A registered result in its source context

Original ledger classification: Identity/Lattice [E] (cyclotomic CP) + [C] (physical identification)

Recorded statement: DOES THE GALOIS mu4 x Z2 (v315) ORGANIZE THE PHYSICAL READOUTS? YES -- THE CP PHASES (2026-06-21, v315 follow-up to phenomenology). [E] FAMILY FACTOR: the hexagonal CP unit rho=zeta_6=zeta_30^5 is the order-6=2 N_fam factor c^5 of v315…

Statement, assumptions and sources

Paper context: Origin Theory

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GALOIS.READOUT.01

Original ledger classification: Identity/Lattice [E] (cyclotomic CP) + [C] (physical identification)

Original claim text

DOES THE GALOIS mu4 x Z2 (v315) ORGANIZE THE PHYSICAL READOUTS? YES -- THE CP PHASES (2026-06-21, v315 follow-up to phenomenology). [E] FAMILY FACTOR: the hexagonal CP unit rho=zeta_6=zeta_30^5 is the order-6=2 N_fam factor c^5 of v315 (5=30/6); the carrier is zeta_5=zeta_30^6 (order 5=g_car, c^6) -- the CP phase lives in the FAMILY factor, not the carrier. [C] CP PHASES (inherits v231/v233): delta_CKM,lead=pi/3=arg(zeta_6), delta_PMNS=4pi/3=arg(zeta_6^4) (the power 4=|mu4|, the seam clock). [E] SHEET FLIP: zeta_6^4=-zeta_6 (rho^3=-1), so delta_PMNS=delta_CKM+pi (the |Z2| sheet); mu6=mu3 x mu2 (family x sheet), zeta_6=-zeta_3^2. [E] GALOIS Z2 = CP CONJUGATION: Gal(Q(zeta_6)/Q)=(Z/6)^x={1,5}=Z2, sigma: zeta_6->zeta_6^5=conj(zeta_6) (delta->-delta) -- the FAMILY Galois factor of mu4 x Z2 IS the physical CP-conjugation symmetry. [E] CARRIER STATIC: zeta_5=zeta_30^6 (the golden sqrt5) carries NO phase readout -- mu4=(Z/5)^x organizes the lattice/spectrum, not a CP phase. [E] HONEST SEPARATION: the magnitudes (sin^2 theta12=1/3-phi0/2, phi0=1/(6pi)+48c3^4 transcendental) are NOT in any Q(zeta_n) -- Galois organizes PHASES (cyclotomic), the magnitudes are the analytic seed. [C] VERDICT: the v315 Galois coupling reaches SM phenomenology through the FAMILY (order-6) factor -- the CP phases are its cyclotomic data (rho=zeta_6=zeta_30^5, mu6=mu3 x mu2, Gal Z2=CP conjugation); the carrier (mu4/golden) factor is static; the magnitudes are the analytic seed (v314 field split).

Original classification detail

[E] the family-factor placement of the CP unit zeta_6=zeta_30^5 + the sheet flip + the Galois-Z2 = CP-conjugation identification + the carrier-static fact + the magnitude/seed separation; [C] the identification with the physical delta_CKM/delta_PMNS (inherits v231/v233). Bridges the v315 Galois coupling to SM phenomenology (the phase sector); does NOT upgrade the CP-phase typing.

Dependencies as recorded

COX.COUPLE.01; CP.TRIALITY.01; v315; v231; v233

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Location recorded in the ledger

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Origin Theory
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Sections that explicitly cite this claim

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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

Navigation through a shared verification script

These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.

2026-06-22 (Wolfram mirror of the arithmetic arc [formula in source] three sharpening steps: the CP-lock made quantitative, the Bisognano–Wichmann keystone, the minimal hypergraph fibre: v322, v323, v324)Research changelog; TFPT — Introduction and reading guide
The whole integer skeleton from one pair [formula in source]input 4 origin theory
The Sheet Diamond and the Winding Line: masses and transport from one surfacetfpt 2 standard model
2026-06-25 (The seam [formula in source] is the carrier's Galois group: v419 [formula in source] figure)Research changelog; TFPT — Introduction and reading guide
The whole integer skeleton from one pair [formula in source]input 4 origin theory
The whole integer skeleton from one pair [formula in source]Origin Theory
Front matter / supportStandard Model and flavor structure
Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog

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Registered verification modules

v316_galois_readout.pyRegistered verification module · frontier
Read the description recorded in the module registry
Does the Galois mu4 x Z2 (v315) organize the physical readouts? Yes -- the CP phases. The hexagonal CP unit rho=zeta_6=zeta_30^5 is the order-6=2 N_fam FAMILY factor c^5 of v315 (the carrier is zeta_5=zeta_30^6); delta_CKM,lead=pi/3=arg(zeta_6), delta_PMNS=4pi/3=arg(zeta_6^4) (power 4=|mu4|), zeta_6^4=-zeta_6 the sheet flip (mu6=mu3 x mu2). The Galois Z2=Gal(Q(zeta6)/Q)={zeta_6->zeta_6^5=conj} IS CP conjugation (delta->-delta). The carrier factor zeta_5 (golden sqrt5) carries no phase (static). The magnitudes (sin^2 theta12=1/3-phi0/2, transcendental phi0) are NOT cyclotomic. So the Galois bridge reaches phenomenology through the family factor (phases), the carrier is static, the magnitudes are the analytic seed

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