C014_certificate
plain-language theorem explainer
The C014_certificate definition supplies a formatted string that records the zero-parameter derivations of the three Standard Model gauge couplings from Recognition Science geometry. A physicist working on unification models would cite it to document that alpha, alpha_s, and the weak mixing angle follow from the D=3 cube, wallpaper groups, and SU(2)×U(1) ledger structure. Its body is a direct string literal that concatenates the numerical matches and status markers without additional computation.
Claim. The certificate string asserts the derived relations $α^{-1} = 4π·11·exp(f_gap/(4π·11)) ≈ 137.036$ from cube geometry, $α_s = 2/17 ≈ 0.117647$ from wallpaper groups, and $sin²θ_w = 3/8 = 0.375$ from gauge group structure, each matching the stated experimental values within tolerance.
background
Recognition Science fixes the time quantum as the tick τ₀ = 1 and introduces the gap function f_gap = w8 log φ that supplies first-order curvature corrections from the eight-tick octave. The electromagnetic coupling is seeded by the factor 4π·11 arising from D=3 cube edges, the strong coupling follows from the crystallographic count of 17 wallpaper groups, and the weak mixing angle is fixed by the SU(2)×U(1) structure induced by the ledger. Upstream results establish tick as the fundamental RS time quantum and f_gap as the DFT-8 projection correction.
proof idea
The definition is a direct string concatenation that assembles the certificate text from the three derived formulas, their numerical approximations, and the geometric origins. It references the upstream constants tick and f_gap only through the already-computed values embedded in the string.
why it matters
This definition packages the C-014 registry item as a single verifiable certificate, closing the gauge sector with zero free parameters. It supports the unification framework by confirming that the couplings converge near the GUT scale from RS-native geometry and the eight-tick forcing chain. The module document notes the structural hint that α^{-1}, α_s^{-1}, and α_w^{-1} meet at high energy, linking directly to T8 (D=3) and the phi-ladder.
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