Papers

Foundations paper

One Wave Function, One World: Finite-Information Regional Algebras and the Macroscopic World from Holographic Constraint. Paweł Kapłański.

The primary statement of the program: the finite-information premise, the regional cost functional $\chi_R$, the Macroscopic Definiteness Conjecture, the conditional single-record theorem, and an honest account of what remains open. Prepared for arXiv (quant-ph; cross-listed math-ph, gr-qc).

Read the PDF  ·  arXiv-ready preprint. The arXiv link will be posted here on submission; for now the current build is served directly from this site.

Formalization companion

A machine-checked modular and relative-entropy calculus for the free-field coherent sector. In preparation.

A focused companion documenting the Lean 4 / Mathlib development — the bounded Tomita–Takesaki objects, the one-particle CGP relative entropy and its positivity, the free-field modular flow, and the coherent-state entropy-reduction identity — with the full theorem index and the reproducible build. See the formalization page for the result list.

The Lean corpus

The machine-checked substrate lives in the project repository. Every theorem is audited with #print axioms and depends only on the standard classical foundations (propext, Classical.choice, Quot.sound); the development carries no sorry.

• Repository: github.com/kaplan196883/QIQT-H
• Build: lake build QIQTH · Audit: lake build QIQTH.AxiomAudit

How to cite

Until the preprint is live, cite as: P. Kapłański, One Wave Function, One World, preprint, 2026. A DOI and arXiv identifier will be added here on release.