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Cohesion Dynamics (CD)

Paper B4 — Quantum Dynamics from Commit-Based Evolution

Paper B4 demonstrates that quantum dynamics (unitary, Schrödinger-class evolution) emerge as the unique closure-preserving transport law for amplitude states over the discrete spectral basis established in B3. Given discrete amplitude basis and linear superposition (B1), only unitary evolution preserves closure, compatibility, and total amplitude measure across commit cycles under finite tolerance WW.

Key Results:

  • Evolution between commits must preserve closure conditions stabilizing discrete modes; this uniquely determines unitary transformation structure
  • Generic evolution laws destroy closure or violate coherence; only linear, norm-preserving transformations survive substrate constraints
  • Hamiltonians are derived descriptors of stable transport—bookkeeping devices for closure-preserving dynamics, not fundamental operators
  • Time evolution emerges as ordering structure of commit cycles, not primitive background; decoherence corresponds to tolerance violation and partition (AX-PAR)

Epistemic Status: This paper establishes structural origin of quantum dynamics without importing Hamiltonians, energy principles, wave equations, or time-evolution postulates. Dynamics are representationally necessary, not empirically postulated. Enables B5 (measurement and Born rule) by providing evolution framework over which discrete outcomes are weighted.

Substrate Assumption: Assumes quantum-capable substrate (DCC-QM) with finite tolerance, coherence, admissibility, and partition semantics. Cites AX-TOL (tolerance), AX-PAR (partition on violation), AX-SEL (precedence selection), AX-REL (relational evolution).

Paper ID: CD-B4 | Series: B-series (Derived Physics) | Status: Draft | Dependencies: A, M4 (refines), B1–B3, AX-TOL; informed by R-DCC