ChronoCell: A Discrete Substrate Theory of Emergent Gravity and Matter

ChronoCell: A Discrete Substrate Theory of Emergent Gravity and Matter ChronoCell is a foundational theoretical framework in which gravity, matter, horizons, and gauge fields emerge operationally from the local synchronization dynamics of a discrete cellular substrate. The theory replaces a continuous spacetime manifold with a neighborhood graph G = (V, E) of interacting vacuum cells. Each cell carries an internal cycle characterized by a rhythm τ (cycle duration) and a phase φ (cycle position). Physical space is identified with graph connectivity, while time is defined operationally as accumulation of local cycles. An ideal synchronized configuration (τ_i = τ_0, φ_i = const) serves as a reference state with no operational observables. Physics begins when synchronization fails beyond a finite communication threshold ε_sync, producing persistent inhomogeneities of the rhythm field τ(x). These inhomogeneities define: • energy as mismatch cost, • mass as persistent localized energy (m = E / c²), • an irreversible arrow of time as a consequence of locality and relaxation. Gravitation arises without postulating geometric spacetime curvature. A rhythm-based redshift factor is defined as Z = τ / τ_inf, with an associated potential ψ = ln(τ / τ_inf). In the weak-field regime this yields an effective gravitational potential Φ = −c² ψ and acceleration g = −∇Φ, reproducing Newtonian dynamics and gravitational time dilation. Horizons are defined operationally as loss of connectivity in the viable-communication subgraph G_ok, rather than as spacetime singularities. Matter is described as stable topological defects of the phase field (vortex loops) carrying quantized winding q ∈ Z and exhibiting a finite stable size R*. Gauge fields emerge from phase differences on graph edges via a discrete exterior calculus formulation, reproducing Maxwell-type dynamics in the long-wavelength limit. This Zenodo record contains: • The complete Master Theory document (Chapters 1–11), defining the ontology, emergent dynamics, and validation gates. • Supplementary Appendices with geometric realizations, discrete calculus tools, and a detailed simulation and falsification roadmap. ChronoCell is designed to be empirically testable and falsifiable, with explicit validation protocols for gravity, electrodynamics, defects, and horizon formation.