Paper
The Trinity-Infinity Framework, Series I
A Conceptual Model with Illustrative Applications in Game Theory, Mathematical Logic, and Mechanical Engineering
ORCID0009-0000-1406-0547
VersionRevised edition — August 2026
Proves that the three-element recursive operator converges geometrically to a unique fixed point, and sets out the connections to game theory, logic and engineering with proved results, known results and analogies marked apart.
Where it lives
The same text exists in several places. Cite the Zenodo DOI.
Zenodo 10.5281/zenodo.22058624Canonical. It carries the DOI and fixes the version
PDF on GitHubThe distributed file itself — a copy, not the canonical record
Superseded — do not cite 10.5281/zenodo.17173703The first edition this paper corrects. The current DOI is the one on this page
The record
Defects found, and what could not be fixed. Nothing has been deleted.
ErrataDefects found, and what could not be fixed. Nothing has been deleted.
Route of the rediscoveryNine stages from the initial idea to identifying it as a rediscovery of standard results
Verification scriptsChecks the theorems, and every number printed on the page, by machine
Correction register（TI-…）Every error found after publication, recorded one by one
External evaluationsEvaluations received, and how they were checked
Use of language models
What language models were used for. A language model is not an author.
The theorem is not new mathematics: it is a rediscovery of affine (stationary) iteration, and convergence follows from the Banach fixed-point theorem. The first draft was generated by a language model.
This repository's disclosure of language-model useWhat language models were used for. A language model is not an author.
Not peer-reviewedA DOI does not imply peer review
Citation
Cite in a form that makes the version clear.
Nemoto, T. (2026). The Trinity-Infinity Framework, Series I: A Conceptual Model with Illustrative Applications in Game Theory, Mathematical Logic, and Mechanical Engineering. Zenodo. https://doi.org/10.5281/zenodo.22058624Cite in a form that makes the version clear.