Reconstruction Before Dynamics: A Premetric Framework for Selecting Physical Laws

Abstract

Why do the laws represented by the Standard Model and general relativity have their observed forms, and why do their particular symmetry groups and numerical inputs occur? The reconstruction program proposes that these structures arise from a premetric selection layer logically prior to dynamical evolution. This article develops the laws side of that program as a conditional physical reconstruction framework with a theorem-level mathematical core. It is neither a replacement for established post-read-out physics nor a completed theory of quantum gravity. The Indefinite Reconstruction Stability Principle (IRSP) is formulated as an existence condition: once an observable quotient and a class of admissible continuations have been declared, a candidate physical identity cannot depend on an unread representative or on an arbitrary terminal refinement. A structure that fails this requirement may be an intermediate mathematical configuration, but it is not a reconstruction-independent physical identity. This persistence is not temporal immortality: unstable particles and other transient systems remain admissible when their identities and changes are unambiguously readable. An exact descent theorem formalizes representative independence. A single neutral parent, understood as a common premetric archetype rather than an additional particle, then organizes the conditional read-out bridges. Primitive complement readability, compact scalar return, and smooth holonomy yield codimension-two loop structure and a local U(1) connection. A continuum stability implementation of IRSP forces real-root hyperbolicity, while a separate full-dimensional reciprocal-response bridge supplies a nondegenerate quadratic principal form and hence Lorentzian signature with one temporal direction. Conformal descent of the reconstructed curvature two-form independently fixes the total dimension to four. On the selected (3+1)-dimensional platform, gauge invariance and nativeness yield a source-free Abelian Maxwell law, while a readable metric scale yields Einstein–Hilbert dynamics at leading order. A separate conditional 3+2 internal read-out selects S(U(3)×U(2)), equivalently, the Standard Model gauge group with maximal Z6 quotient. These results are conditional on explicitly audited bridges. Reconstruction may consequently offer quantum-gravity programs, including string theory, an additional persistence-and-read-out filter on candidate microscopic phases or vacua; applying that filter to solve the landscape problem remains an open program rather than a result established here.