GoE - Genesis of Existence: The Axiomatic Observer V.41

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 experience1 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 derives finite descriptive depth: exact η = 0 precision is excluded, setting a positive resolution floor for finite observers while rate-pricing infinite refinement. 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. Supercritical DM-III eruptions should generate anomalous transient energetic bursts lacking binary chirps. Finite particle-lifetime families admit exact factor-graph compilation and certified truncation. Numerically, GoE gives 1/α = 137.03599917798026, the calibrated strong node αs_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.