Reconstruction Before Dynamics: A Premetric Framework for Selecting Physical Laws

Why do the laws represented by the Standard Model and general relativity have their observed forms, why do their particular symmetry groups govern physical interactions, and why do particular constants and ratios enter them? The reconstruction program proposes that these laws, symmetries, and numerical parameters originate in a premetric selection layer logically prior to dynamical evolution in time. Earlier applications showed that invariant reconstruction structures can produce quantitative predictions for constants and particle ratios. This article develops the complementary laws side of the program. Reconstruction is not proposed as a replacement for the Standard Model or general relativity. Its role is to select persistent physical identities and a shared read-out platform—a structured, non-empty vacuum support equipped with the causal geometry, phase-comparison structure, and internal-comparison data on which those effective theories operate. The Indefinite Reconstruction Stability Principle ("IRSP") requires protected identities and readable relations to survive every admissible continuation and requires physical conclusions to be independent of arbitrary unread choices. A single neutral parent, understood as a common premetric archetype rather than an additional particle, organizes the resulting read-out channels. For a localized identity to qualify as physically existent, IRSP requires it to remain readable from its complement through a primitive closed detector; together with the primitive-loop and smooth-holonomy bridges, this existence condition selects codimension-two loop-readable structure and a local U(1) connection. The central geometric result is then the conditional selection of a (3 + 1)-dimensional Lorentzian read-out platform. Continuum IRSP and full-dimensional reciprocal response select Lorentzian signature and one temporal direction, while the resulting curvature two-form and conformal descent independently fix the total spacetime dimension to four. On the selected platform, gauge invariance and nativeness yield a source-free Abelian Maxwell law, while readable metric scale yields Einstein–Hilbert dynamics at leading order. A separate conditional internal 3 + 2 read-out selects the global Standard Model gauge group SU(3) × SU(2) × U(1) with its maximal Z6 quotient. Laws and constants thereby become complementary outputs of one prior architecture, while the Standard Model and general relativity remain the indispensable effective theories after read-out.

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Publication Details

Journal
Symmetry
Published
2026-08-24
DOI
https://doi.org/10.3390/sym18091420
Primary Topic
Noncommutative and Quantum Gravity Theories
Type
article
Field-Weighted Citation Impact
0.00
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article

Reconstruction Before Dynamics: A Premetric Framework for Selecting Physical Laws

Bin Li
Symmetry
Noncommutative and Quantum Gravity Theories
article

Reconstruction Before Dynamics: A Premetric Framework for Selecting Physical Laws

Bin Li
article en

Abstract

Why do the laws represented by the Standard Model and general relativity have their observed forms, why do their particular symmetry groups govern physical interactions, and why do particular constants and ratios enter them? The reconstruction program proposes that these laws, symmetries, and numerical parameters originate in a premetric selection layer logically prior to dynamical evolution in time. Earlier applications showed that invariant reconstruction structures can produce quantitative predictions for constants and particle ratios. This article develops the complementary laws side of the program. Reconstruction is not proposed as a replacement for the Standard Model or general relativity. Its role is to select persistent physical identities and a shared read-out platform—a structured, non-empty vacuum support equipped with the causal geometry, phase-comparison structure, and internal-comparison data on which those effective theories operate. The Indefinite Reconstruction Stability Principle ("IRSP") requires protected identities and readable relations to survive every admissible continuation and requires physical conclusions to be independent of arbitrary unread choices. A single neutral parent, understood as a common premetric archetype rather than an additional particle, organizes the resulting read-out channels. For a localized identity to qualify as physically existent, IRSP requires it to remain readable from its complement through a primitive closed detector; together with the primitive-loop and smooth-holonomy bridges, this existence condition selects codimension-two loop-readable structure and a local U(1) connection. The central geometric result is then the conditional selection of a (3 + 1)-dimensional Lorentzian read-out platform. Continuum IRSP and full-dimensional reciprocal response select Lorentzian signature and one temporal direction, while the resulting curvature two-form and conformal descent independently fix the total spacetime dimension to four. On the selected platform, gauge invariance and nativeness yield a source-free Abelian Maxwell law, while readable metric scale yields Einstein–Hilbert dynamics at leading order. A separate conditional internal 3 + 2 read-out selects the global Standard Model gauge group SU(3) × SU(2) × U(1) with its maximal Z6 quotient. Laws and constants thereby become complementary outputs of one prior architecture, while the Standard Model and general relativity remain the indispensable effective theories after read-out.

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