A Connected Positive Model with a Nonsemialgebraic Likelihood Cell
Manuscript 18 October 2026 · Online 18 October 2026
Abstract
We give a connected compact rational polygonal model on four outcomes, all of whose probabilities are at least 1/32, with a nonsemialgebraic logarithmic Voronoi cell at a smooth rational point. Near a positive data vector, the cell is the epigraph of an explicit binary entropy expression in rational coordinates. A uniform likelihood gap shows that the connecting segment does not alter this boundary. An elementary proof establishes nonsemialgebraicity over the real numbers. Four outcomes are minimal at a positive-dimensional smooth interior model point, by log-normal containment and convexity. This five-page note complements the earlier work of Alexandr and Heaton and Alexandr's 2026 nonalgebraicity results. It provides a complete explicit theorem relevant to AIM-COMPUTATION-0040, not a full closure of the open-ended AIM Question 26. AI-assisted, self-audited and unrefereed; no formal verification, independent peer review, or absolute priority is claimed.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Explicit theorem and sharp bound
- Categories
- math.ST · math.AG
- Manuscript
- 18 October 2026
- Online release
- 18 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, “A Connected Positive Model with a Nonsemialgebraic Likelihood Cell,” EulerSolve Research Papers, AIM-COMPUTATION-0040, 2026. https://doi.org/10.5281/zenodo.23444649.
BibTeX
@misc{ferudun2026connectedlikelihood,
author = {Ferudun, Alper},
title = {A Connected Positive Model with a Nonsemialgebraic Likelihood Cell},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/aim-computation-0040/},
doi = {10.5281/zenodo.23444649},
note = {AIM-COMPUTATION-0040; unrefereed preprint}
}