Emergent Gauge Structure and Gravitational Response in a Scalar Lattice Model: A First-Principles Account from Microstructure to the Classical World

Modern physics typically begins by postulating the field content of the Standard Model and the spacetime geometry of General Relativity. This monograph instead adopts a single microscopic ontology: the vacuum is a stable phase of one complex microfield defined on a lattice.

The central result is that this minimal one-medium framework is sufficient to generate the known phenomenology of physics without introducing separate fundamental photons, fermions, or metric fields. Matter appears as stable, localized twist-defects (motifs) in the medium. Forces arise as long-distance constraints imposed by the medium’s equilibrium structure, manifesting as induced gauge and texture sectors.

Within this framework, dimensionless constants are not assumed or fitted but calculated from lattice geometry and internal stability constraints. In particular, the fine-structure constant is computed from first principles, yielding a definite numerical value in close agreement with the observed constant.

Quantum mechanics and gravitation are not treated as independent frameworks, but as complementary limiting descriptions of the same underlying equilibrium state. Vacuum selection, particle hierarchy, and gravitational response are computed end-to-end from internal consistency constraints, with explicit unit anchors introduced only to relate dimensionless results to physical units.

This document presents the full formal specification of the framework, including derivation ledgers, numerical tests, and falsifiable predictions. It is intended to be read as an auditable construction rather than a pedagogical narrative.

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