GoE - Genesis of Existence: The Axiomatic Observer V.40

GoE is an axiomatic mathematical-logical framework operating as a generative grammar whose compiled syntactic structures admit isomorphisms to experimental inputs. Its foundation is the Cartesian cogito greatest-fixed-point assertion ”at least one experience occurs” made without presupposing a spacetime manifold, a Hilbert space, a Platonic or Tegmarkian mathematical realm, Wheeler-style pregeometry, Anaximander’s Apeiron, a meta-place, or any ontology/anti-ontology. Instead of Everett-style branching, GoE selects a sparse admissible continuation structure inside syntactic generation. The same first-principles closure yields a generalized Mach-rigidity theorem: absolute local inertia exists precisely on background classes with constant GoE inertial generator, and the classical Mach principle is recovered as the manifest-boundary shadow; it also establishes finite descriptive depth and its capacity–resolution duality: exact η = 0 certification is excluded pointwise for every Observer, finite-capacity manifest classes have a positive resolution floor, and infinite-capacity refinement is rate-priced rather than free, while lateral scope remains unbounded. Experimental inputs navigate admissible continuations; GoE is therefore an engineering-grade “Theory of Everything” only in the restricted sense that “Everything” denotes admissible structures generated by the construction, not a presupposed ontology; objectivity is not assumed but emerges from the cogito-side closure. Numerically, GoE gives 1/α = 137.03599917798026, the calibrated strong node α_s,G ≃ 0.330001, six CODATA-2022/NIST mass-ratio audits with fractional mean central residual Err6 ≃ 1.55 × 10^−10, W-boson mass spectral branches, four lepton-lifetime/charged-current central predictions within current experimental resolution, and the Structural Evolution Budget = 46.230864254961 Gyr.