The Nabla Lune Operator A Resonant Differential Extension of Lorentz Invariance and a Certified Constraint Proof of the Collatz Conjecture

The Nabla Lune Operator: A Resonant Differential Extension of Lorentz Invariance and a Certified Constraint Proof of the Collatz Conjecture This deposit presents the verified mathematical and computational proof structure linking the Collatz Conjecture to harmonic curvature dynamics within the Lunecitic Framework. The accompanying artifacts include the verified constraint sets (constraints.smt2, constraints.json), solver certificates (online_sat.json, certificate_A_14_B_6_K4.json), provenance manifests, and resonance parameter data that confirm the boundedness and contraction criteria derived from the Nabla Lune Operator. These results unify discrete dynamical contraction mappings with continuous Lorentz-harmonic curvature under the extended differential operator $\nablal$, establishing a reproducible bridge between number-theoretic and relativistic invariants. The mathematical formulation is detailed in the associated paper, The Nabla Lune Operator: A Resonant Differential Extension of Lorentz Invariance, DOI 10.5281/zenodo.17292931. Data and Code Availability:The verification artifacts and summary scripts provided here are released for independent validation and citation. Core engine components (constraint generator, resonance synthesis modules, and Lunecitic Engine libraries) remain proprietary. Related works:– Harte (2025), The Lunecitic Framework™: Reconciling the Hubble Tension via a Lunic Projection of Space Time, Zenodo 10.5281/zenodo.17216399– Harte (2025), Beyond the Stiffness Limit: Resonant Metrics, Delay Compression, and Superluminal Transit in the Lunecitic Framework™, Zenodo 10.5281/zenodo.17180352– Harte (2025), The Lunecitic Lens: A Framework for Parsimony in Quantum and Relativistic Systems, Zenodo 10.5281/zenodo.17249805 Keywords: Collatz Conjecture, Certified Proof, Constraint Verification, SMT Solver, Z3, Number Theory, Resonant Geometry, Lorentz Invariance, Lunecitic Framework, Nabla Lune Operator, Mathematical Physics, Computational Proof, Open Verification. Correspondence: Shane A. J. Harte — [email protected] | psychotherapy.harteessence.ie