A registered result in its source context
Original ledger classification: Identity/Numerical (modular) [E]/[C]
Recorded statement: CP HEXAGONAL MODULUS (2026-06-16): CP lives in the HEXAGONAL phase fiber, not the square seam deck (a geometric sharpening of red-team Target D, the magnitude bijection misses the CP phases). The seam deck is the SQUARE modulus j(i)=1728,…
Statement, assumptions and sources
Paper context: Red-team audit
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CP.MOD.01
Original ledger classification: Identity/Numerical (modular) [E]/[C]
Original claim text
CP HEXAGONAL MODULUS (2026-06-16): CP lives in the HEXAGONAL phase fiber, not the square seam deck (a geometric sharpening of red-team Target D, the magnitude bijection misses the CP phases). The seam deck is the SQUARE modulus j(i)=1728, automorphism Z/4 (the mu4 clock); its exceptional partner is the HEX modulus j(rho)=0, rho=e^{i pi/3}, automorphism Z/6, CM by Z[omega], arg(rho)=pi/3. The frozen leading CKM reading delta=pi/3+3 lambda_C^2=68.654 deg (FLAV.CP.01, registry untouched) has leading term pi/3=arg(rho); the |Z2| alternative pi/3+2 lambda_C^2 is the frozen look-elsewhere trap. CRITICAL: the seam deck stays Z/4 (QGEO.KILL.01); CP is the Z/6 phase fiber OVER it. SCOPED (2026-07-29, T177/v561): the [C] is relative to a declared branch -- the invariant part of the reading is the leading term arg(rho) = pi/3; the full delta = pi/3 + 3 lambda_C^2 is a branch/frame-relative quantity (it has NO character under the parity/sector involution: a CP-even correction added to a CP-odd angle). The frozen reading itself is untouched (REG.FREEZE.01).
Original classification detail
[E] j(i)=1728 (Z/4) vs j(rho)=0 (Z/6, arg=pi/3); delta=pi/3+3 lam^2 leading term = the hex CM phase; deck stays Z/4, CP is the Z/6 fiber [C]. NOT a CP derivation; scope narrowed: the invariant part is the leading term pi/3, the full delta is branch/frame-relative (T177/v561)
Dependencies as recorded
FLAV.CP.01; QGEO.PILLOW.01; QGEO.KILL.01
Open the original ledger source, row 312Location recorded in the ledger
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- Red-team audit
Sections that explicitly cite this claim
A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.
- 2026-06-16 (the icosahedral bedrock, CM-norm duality, and a structural-finds round)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.
- 2026-06-17 (CP phases as [formula in source] powers — a reduction of red-team Target D)Research changelog; TFPT — Introduction and reading guide
- Charged leptons: completely closed in [formula in source]tfpt 2 standard model
- The unique attractor: a gapped transport selects ONE fixed pointorigin theory
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- Target D — [formula in source]Red-team audit
- OutcomeRed-team audit
- 2026-06-24 (The arithmetic hull + the [formula in source] -character CM duality: v403, v404)Research changelog; TFPT — Introduction and reading guide
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
Registered verification modules
- v220_cp_hexagonal_modulus.pyRegistered verification module · flavor
Read the description recorded in the module registry
CP lives in the HEXAGONAL phase fiber, not the square seam deck (a geometric sharpening of red-team Target D). The seam deck is the SQUARE modulus j(i)=1728, Aut Z/4 (the μ₄ clock); its exceptional partner is the HEX modulus j(ρ)=0, ρ=e^{iπ/3}, Aut Z/6, CM by ℤ[ω], arg(ρ)=π/3. The frozen leading CKM reading δ=π/3+3λ_C²=68.654° (v88) has leading term π/3=arg(ρ); the |Z₂| alternative π/3+2λ_C² is the frozen look-elsewhere trap. The deck stays Z/4 (v215); CP is the Z/6 fiber over it.
- v561_cp_channel_identities.pyRegistered verification module · flavor
Read the description recorded in the module registry
CP.CHANNEL.IDENT.01: the CP channel / invariant identities (T177, contract CP.INVARIANT) — the CP mirror as algebra: the prime-front gauge-degree toolkit turned on the four CP ledger rows, promoted as exact narrowings (no marker moves, no CP derivation claimed): (1) the HEXAGONAL CHANNEL IDENTITY — on the CM unit ρ = e^{iπ/3} the E₈ split 248 = 120+128 has an EXACT fiber realisation, Σ_k ρ^{d_k} = 4ρ (arg = π/3 exactly) and Σ_k ρ^{m_k} = 4 (arg = 0 exactly), with the parity typing forced by integer parity (degrees even ⇒ phase channel SHEET-EVEN, exponents odd ⇒ magnitude channel SHEET-ODD) — consequence: the phase-channel angle is sheet-blind, it carries π/3 but cannot distinguish quark from lepton; mutations break on e^{iπ/5} and on mutated lists; honest caveat wired as a check (reality of the exponent sum alone is not hexagon-specific); (2) ZERO PHASE IN THE MAGNITUDE DATA — arg(∏c) = 0 exactly on both TFPT sectors, and the μ₃ branch group is the kernel because its order divides N_fam = 3 (a μ₄ branch already shifts the phase): the REDTEAM.D.01 residual is a FIBER datum, not a magnitude datum; (3) TIER-1 EMPTINESS by the blindness theorem — both kernels commute with conjugation, so every π/3-carrier is κ-odd and invariant+odd ⇒ Im F = 0: strict invariance is empty on π/3-carriers, per algebra; (4) the FRAME REMOVAL — det(1,d,n) = 21 and Im det(1,d,ρn) = 21 sin(π/3) exactly, the orientation functional homogeneous of degree +1 in the frame normalisation (21 sin(π/3) is FRAME data), and Im(ρ det)/det = Im ρ = sin(π/3) exactly: the invariant core is a fiber datum, the sign a declared orientation (the DUAL.FRAME.01 narrowing); (5) the TWO TIER-2 CHARACTERS — P2 = arg Σρ^{d_k} at (χ(κ),χ(σ)) = (−1,+1), V5 = Im(ρ det)/det at (−1,−1), homomorphisms verified on the full four-group: two INEQUIVALENT invariants carry the same π/3 (the DEGENERATE verdict as algebra), neither frame-coupled — plus the Jarlskog anchor (TFPT CKM rebuild unitary to 1e-41, J = 3.327021e-5 = v88; J passes rephasing/CP-oddness and fails only the π/3-carrier test: the benchmark validates the criterion, the full δ = π/3 + 3λ_C² has no character — the CP.MOD.01 scope narrowing); R1/R2 typed OPEN, REG.FREEZE.01 untouched (25 checks, ~1 s)
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