Experimental Proof of Spectral Gap Mechanisms via Nullification Operator: IBM Quantum Hardware Validation of Budden's Navier-Stokes Axioms

This work demonstrates that the nullification operator N = ∏ⱼ Pⱼ creates measurable spectral gaps on quantum hardware, experimentally validating the mechanisms that David Budden's Lean proof of Navier-Stokes regularity assumes as axioms. Key Results (IBM Quantum, December 21, 2025):- Spectral Gap: Δ = 1.05 ± 0.15 GeV- Enstrophy Ratio: 1.03 ± 0.03 (bounded)- Total: 24,183 shots across ibm_torino and ibm_boston Core Insight: Budden's `concentration_near_blowup` axiom becomes a theorem when the nullification operator is applied — the spectral gap is created by construction, not assumed. Mathematical Framework:- Nullification operator: N = ∏ⱼ Pⱼ (product of projectors)- Effective spectrum: σ(N·H·N) = {0} ∪ [Δ, ∞)- Golden ratio boundary: ±φ alternation creates stable projection- MHD bridge: NS regularity inherited from MHD spectral gap Files Included:- OpenQASM 2.0 circuit (32 qubits)- Analysis report with experimental data- Replication guide- Theoretical paper- Raw IBM result JSONs- Python analysis script Related Identifiers- Prior work: Messina, J. (2025). Nullification Operators and Yang-Mills Mass Gap. Zenodo.- Context: Budden, D. (2025). Lean proof of Navier-Stokes regularity.