| _version_ | 1866901208399085568 |
|---|---|
| author | Elliott, Jacob Alexander |
| author_facet | Elliott, Jacob Alexander |
| contents | <p>We develop a mathematical framework for understanding physical constants through renor-</p> <p>malization group theory, percolation phenomena, and categorical invariants. A carefully cir-</p> <p>cumscribed set of dimensionless invariants measured at the unit scalethe RG plateau where</p> <p>|∂φ/∂log L|≈0behave as true mathematical constants, while observations at quantum and</p> <p>cosmic scales represent these constants modulo systematic obstructions. The framework syn-</p> <p>thesizes the Chicago school's categorical universality, the Russian tradition of ergodic theory,</p> <p>and the French geometric approach to information theory. We establish identity verication</p> <p>protocols for Feigenbaum, Ising, and KPZ universality classes, introduce the organizer eld</p> <p>construction for percolation, and formalize ordinal superiority as a category-theoretic criterion</p> <p>for hypothesis comparison.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17552567 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Unit Primacy and Ordinal Superiority: the Mathematical Foundations of Scale-Invariant Physical Constants Elliott, Jacob Alexander <p>We develop a mathematical framework for understanding physical constants through renor-</p> <p>malization group theory, percolation phenomena, and categorical invariants. A carefully cir-</p> <p>cumscribed set of dimensionless invariants measured at the unit scalethe RG plateau where</p> <p>|∂φ/∂log L|≈0behave as true mathematical constants, while observations at quantum and</p> <p>cosmic scales represent these constants modulo systematic obstructions. The framework syn-</p> <p>thesizes the Chicago school's categorical universality, the Russian tradition of ergodic theory,</p> <p>and the French geometric approach to information theory. We establish identity verication</p> <p>protocols for Feigenbaum, Ising, and KPZ universality classes, introduce the organizer eld</p> <p>construction for percolation, and formalize ordinal superiority as a category-theoretic criterion</p> <p>for hypothesis comparison.</p> |
| title | Unit Primacy and Ordinal Superiority: the Mathematical Foundations of Scale-Invariant Physical Constants |
| url | https://doi.org/10.5281/zenodo.17552567 |