Cutoff-Uniform Enstrophy Bounds, Fractional Riccati Integrability Thresholds, and Resonant-Triad Depletion in Dyadic and Toroidal Fluid Hierarchies: A Machine-Checked Investigation of Ten Frontier Hypotheses
- 1SocrateAI Lab
Abstract
We conduct a systematic, machine-checked mathematical physics investigation of ten coupled frontier hypotheses governing enstrophy production, fractional hyperviscous regularity thresholds, dispersive second-harmonic-generation (SHG) regulators, and three-dimensional resonant-triad hypergraph depletion across the Katz–Pavlović dyadic hierarchy and toroidal Fourier lattices. Rather than restricting formalization to known textbook identities, we evaluate an open ten-hypothesis research programme in which six of the ten hypotheses (60.0%) are positively proved and four plausible conjectures (40.0%) are formally refuted or obstructed by explicit counterexamples, integrability deficits, and arithmetic parity theorems. All twelve theorems (eight positive theorems and four formal counterexample/obstruction theorems) are machine-checked in the Lean 4 theorem prover (ANSE.DyadicNavierStokesRegulator) with zero sorryAx axioms and verified via environment-level definitional equality against a frozen canonical specification (ANSE.DyadicNavierStokesRegulatorSpec), accompanied by an exact arbitrary-precision rational and integer combinatorial replication harness and a 20-record 5-tier Elenchus epistemic ledger.
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BibTeX
@misc{callens2026cutoffuniform,
title = {{Cutoff-Uniform Enstrophy Bounds, Fractional Riccati Integrability Thresholds, and Resonant-Triad Depletion in Dyadic and Toroidal Fluid Hierarchies: A Machine-Checked Investigation of Ten Frontier Hypotheses}},
author = {Xavier Callens},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23458238},
url = {https://zenodo.org/records/23458238},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cutoff-Uniform Enstrophy Bounds, Fractional Riccati Integrability Thresholds, and Resonant-Triad Depletion in Dyadic and Toroidal Fluid Hierarchies: A Machine-Checked Investigation of Ten Frontier Hypotheses
AU - Xavier Callens
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23458238
UR - https://zenodo.org/records/23458238
AB - We conduct a systematic, machine-checked mathematical physics investigation of ten coupled frontier hypotheses governing enstrophy production, fractional hyperviscous regularity thresholds, dispersive second-harmonic-generation (SHG) regulators, and three-dimensional resonant-triad hypergraph depletion across the Katz–Pavlović dyadic hierarchy and toroidal Fourier lattices. Rather than restricting formalization to known textbook identities, we evaluate an open ten-hypothesis research programme in which six of the ten hypotheses (60.0%) are positively proved and four plausible conjectures (40.0%) are formally refuted or obstructed by explicit counterexamples, integrability deficits, and arithmetic parity theorems. All twelve theorems (eight positive theorems and four formal counterexample/obstruction theorems) are machine-checked in the Lean 4 theorem prover (ANSE.DyadicNavierStokesRegulator) with zero sorryAx axioms and verified via environment-level definitional equality against a frozen canonical specification (ANSE.DyadicNavierStokesRegulatorSpec), accompanied by an exact arbitrary-precision rational and integer combinatorial replication harness and a 20-record 5-tier Elenchus epistemic ledger.
ER -