Conditionality Footer

Dependencies

Framework: the four axioms {S, B, R, C} from Notebook I; AP05 (actualisation creates g, c, time); AP10 (N = 3 spatial dimensions from {C, S, B}); AP09 (complex Hilbert space, Born rule; fermion/boson, ε = electron via The Lock, Edition 04); AP11 (the spacetime spin SU(2) double cover, spin-½ — context only, not the gauge SU(2)); AP15 (the gauge U(1) from Hilbert-space phase freedom, and substrate stiffness λ ≈ 2.15 × 10⁴⁶); AP27 (the gauge SU(2) × U(1)_Y); AP16 (Higgs mechanism = Axiom B, the electroweak breaking pattern); AP20 (Embedding Hypothesis; §4.2 carries the independence of {C, S, B}, fenced KS-P.2).

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

Dependents

AP24 (Residual) — the six faces of ε and the leakage-tolerance reframe on α_em; the three-orientations of §9 here connects to the generation structure AP24 addresses. AP14 (Correction) — Planck-scale corrections must be consistent with SU(3) exact. AP28 (Constant) — G via channel counting; the 6 × 3 spatial face-projections rest on the three-face structure of §2. The Notebook V matter sector — the full fermion content beyond the electron, including the generation-structure derivation AP19’s §9 names as conjecture (D2).

Kill switches engaged

KS-48c (orientation = colour): LIVE — EMPIRICAL. Identifies the SU(3) internal index with face-space orientation.

KS-49b (confinement from isotropy): LIVE — EMPIRICAL. Identifies confinement with substrate-stiffness-enforced isotropy.

KS-50 (SU(3) from non-derivability): LIVE — HARD. Rests on the independence of {C, S, B}, carried at AP20 §4.2 (fenced KS-P.2).

Structural debts owed

D1 (quantitative confinement — string tension from axioms). D2 (generation mass hierarchy m_e : m_μ : m_τ). D3 (running coupling α_s(Q²) from stiffness/isotropy mechanism). All named items; treated as open programmes.

Items held open without claiming debt status

The global structure of the Standard Model gauge group (SU(3) × SU(2) × U(1))/ℤ₆ — this paper derives the Lie algebra structure only. The detailed flavour-structure embedding of the three-generation conjecture into full quark/lepton representation theory — downstream of D2 and Notebook V.