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A registered result in its source context

Original ledger classification: Identity (exact) [E]/[C]

Recorded statement: CP PHASES AS MU6 POWERS (2026-06-17): both CP phases are mu6 powers of ONE hexagonal CM unit, split by the sheet -- a structural reduction of red-team Target D, sharper than v220/v225 (which only located the residual). With rho=e^{i pi/3}…

Statement, assumptions and sources

Paper context: Red-team audit

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CP.MU6.01

Original ledger classification: Identity (exact) [E]/[C]

Original claim text

CP PHASES AS MU6 POWERS (2026-06-17): both CP phases are mu6 powers of ONE hexagonal CM unit, split by the sheet -- a structural reduction of red-team Target D, sharper than v220/v225 (which only located the residual). With rho=e^{i pi/3} the primitive 6th root (j=0 Eisenstein CM, CP.MOD.01): (1) rho^6=1, rho^3=-1 (the Z2 sheet half-turn); (2) delta_CKM leading = arg(rho^1)=pi/3 (quark, FLAV.CP.01), delta_PMNS = arg(rho^4)=4 pi/3 (lepton, the tfpt_2 neutrino phase lattice); (3) rho^4=-rho => delta_PMNS = delta_CKM,lead + pi = (CM unit) x (Z2 sheet) -- the two CP phases are ONE hexagonal unit on the two sheets, NOT two independent inputs; (4) the C6/mu6 monodromy U6 has charpoly t^6-1 (spectrum mu6 carries rho); (5) the dual-normal-frame orientation (DUAL.FRAME.01) is sheet-flipped: Im det(1,d,rho^1 n)=+21 sin(pi/3) (quark), Im det(1,d,rho^4 n)=-21 sin(pi/3) (lepton); (6) NEG: mu3 (cube roots) has no -1, so it cannot relate the two phases by a half-turn (mu6=mu3 family x mu2 sheet required). REDUCTION: removes one of Target D's two phase inputs (the lepton phase is the quark phase x the sheet); the quark seam correction 3 lambda_C^2 stays the v88 misalignment, the deck stays Z/4 (QGEO.KILL.01). Does NOT close Target D.

Original classification detail

[E] delta_CKM,lead=arg(rho)=pi/3, delta_PMNS=arg(rho^4)=4pi/3, rho^4=-rho so the two CP phases = one hexagonal unit x the Z2 sheet; sheet-flipped Jarlskog orientations; reduces Target D's CP inputs from 2 to 1, physical derivation [C]

Dependencies as recorded

CP.MOD.01; DUAL.FRAME.01; FLAV.CP.01

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Registered verification modules

  • v231_cp_mu6_phases.pyRegistered verification module · flavor
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    Both CP phases are mu6 powers of ONE hexagonal CM unit, split by the sheet -- a structural reduction of red-team Target D. With rho=e^{i pi/3} (the j=0 Eisenstein CM unit): delta_CKM leading = arg(rho^1)=pi/3 (quark), delta_PMNS = arg(rho^4)=4pi/3 (lepton, the phase lattice); rho^4=-rho so delta_PMNS = delta_CKM,lead + pi = (CM unit)x(Z2 sheet, rho^3=-1) -- the two CP phases are ONE hexagonal unit on the two sheets, not two independent inputs. The C6/mu6 monodromy carries rho (charpoly t^6-1); the dual-frame orientations are sheet-flipped Im det(1,d,rho^1 n)=+21 sin(pi/3), Im det(1,d,rho^4 n)=-21 sin(pi/3). NEG: mu3 has no -1 (no sheet). Removes one of Target D's two phase inputs; the quark seam correction 3 lambda_C^2 stays the v88 misalignment, the deck stays Z/4.

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