A registered result in its source context
Original ledger classification: Identity (exact) [E]/[C]
Recorded statement: CP = THE UNIVERSAL TRIALITY PHASE, SHEET-SPLIT (2026-06-17): one step past CP.MU6.01/v231 in the canonical mu6 = mu3 (family/triality) x mu2 (sheet) factorisation. (1) mu6=mu3 x mu2 (gcd(3,2)=1): the Z3 triality centre {1,omega,omega^2} =…
Statement, assumptions and sources
Paper context: Red-team audit
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CP.TRIALITY.01
Original ledger classification: Identity (exact) [E]/[C]
Original claim text
CP = THE UNIVERSAL TRIALITY PHASE, SHEET-SPLIT (2026-06-17): one step past CP.MU6.01/v231 in the canonical mu6 = mu3 (family/triality) x mu2 (sheet) factorisation. (1) mu6=mu3 x mu2 (gcd(3,2)=1): the Z3 triality centre {1,omega,omega^2} = the cusp weights {0,1/3,2/3} x 2pi, the sheet is mu2={1,-1}; the hexagonal CM unit factors as rho = omega^2 * (-1). (2) SAME FAMILY CLASS: rho^4 = rho^1 * rho^3 with rho^3 in mu2, so the quark (rho^1) and lepton (rho^4) CP phases have the SAME image in the family quotient mu6/mu2 ~ mu3 (the same triality-centre element) and OPPOSITE sheet ((-1)^1 vs (-1)^4). (3) so the CP phase IS the universal triality phase omega^2 (the 2/3 cusp-weight Z3 centre), read on the two sheets -- NOT a free choice of mu6 power; the power choice from v231 is removed. (4) omega is the mu3 factor of the order-30 (2,3,5) Milnor/Coxeter monodromy that builds E8 (TOPO.E8.01/v232), so CP lives inside the same cycle as the hull. (5) NEG: mu2-only carries no triality, mu3-only carries no sheet; only the full mu6 gives one triality phase on two sheets. Reduces red-team Target D from 'one hexagonal unit + sheet' to 'the universal triality phase + sheet'; the physical CP derivation stays [C] (the quark seam correction 3 lambda_C^2 is the v88 misalignment).
Original classification detail
[E] mu6=mu3 x mu2; quark rho^1 and lepton rho^4 share the family triality class omega^2 (the 2/3 cusp centre), opposite sheet; CP = universal triality phase + sheet, power choice removed; physical derivation [C]
Dependencies as recorded
CP.MU6.01; FLAV.CP.01; TOPO.E8.01
Open the original ledger source, row 319Location recorded in the ledger
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- Red-team audit
Sections that explicitly cite this claim
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- 2026-06-17 (CP phases as [formula in source] powers — a reduction of red-team Target D)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- 2026-06-21 (does the Galois [formula in source] organize the readouts? Yes — the CP phases are the family-factor cyclotomic data, Galois [formula in source] CP conjugation: v316)Research changelog; TFPT — Introduction and reading guide
- 2026-06-18 (Three open-residual advances: the [formula in source] solver, [formula in source] from [formula in source] , and the raw-seam [formula in source] mark-locality reduction, v262– v264)Research changelog; TFPT — Introduction and reading guide
- Neutrinostfpt 2 standard model
- The whole integer skeleton from one pair [formula in source]Origin Theory
- NeutrinosStandard Model and flavor structure
- OutcomeRed-team audit
Registered verification modules
- v233_cp_triality_phase.pyRegistered verification module · flavor
Read the description recorded in the module registry
The CP phase is the UNIVERSAL family/triality phase, only sheet-split -- one step past v231 in mu6 = mu3 (family/triality) x mu2 (sheet). mu6=mu3 x mu2 (gcd(3,2)=1): the Z3 triality centre {1,omega,omega^2} = cusp weights {0,1/3,2/3}x2pi, sheet mu2={1,-1}; rho = omega^2*(-1). SAME FAMILY CLASS: rho^4 = rho^1*rho^3 with rho^3 in mu2, so quark (rho^1) and lepton (rho^4) CP phases have the SAME image in mu6/mu2~mu3 and OPPOSITE sheet -- so the CP phase IS the universal triality phase omega^2 (the 2/3 cusp-weight Z3 centre), NOT a free power choice. omega is the mu3 factor of the order-30 (2,3,5) monodromy that builds E8 (v232). Reduces Target D from 'one hexagonal unit + sheet' (v231) to 'the universal triality phase + sheet'; physical CP derivation stays [C].
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