Length-Mass Reduction (LMR) Theory: Paper III — Emergence and Structure

This paper develops the emergence and structural framework of Length–Mass Reduction (LMR) Theory, a predynamical geometric formalism in which physical quantities arise from routing and admissibility within a constrained lattice grammar. Building on the codex foundations established in Paper I and the lattice and persistence framework of Paper II, this work formalizes the structural emergence of stable configurations, including electron, proton, and neutron constructions, without recourse to force laws or dynamical evolution. Central to this treatment are half-fold (HF) configurations, π-torsion bookkeeping, and the distinction between intrinsic structure, interface admissibility, and lattice routing. The proton is treated as a reflective resonator with multiple admissible interface facings, while the neutron is constructed as a torsion-bound composite enforcing interior neutrality. The paper introduces a strict separation between structural invariants and observer-side overlays, maintaining a predynamical framework in which admissibility, normalization, and routing determine persistence. This work serves as the structural bridge toward electromagnetic and gravitational treatments in subsequent papers. Supplement S1 provides interpretive routing-mode correspondences for phenomenological mapping. These interpretations are explicitly non-mechanistic and are not part of the core LMR structure.