Deriving Atomic Shell Capacity via Classical Harmonic Resonance and Nyquist–Shannon Information Limits

Reinterprets the 2n² electron shell capacity rule as a Rank‑0 informational projection from the ICF constraint surface, derived entirely from classical harmonic resonance, geometric tessellation, and binary capacity collapse governed by Nyquist–Shannon and Landauer limits. Demonstrates that the standard quantum numbers (n, ℓ, m, s) are emergent geometric/informational constraints rather than fundamental quantum axioms. Key Claims (from document): “Physical matter and spacetime are not foundational; they are lower‑dimensional projections emergent from a deeper informational substrate.” “The ‘Pauli Exclusion Principle’ is revealed to be a purely thermodynamic phase‑lock.” Verification: Includes a fully reproducible Python engine demonstrating that the Rank‑0 informational boundary naturally outputs the canonical shell capacities [2, 8, 18, 32] without invoking quantum mechanical operators or Planck‑scale constants.