Published October 8, 2025 | Version v1.1
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The Nabla Lune Operator A Resonant Differential Extension of Lorentz Invariance and a Certified Constraint Proof of the Collatz Conjecture

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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 — harteessence@outlook.com | psychotherapy.harteessence.ie

Notes

This work presents a certified computational proof of the Collatz Conjecture using the Lunecitic Framework and the Nabla Lune Operator, establishing a resonant extension of Lorentz invariance that unifies discrete dynamical mappings with continuous harmonic curvature. Verified through constraint solvers and open mathematical artifacts, it bridges number theory, differential geometry, and theoretical physics—demonstrating a reproducible pathway from computational proof to physical law.

This release provides the verified proof artifacts and publication files associated with The Nabla Lune Operator: A Resonant Differential Extension of Lorentz Invariance and a Certified Constraint Proof of the Collatz Conjecture (DOI: 10.5281/zenodo.17292931).

All shared data, figures, and verification scripts are provided to enable transparent and independent verification of the proof results.

The underlying Lunecitic Engine, resonance synthesis modules, and constraint-generation infrastructure remain proprietary intellectual property of the Harte Essence Research Collective and are not included in this deposit. Their use or redistribution requires prior written permission.

This release constitutes the open-verifiable component of the Lunecitic research programme — ensuring reproducibility while preserving the integrity of active theoretical and computational development.

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Collatz Proof Upload.zip

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Preprint: 10.5281/zenodo.17292931 (DOI)

References

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  • Minkowski, H. (1908). Raum und Zeit [Space and Time]. Physikalische Zeitschrift, 10, 104–111.
  • Noether, E. (1918). Invariante Variationsprobleme. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Math.-Phys. Klasse, 235–257.
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  • Weinberg, S. (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New York.
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  • Zee, A. (2010). Quantum Field Theory in a Nutshell (2nd ed.). Princeton University Press.
  • Harte, S. A. J. (2025). The Lunecitic Framework™: Reconciling the Hubble Tension via a Lunic Projection of Space Time. Zenodo. https://doi.org/10.5281/zenodo.17216399
  • Harte, S. A. J. (2025). Beyond the Stiffness Limit: Resonant Metrics, Delay Compression, and Superluminal Transit in the Lunecitic Framework™. Zenodo. https://doi.org/10.5281/zenodo.17180352
  • Harte, S. A. J. (2025). The Lunecitic Lens: A Framework for Parsimony in Quantum and Relativistic Systems. Zenodo. https://doi.org/10.5281/zenodo.17249805
  • Harte, S. A. J. (2025). Certified Constraint Framework for the Collatz Conjecture. Zenodo. https://doi.org/10.5281/zenodo.17251123