Explicit Rotation and Arithmetic Obstructions for Null Chains on a Lorentz Ellipsoid
Manuscript 14 October 2026 · Online 14 October 2026
Abstract
For a Lorentz ellipsoid, we compute the positive unreduced rotation lift of the equator return map formed by alternating null geodesics. A global conformal cylinder and an explicit real integral give a complete closure criterion, with an even-leg condition for literal tropic-to-tropic chains.
For positive algebraic parameters with unequal horizontal axes, the rotation is transcendental and no chain closes. The proof uses Wüstholz’s analytic subgroup theorem on a twice-punctured elliptic curve. For equal horizontal axes, closure is equivalent to rationality of a square root. Fixed positive rational-rotation loci on the unequal-axis chamber are not semialgebraic over the real algebraic numbers and are Zariski dense over the algebraic numbers.
GKT’s porism, classical generalized-Jacobian theory, Huber–Wüstholz and Wüstholz’s earlier arithmetic announcement are credited. This is a self-audited, unrefereed, AI-assisted preprint; no absolute priority, independent review or formal verification is claimed.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete proof
- Categories
- math.DG · math.DS · math.NT
- Manuscript
- 14 October 2026
- Online release
- 14 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “Explicit Rotation and Arithmetic Obstructions for Null Chains on a Lorentz Ellipsoid,” EulerSolve Research Papers, AMR-005-0008, 2026. https://doi.org/10.5281/zenodo.23371160.
BibTeX
@misc{ferudun2026nullchains,
author = {Ferudun, Alper},
title = {Explicit Rotation and Arithmetic Obstructions for Null Chains on a Lorentz Ellipsoid},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/amr-005-0008/},
doi = {10.5281/zenodo.23371160},
note = {AMR-005-0008; unrefereed preprint}
}