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Cohesion Dynamics (CD)

Paper B1 — Emergence of Quantum State Representation

Paper B1 demonstrates that linear amplitude-based state representation is a representational necessity for cohesive substrates exhibiting mergeable divergent histories under finite tolerance WW. Any representational calculus capable of faithfully tracking substrate evolution through branching constraint resolution paths must employ a linear composition rule, derived from substrate mechanics (A) and formal mechanisms (M1–M4) without importing quantum axioms.

Key Results:

  • Amplitudes emerge as bookkeeping objects for compatibility and provenance relationships between uncommitted substrate alternatives
  • Linearity is forced by consistency requirements: regrouping, associativity, invariance under history reordering
  • Resulting amplitude space is minimal structure required to represent substrate behavior prior to entanglement, spectral discreteness, dynamics, or measurement

Epistemic Status: Establishes what a quantum state is as a representational object. Does not yet explain why states evolve (B4), why spectra are discrete (B3), how composite systems factor (B2), or how outcomes are weighted (B5)—those follow in subsequent B-series papers.

Substrate Assumption: Quantum-capable substrate (DCC-QM). Cites AX-REL (relational evolution), AX-TOL (tolerance), AX-COH (cohesive units), AX-PAR (partition), AX-ADM (admissible moves), AX-SEL (precedence), AX-MEM (persistence).

Paper ID: CD-B1 | Series: B-series (Derived Physics) | Status: Draft | Dependencies: A, M1–M4 (refines), AX-TOL; informed by R-DCC