Paper B3 — Spectral Discreteness from Closure Stability
Paper B3 demonstrates that discrete spectra (quantisation) emerge as a representational necessity for cohesive substrates governed by commit-based closure and finite tolerance . Only discrete mode configurations admit stable, repeatable closure, while continuous configurations generically fail closure and cannot persist as representable states.
Key Results:
- Quantisation is not a boundary condition or empirical postulate—it is a selection effect imposed by closure stability
- Closure requires global compatibility satisfaction, generically met only at isolated points in parameter space forming discrete families indexed by integers
- Continuous spectra exhibit structural instability: small perturbations accumulate mismatch across commit cycles, preventing repeatable closure
- Discrete modes correspond to configurations where closure conditions are exactly satisfied, enabling stable reconstruction and persistent identity
Epistemic Status: Establishes structural origin of quantisation without importing quantum axioms, eigenvalue problems, Hamiltonians, or energy minimization principles. Discreteness forced by tolerance-limited admissibility, not imposed by measurement or boundary conditions. Enables B4 (dynamics over discrete spectral bases) and B5 (outcome weighting).
Substrate Assumption: Quantum-capable substrate (DCC-QM). Cites AX-TOL (tolerance).
Paper ID: CD-B3 | Series: B-series (Derived Physics) | Status: Draft | Dependencies: A, M3 (refines), M4 (refines), B1–B2, AX-TOL; informed by R-DCC