Principal Dynamics: The Physics Regime Extension I

Joshua K. Cliff, 2026 179 pages · 13 chapters · 4 appendices · 110 formal results · 83 proofs · CC BY 4. 0 Overview This volume is the baseline monograph-to-physics bridge for Principal Dynamics. It specializes the domain-neutral foundation of the PD monograph (10. 5281/zenodo. 19334802) to the declared physics regime and proves theorem-bearing reductions to standard physics forms on declared admissible classes. The volume is positioned as a Layer 2 baseline regime extension under the Program Guide's claim taxonomy and EC1–EC8 charter. It does not alter axioms A1–A5 or any proved foundation theorem; it specializes the foundation to physics and closes the minimum bridge obligations required to make that specialization explicit and theorem-bearing. Quantitative closure, frontier closure, and empirical adequacy are routed outward to later regime extensions and a later quantitative-synthesis volume. Baseline-bridge results The following physics-regime targets are closed within the volume on declared admissible classes: Schrödinger / Hilbert / CCR / unitarity at the Hamiltonian-window bridge grade, with local-core CCR, projected Hilbert sector, and Stone-unitary evolution from a self-adjoint Hamiltonian generator. Born rule and observable-functor uniqueness as a trace-form representation on the declared projected Hilbert readout class, with a target-blindness audit of the admissibility predicates. No-signaling for local CPTP/Kraus operations on tensor-product subsystems. Einstein equations as a variational reduction on the declared Lorentzian curvature branch with explicit boundary discipline (compact support or Gibbons–Hawking–York term) and the coupling identification κEH = cₑff⁴/ (16πGₑff). Geodesic, Newtonian, and weak-field gravitational waves as branch-qualified asymptotic specializations. Yang–Mills and Maxwell equations as direct connection-variation bridges, with the spacetime base manifold and corrected configuration domain explicitly distinguished, and current conservation derived via Noether's second theorem. Free-energy dissipation and entropy-gate admissibility budget on declared dissipative branches. Lorentz emergence as capture on the declared connected Lorentz-admissible component satisfying the capture hypotheses, with global hyperbolicity treated as part of the Lorentz-window package. One-generation Standard-Model gauge-sector pattern selection within the declared admissible one-generation compact-connected envelope, with hypercharge rigidity (cubic anomaly identically satisfied; Witten anomaly satisfied by even doublet count) and a target-blindness audit. Routed outward The volume explicitly does not claim, and routes to later regime extensions or to a later quantitative-synthesis volume: Yang–Mills mass gap and confinement closure Standard Model parameter synthesis (couplings, Yukawa matrices, mixing angles, mass spectrum) Family count and generation-multiplicity selection Full Osterwalder–Schrader / Wightman reconstruction Quantum gravity, cosmology, dark sector, and horizon thermodynamics Strict persistence-cost positivity m (τ) > 0 for nontrivial topological sectors Identification of emergent constants (ℏₑff, cₑff, Gₑff, Λₑff) with measured values Benchmark concordance and empirical adequacy Structure Part I (Direct reductions): quantum, gravity, gauge — Schrödinger, Hilbert sector, CCR, unitarity, Born rule, no-signaling; Einstein, geodesic, Newtonian limit, weak-field waves; Yang–Mills, Maxwell, gauge invariance, current conservation, stress–energy. Part II (Closure infrastructure): admissible functionals, coarsening semigroup, thermodynamic / entropy-gate bridge, universality, Lorentz emergence, observable uniqueness. Part III (Selection and integration): gauge-sector selection (factor reduction, weak/color identification, hypercharge rigidity, closure theorem, target-blindness audit), baseline global consistency with explicit dependency audit. Part IV (Residual claims): open bridges, routing destinations, scope boundary. Appendices: canonicality of the Lorentz defect class, gauge-completeness / classification envelope, standard external results, universality verification. Corpus context This volume is part of the Principal Dynamics public corpus governed by the Program Guide. Related volumes: Foundation Monograph: 10. 5281/zenodo. 19334802 Intelligence and Computation Regime Companion: 10. 5281/zenodo. 19334839 Keywords: Principal Dynamics, Physics Regime Extension, monograph-to-physics bridge, baseline regime closure, direct reduction, regime-closure theorem, Schrödinger reduction, Hamiltonian-window unitarity, Hilbert sector, canonical commutation relations, Born rule, no-signaling, Einstein reduction, Yang–Mills bridge, Maxwell, Noether second theorem, free-energy dissipation, entropy-gate admissibility, universality, Lorentz emergence, observable-functor uniqueness, gauge-sector selection, hypercharge rigidity, target-blindness audit