−1) = {(0,2),(2,0)}, 8 anyons. [E] modular S_ab=(1/√16)e^{−2πi B(a,b)} unitary, symmetric, S²=C (charge conjugation), S⁴=I. [E] Verlinde N_ab^c = Σ_x S_ax S_bx S*_cx / S_0x = δ(c,a+b) — fusion recovered from modular data. [E] Gauss–Milgram (1/√16)Σθ_a = e^{2πi c/8} with c=8=g_car+N_fam = the (E8)₁ central charge (v156/v175) — statistics and c=8 are one fact. [C] the boson/fermion split is the kinematic skeleton; sector↔multiplet map is the interpretation.

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