Principal Dynamics: The Physics Regime Extension I

Physics Regime Extension, Volume I Joshua K. Cliff, 2026 143 pages · 12 chapters · 9 appendices · CC BY 4.0 Overview This volume is the first volume of the physics regime extension to the Principal Dynamics foundation monograph (10.5281/zenodo.19334803). It specializes the domain-neutral PD foundation to the declared physics regime and closes only the baseline bridge obligations that the monograph defers to the regime-extension program. Extension I is a monograph-to-physics bridge volume, not a mature domain compendium. It retains two kinds of result: direct physics-regime reductions needed to make the monograph-to-physics bridge explicit, and the minimum regime-closure machinery needed to make that bridge theorem-bearing on the declared class. Every theorem is either a direct specialization of a monograph result or a consequence of such specializations composed with explicitly stated regime work internal to this volume. In the realization-layer architecture of the monograph, this extension is geometric-dominant: the main theorem chain proceeds through the analytic/geometric realization developed under KR1–KR6 and bounded geometry. Direct Reductions (Part I) The Coherence Transformation Equation, specialized to the physics regime window, reproduces the baseline equations and structures of quantum mechanics, gravity, and gauge theory as direct reductions: Schrödinger dynamics, Hilbert-space structure, canonical commutation relations, unitarity, Born-rule reduction, no-signaling, Einstein and geodesic reductions, the Newtonian and weak-wave limits, Yang–Mills reduction, and the low-order scalar/Yukawa datum needed by the retained gauge-selection chapter. Baseline Regime Closure (Part II) The minimum closure machinery needed to stabilize the baseline bridge: admissible functionals, coarsening and obstruction control, universality support on the declared admissible component, Lorentz emergence, observable-functor uniqueness, gauge-sector selection, and global consistency / non-conflict with the frozen monograph. Claim Boundary and Extension Routing (Part III) Volume 1 closes 6 of 8 monograph physics targets. The two remaining targets — Yang–Mills mass-gap / confinement closure and Standard Model parameter synthesis — are routed explicitly to dedicated regime monographs and a later Volume 2 synthesis. Every open bridge is named and routed to a specific later regime extension with an authoritative charter position. What Is Not Claimed No benchmark concordance, executed-row claim, or empirical adequacy claim is made in this volume. Yang–Mills mass-gap / confinement closure is deferred to the gauge regime extension. Standard Model parameters are deferred to later extensions and a Volume 2 integrated synthesis. Gravity-side closure beyond the retained direct Einstein / geodesic / weak-field bridge is deferred. Quantum-mechanical closure beyond the retained Schrödinger / Born / observable bridge is deferred. Family count, quantitative parameter synthesis, mixed quantum–gravity, cosmology, dark-sector, and black-hole / horizon closure are all routed to dedicated regime monographs. All results are branch-qualified: they hold on the declared admissible class and canonical branch. Related Volumes Foundation Monograph: 10.5281/zenodo.19334803 Intelligence and Computation Regime Extension: 10.5281/zenodo.19334839 Keywords: Principal Dynamics, physics regime, baseline bridge, quantum mechanics, gravity, gauge theory, Lorentz emergence, observable uniqueness, gauge selection, regime extension