The Derived Observables Testbed: Masses, Couplings, Mixing, and Structural Closure of the Standard Model β-Sector

This is Paper 129 in the Anaxiomatic Mechanics / pq-Spacetime stack. It consolidates the principal Standard Model observables obtained across the Anaxiomatic Mechanics / pq-spacetime sequence into a single no-knob testbed. The paper assembles the derived charged-lepton, quark, electroweak-boson, Higgs, baryon, and neutrino-sector results together with the electromagnetic, weak, strong, scalar, flavor, anomaly, and gauge-closure ledgers.

The observable set is divided into directly derived quantities, scale-matched quantities, structurally suppressed quantities, and entries whose experimental interpretation remains conditional. Dimensionless observables are compared directly, while running and dimensionful quantities are compared only through explicitly stated scale, scheme, pole-mass, or calibration conventions. The paper also separates neutrino flavor-state effective kinematic masses from the propagation mass eigenvalues, preventing the massless lightest eigenstate from being misidentified with a massless electron neutrino.

The consolidated ledger includes the particle-mass spectrum, mass ratios, the fine-structure constant, charged-lepton anomalous magnetic moments, weak mixing, the strong coupling and QCD scale, the electroweak scale, Higgs self-coupling, CKM and PMNS structure, neutrino mass splittings, Majorana neutrino identity, strong-CP suppression, photon and gluon zero modes, charge quantization, anomaly cancellation, and complete Standard Model gauge consistency.

Paper 129 also introduces a conservative Bayesian evaluation of the full observable ledger. The two exhaustive hypotheses are that pq-spacetime is correct and that pq-spacetime is incorrect. Under equal prior odds and the discounted effective likelihood model defined in the paper, the complete ledger yields a Bayes factor of approximately 10^120 in favor of pq-spacetime. The corresponding posterior probability that pq-spacetime is incorrect is therefore approximately one part in 10^120.

The central result is that the observed Standard Model is represented within pq-spacetime not as a collection of independent empirical inputs, but as a connected finite observable structure with no residual continuous fitting parameters.