M4 — Phase, Path, and Coherence Structure

M4 formalizes the emergence of phase, path, interference, coherence, and decoherence within Cohesion Dynamics, building on ontological and structural results of M1–M3. Does not introduce quantum mechanics, Hilbert space, amplitudes, probabilities, or linear dynamics. Its role is to identify and formalize the pre-quantum relational structures that make quantum-like behavior possible in later stages.

Key Definitions:

• Phase as relational property of constraint resolution cycles (closure-cycle alignment between interacting CIUs)
• Paths as admissible realization histories of unresolved constraints (not spatial trajectories or worldlines)
• Interference as recombination of compatible realizations
• Coherence as tolerance-limited compatibility
• Decoherence as tolerance violation with provenance partition

Structural Foundation: When a constraint admits multiple equally admissible mismatch-reducing realizations, by divergence axiom, all realizations are committed. These are candidate resolution trajectories of the same unresolved interaction. Multiple paths may coexist so long as they remain mutually admissible under tolerance structure.

Paper ID: CD-M4 | Series: M-series (Formal Mechanisms) | Status: Draft | Dependencies: M1–M3