Primitive Winding, Fission Thresholds and Resonance on Toroidal Systems
- 1Evrmind Labs
Abstract
This paper develops a mathematical account of persistence and fragmentation for primitive integer windings. It proves a least-cost fission theorem for strictly convex homogeneous winding energies under stated state-admission rules. Positive inverse-length corrections produce a different global minimum: a worked primitive-only model requires three fragments, with an exact finite-parent phase diagram and calculated large-winding crossovers.
The analysis connects these arithmetic results to an interacting winding-field energy and a separate mechanism for winding-changing transitions. The original tokamak, asteroid-belt, planetary-ring, cardiac-conduction and accelerator examples are retained with explicit sampling and dynamical controls. The paper provides exact results for the defined winding models and a testable programme for assessing their relevance to physical resonances, without identifying the different empirical mechanisms as one established universal law.
Related
- The Axis of the World: a global, designated axis of winding in the toroidal universe.
- Toroidal Black Holes II E = mc3, 5D Continuous Poloidal Winding, Mass–Energy Packaging, and the Dimensional Signature of c
- E8 Sulba-Babylonian Lattice Resonance: Sexagesimal φ-Winding Frequencies in Icosahedral Forbidden Zones — E8 Intelligence Research
- 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
- THE LAW OF DYNAMIC VACUUM RESONANCE: SYNTHESIS OF TOROIDAL EVERSION AND COMPLEX QUANTUM ROTATOR AS THE FINAL GEOMETRIC MODEL OF THE SPATIAL MEDIUM
BibTeX
@misc{vandenberg2026primitive,
title = {{Primitive Winding, Fission Thresholds and Resonance on Toroidal Systems}},
author = {Ibrahim Vandenberg},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23603890},
url = {https://zenodo.org/records/23603890},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Primitive Winding, Fission Thresholds and Resonance on Toroidal Systems
AU - Ibrahim Vandenberg
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23603890
UR - https://zenodo.org/records/23603890
AB - This paper develops a mathematical account of persistence and fragmentation for primitive integer windings. It proves a least-cost fission theorem for strictly convex homogeneous winding energies under stated state-admission rules. Positive inverse-length corrections produce a different global minimum: a worked primitive-only model requires three fragments, with an exact finite-parent phase diagram and calculated large-winding crossovers. The analysis connects these arithmetic results to an interacting winding-field energy and a separate mechanism for winding-changing transitions. The original tokamak, asteroid-belt, planetary-ring, cardiac-conduction and accelerator examples are retained with explicit sampling and dynamical controls. The paper provides exact results for the defined winding models and a testable programme for assessing their relevance to physical resonances, without identifying the different empirical mechanisms as one established universal law.
ER -