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A registered result in its source context

Original ledger classification: Identity (exact ring arithmetic)

Recorded statement: CM-NORM DUALITY (2026-06-16): the two exceptional CM moduli give two central TFPT integers as ideal NORMS. SQUARE seam (Gaussian Z[i], j=1728): N(g_car+i|mu4|)=5^2+4^2=41=10 b1 -- the EM index IS the Gaussian norm of the carrier-glue…

Statement, assumptions and sources

Paper context: Origin Theory

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CMNORM.DUAL.01

Original ledger classification: Identity (exact ring arithmetic)

Original claim text

CM-NORM DUALITY (2026-06-16): the two exceptional CM moduli give two central TFPT integers as ideal NORMS. SQUARE seam (Gaussian Z[i], j=1728): N(g_car+i|mu4|)=5^2+4^2=41=10 b1 -- the EM index IS the Gaussian norm of the carrier-glue vector; N(3+2i)=13=Delta_Q. HEX partner (Eisenstein Z[omega], j=0): N(3+2 omega)=3^2-3*2+2^2=7=scalaron exponent. The (3,2)=(colour,weak) split generates (5,6,7,13)=(g_car,|R^+(A3)|,scalaron,Delta_Q) by sum/product/Eisenstein-norm/Gauss-norm; rings rigid (Eisenstein of (5,4)=21!=41, Gauss of (3,2)=13!=7).

Original classification detail

[E] 41=N_Zi(5,4)=10 b1, 13=N_Zi(3,2)=Delta_Q, 7=N_Zomega(3,2)=scalaron; (3,2)->(5,6,7,13); the square<->EM, hex<->scalaron architecture bridge [C]

Dependencies as recorded

ANCHOR.GEN.01; EM.B1.01; SEAM.KHALF.01

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Registered verification modules

  • v222_cm_norm_duality.pyRegistered verification module · core
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    CM-norm duality: the two exceptional moduli give 41 and 7. SQUARE (Gaussian ℤ[i], j=1728): N(g_car+i|μ₄|)=5²+4²=41=10b₁ (the EM index IS the Gaussian norm of the carrier-glue vector); N(3+2i)=13=Δ_Q. HEX (Eisenstein ℤ[ω], j=0): N(3+2ω)=3²−3·2+2²=7=scalaron. The (3,2)=(colour,weak) split generates (5,6,7,13) by sum/product/Eisenstein/Gauss norm; rings rigid (Eisenstein of (5,4)=21≠41).

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