Physics as the Topology of a Non-Invertible Projection

A single structural condition — a globally conserved Noether flow under restricted accessibility — forces by necessity, without additional input, the Majorana bulk field, the rank-5 non-invertible projection, and the representational manifold ℝ⁴ × S¹ (τ). The physical mechanism: the conserved flow carries a compact internal phase χ ∈ S¹, the zero mode. At the projection interface this zero mode becomes evanescent. What does not cross does not disappear — it returns as boundary tension λ|Ψ|^ (4/3) and as the discrete invariant structure of the observable world. From this single evanescent zero mode, with no free parameters, emerge: the fine-structure constant α⁻¹ = (F₅ + F₄√5) ² = (5 + 3√5) ² ≈ 137. 08, the gauge group U (1) × SU (2) × SU (3), the Weinberg angle sin²θW = 3/13 (unconditional theorem), charge quantisation 6Q ∈ ℤ, the discrete coherence renormalisation law B₊+₁ = 2Bₖ^2/3, and time as the irreversible ordering of coherence loss. The absolute dimensional scale belongs to ker (Π*) by a model-independent structural theorem (DOI: 10. 5281/zenodo. 19402305). A single external anchor is necessary and sufficient: R∞. The spectral factor Fₙm = (2√5) ^ (5/2) φ²/ (9π²) closes the dimensional cascade R∞ → f_τ → R₅ → G → ℓP → TCMB (P13, DOI: 10. 5281/zenodo. 19392738). This is the axiomatic foundation of the QGT series. Editorial revision (April 2026): citation keys, level labels, internal cross-references, and abstract language aligned with closed results.