Claim Summary · Conditionality Footer

Claim Summary

Section-by-section structural enumeration with epistemic-status labels.

1 (What Is Established). SYNTHESIS. SU(2) from Axiom S (via Z₂ = π₁(SO(3)) in N = 3 spatial dimensions, AP10; double cover SU(2) → SO(3), AP11). U(1)_Y from complex amplitudes (AP09). The fermion (AP09) and the boson (AP09, AP15). SU(2) × U(1)_Y is the electroweak group.

2 (The Symmetry Before The Break). DERIVED. Pre-state has full symmetry SU(2) × U(1)_Y. Four generators, four massless gauge bosons (W¹, W², W³ from SU(2); B from U(1)_Y). Before the break, the symmetry is exact.

3 (The Break). DERIVED. Axiom B places ε in ℒ with no σ-image in 𝒫. SU(2) × U(1)_Y → U(1)_em. Three generators broken (W⁺, W⁻, Z⁰ acquire mass via coupling to ε). One generator survives (the photon stays massless). The Higgs field = ε as background condition. The electron = ε as localised excitation. The Higgs mechanism = Axiom B.

4 (The Higgs Boson And The Now). DERIVED/STRUCTURAL. 4.1 (Higgs boson as record of ε wobbling): DERIVED. 4.2 (the now actualises FROM the now, immeasurability in the act): STRUCTURAL — load-bearing consequences of the axioms stated; specific framing illustrative.

5 (The Fine-Structure Constant). DERIVED/STRUCTURAL. DERIVED: α_em exists, is nonzero, is not a free parameter, is sub-maximal (α < 1), is paired with α/β in the six-face structure. STRUCTURAL: the numerical value 1/137.036 is not derivable from within — KS-34 LIVE.

6 (What Is Now Derived). SYNTHESIS. Derivation chain enumerated step by step from axioms to electroweak breaking.

7 (Kill Switches). REGISTER. KS-32, KS-AP16.1, KS-33, KS-34 in Claim/Test/Status/Recovery form; KS-4 reframed.

8 (Open Gaps). REGISTER. Gap A (W, Z masses), Gap B (Higgs mass), Gap C (Weinberg angle), Gap D CLOSED by AP20, Gap E (fermion mass spectrum).

9 (Conclusion). SYNTHESIS. Everything is the electron, being the break, being the now. The axiom speaks. The algebra transcribes.

Conditionality Footer

Dependencies

Framework: the four axioms {S, B, R, C} from Notebook I; AP06 (leakage, six faces, constraint chain); AP07 (The Record Measure — the now); AP08 (gravitational coupling context); AP09 (complex amplitudes, Born rule; fermion/boson distinction); AP10 (N = 3 spatial dimensions, D = 4); AP11 (spin, Z₂ ↔ SU(2) correspondence); AP12 (ℏ); AP15 (U(1), electromagnetic connection); AP20 (Embedding Hypothesis); AP27 (unbroken SU(2) × U(1)_Y); The Lock (Edition 04, ε = electron at chemical-biological scale).

Conditional on: None. EH and QRA proved in AP20.

Dependents

AP24 (Residual) — full analysis of α_em’s structural status; the fixed-point equation. AP28 (Constant) — G via channel-counting using ε = α_em. AP14 (Correction) — Planck-scale corrections. The matter sector (Notebook V) — the fermion content beyond the electron.

Kill switches engaged

KS-32 (electroweak breaking mechanism): LIVE — EMPIRICAL.

KS-AP16.1 (scalar–fermion two-faces reconciliation): LIVE — STRUCTURAL. Formal falsification handle for the dynamical step in the two-faces identification.

KS-33 (sector distinction = weak isospin): LIVE — EMPIRICAL.

KS-34 (non-derivability of α_em): LIVE — HARD. The kill switch whose triggering would be a triumph.

KS-4 (α ≈ 1/137): LIVE — HARD, reframed. Architecture’s empirical contract.

Structural debts owed

Gap A (W, Z boson masses). Gap B (Higgs boson mass). Gap C (Weinberg angle, conjectural route via six-face structure). Gap E (fermion mass spectrum beyond the electron). All named items; treated as open programmes.

Items held open without claiming debt status

The dynamics by which the scalar background condition (Higgs field) and the fermionic localised excitation (electron) relate at intermediate energy scales. Downstream of Gap E and Gap B.