Skip to main content

A registered result in its source context

Original ledger classification: Identity (exact)

Recorded statement: DEGREE/EXPONENT CHANNEL SPLIT (2026-06-16): 248=120+128 as a magnitude/phase channel typing (replaces the over-strong 'S^- is dark matter'). E8 exponents {1,7,11,13,17,19,23,29} sum=120=|R^+(E8)| (MAGNITUDE channel: positive roots/root…

Statement, assumptions and sources

Paper context: Red-team audit

The exact identifier, original classification and full claim are available below.

The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.

Read the exact registered claim and its dependencies

E8.CHAN.01

Original ledger classification: Identity (exact)

Original claim text

DEGREE/EXPONENT CHANNEL SPLIT (2026-06-16): 248=120+128 as a magnitude/phase channel typing (replaces the over-strong 'S^- is dark matter'). E8 exponents {1,7,11,13,17,19,23,29} sum=120=|R^+(E8)| (MAGNITUDE channel: positive roots/root transitions); E8 degrees {2,8,12,14,18,20,24,30} sum=128=2^(rank-1)=rank*dim S^+ (PHASE/GLUE channel); 248=120+128=adj(D8)+spinor(D8); sum(deg)-sum(exp)=rank=8. The (ratios,product) magnitude bijection (Target D) lives in the 120 channel, the un-covered CP phases in the 128 phase/glue channel; whether 128 hosts a dark sector is Frontier (NOT asserted). STRENGTHENED on the fiber (2026-07-29, T177/v561): the channel typing has an EXACT hexagonal realisation -- sum_k rho^{d_k} = 4 rho (arg = pi/3 exactly) and sum_k rho^{m_k} = 4 (arg = 0 exactly) on the CM unit rho = e^{i pi/3} -- with a parity typing forced by integer parity: all degrees are EVEN (phase channel SHEET-EVEN under rho -> rho^4), all exponents ODD (magnitude channel SHEET-ODD). CONSEQUENCE: the phase-channel angle is sheet-blind -- it carries pi/3 but cannot distinguish quark from lepton (not the CP.MU6.01 sheet split). Honest caveat: reality of the exponent sum alone is not hexagon-specific; only the degree half (= 4 rho) is. The channel typing stays [C].

Original classification detail

[E] 248=120+128, exponents sum 120=|R^+(E8)|, degrees sum 128=rank*dim S^+; magnitude channel 120 / phase channel 128 [C]; dark-sector reading [O]; exact hexagonal realisation sum rho^{d_k}=4rho (arg pi/3, sheet-even) vs sum rho^{m_k}=4 (arg 0, sheet-odd) [E] -- the phase-channel angle is sheet-blind (T177/v561)

Dependencies as recorded

E8.CAS.01; FLAV.CP.01

Open the original ledger source, row 309

Location recorded in the ledger

These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.

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.

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.

Registered verification modules

  • v227_degree_exponent_channel_split.pyRegistered verification module · core
    Read the description recorded in the module registry

    248=120+128 as a magnitude/phase channel typing (replaces the over-strong S⁻-dark-matter reading). E₈ exponents {1,7,11,13,17,19,23,29} sum 120=|R⁺(E₈)| (MAGNITUDE channel); E₈ degrees {2,8,12,14,18,20,24,30} sum 128=2^(rank−1)=rank·dim S⁺ (PHASE/GLUE channel); 248=120+128=adj(D₈)+spinor(D₈); deg−exp sum=rank=8. Ratios+products (Target D) live in 120, the un-covered CP phases in 128; the dark-sector reading of 128 stays Frontier.

  • 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)

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.