A Discrete Information-Theoretic Model of Physics on a Space-Cell Substrate: Local Update Dynamics, Event-Based Time, Continuum Limits, and Candidate Geometric Realizations
Abstract
Abstract This paper develops a discrete information-theoretic framework in which physical systems are modeled on a graph or lattice of locally interacting space cells. Its principal contribution is an integrated architecture separating exact consequences of locality and unitarity, continuum-limit derivations, model-family results, toy-model mechanisms, and unresolved physical mappings. Matter-like identity is treated as propagated relational information rather than persistence of the same occupied cells, and candidate mechanisms are audited for causal locality, conservation or ledger closure, and false reconstruction. The quantum branch assumes finite-dimensional local Hilbert spaces and local unitary or completely positive trace-preserving (CPTP) updates. Under those assumptions, norm preservation, finite causal cones, and reduced-state no-signaling follow directly; spinor quantum walks admit a Dirac-like long-wavelength limit and a secondary nonrelativistic Schrödinger envelope. A representative reciprocal q–χ lattice action shows how compact local dynamics can support continuity, spectral response, action-derived scattering, and internal symmetry/charge, while later extensions supply a provisional local gauge/Gauss/holonomy structure. Two geometric realizations remain deliberately distinct: distortable cells and scalar extrinsic-χ compression. Toy models provide mechanism and failure-boundary evidence for relational identity, reconstruction, scattering, photon-like…
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