Open Gaps

Gap A: W and Z boson masses. The argument derives that three gauge bosons acquire mass and one stays massless. It does not yet derive the specific values m_W ≈ 80.4 GeV, m_Z ≈ 91.2 GeV. These depend on the coupling constants g and g′ of SU(2) and U(1)_Y, and the vacuum expectation value v. v is the energy scale of the break. Derivation requires the detailed structure of ε at the electroweak scale. Depends on: Gap E (mass spectrum).

Gap B: The Higgs boson mass (∼ 125 GeV). The mass of the Higgs excitation depends on the self-coupling of the break. m_H = √(2λ)v. The self-coupling of ε — how strongly the break interacts with itself — is determined by the structure, but the value is not yet computed. Depends on: Gap A (coupling constants), Gap E (mass spectrum), α_em constraint chain.

Gap C: The Weinberg angle θ_W. The mixing angle between SU(2) and U(1)_Y determines the relationship between W and Z masses and the electromagnetic coupling. sin²θ_W ≈ 0.231. This angle measures how SU(2) and U(1)_Y combine in the break. Conjectural route: it may be derivable from the six-face structure — specifically, the angle between Pair 1 (gravity/quantum) and Pair 2 (stiffness/coupling) in AP06 section 10.5. This is a target for future work. Depends on: Gap A, detailed structure of the breaking pattern at the electroweak scale.

Gap D: EH. CLOSED. The Embedding Hypothesis was proved in AP20.

Gap E: The fermion mass spectrum. The electron mass m_e is derived as the self-coupling of the break — the minimum viable splinter. Other fermion masses (muon, tau, quarks) arise from ε-compositions at higher energy scales. The derivation of the full mass spectrum from the axioms is an open programme. Required for: Gap A (boson masses), Gap B (Higgs mass), computation of α_em via the fixed-point equation (AP24 section 5.6).