Paper G2 — Emergent Distance
Paper G2 demonstrates that spatial distance emerges as a representational necessity from Cohesion Dynamics substrate mechanics. Building on emergent time (G1), it shows that distance is not a primitive geometric property or background metric, but the minimal scalar required to consistently represent propagation delay between closure events in a cohesive substrate.
Key Results:
- Distance arises from finite propagation of constraint influence through substrate, commit-based closure cycles requiring sequential propagation, and tolerance-bounded admissibility
- Distance is forced as unique stable bookkeeping quantity for ordering interactions when time exists but spatial separation must be representable
- Additive along propagation chains, symmetric in absence of gradients, necessarily scalar before geometric structure (G3) emerges
- Distance is minimal number of closure cycles required for influence to propagate between regions—a derived measure of causal separation
Ontological Status: Distance does not exist in substrate. What exists are discrete closure events (G1), finite propagation of admissible state transitions, tolerance-bounded constraint resolution domains, and causal ordering through sequential commits. Representationally, distance is pure bookkeeping for propagation delay, not substance.
Scope: Derivation proceeds exclusively from CD primitives and G1 results. No spatial manifolds, coordinate systems, or metric structures assumed. Distance emerges independently of geometric embedding; geometry, angles, dimensions, curvature follow in G3–G4.
Paper ID: CD-G2 | Series: G-series (Gravity and Geometry Derivation) | Status: Draft | Dependencies: A, M1–M4, G1, AX-TOL, AX-COH, AX-REL, AX-ADM; informed by R-DCC