Reconstructing Physical Theories from Homotopy-Coherent Time: Rigorous Categorical Foundations for Quantum, Relativistic, and Thermodynamic Dynamics
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2025
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| _version_ | 1866901470137286656 |
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| author | Yuanjian, Li |
| author_facet | Yuanjian, Li |
| contents | <p>We present a model-specific, rigorously proven reconstruction of core physical theories from a homotopy-coherent definition of time. Addressing five critical issues: (A) we fix Joyal’s quasi-categories as the (∞, 1)-categorical model and carry out all higher-<br>coherence proofs using horn-filler techniques; (B) we regularize Euler characteristics χ(hofib(evf )) by restricting to finite-type homotopy fibers (finite CW or finite simplicial sets) and, where appropriate, invoking categorical Euler characteristic (Leinster;<br>L¨uck); (C) we provide strict, model-aware proofs for theorems on unitary evolution as ∞-natural transformations and on Einstein’s equations as natural transformations of tensor functors via equalizer morphisms; (D) we supply a precise probabilistic/measure framework for weights w([f ]), including Gibbs weights and integrability conditions; (E) we compute a nontrivial finite simplicial groupoid toy-model for S∞ and verify monotonicity numerically. </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17266407 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Reconstructing Physical Theories from Homotopy-Coherent Time: Rigorous Categorical Foundations for Quantum, Relativistic, and Thermodynamic Dynamics Yuanjian, Li ∞-topos categorical entropy ∞-natural transformations Einstein's equations black hole <p>We present a model-specific, rigorously proven reconstruction of core physical theories from a homotopy-coherent definition of time. Addressing five critical issues: (A) we fix Joyal’s quasi-categories as the (∞, 1)-categorical model and carry out all higher-<br>coherence proofs using horn-filler techniques; (B) we regularize Euler characteristics χ(hofib(evf )) by restricting to finite-type homotopy fibers (finite CW or finite simplicial sets) and, where appropriate, invoking categorical Euler characteristic (Leinster;<br>L¨uck); (C) we provide strict, model-aware proofs for theorems on unitary evolution as ∞-natural transformations and on Einstein’s equations as natural transformations of tensor functors via equalizer morphisms; (D) we supply a precise probabilistic/measure framework for weights w([f ]), including Gibbs weights and integrability conditions; (E) we compute a nontrivial finite simplicial groupoid toy-model for S∞ and verify monotonicity numerically. </p> |
| title | Reconstructing Physical Theories from Homotopy-Coherent Time: Rigorous Categorical Foundations for Quantum, Relativistic, and Thermodynamic Dynamics |
| topic | ∞-topos categorical entropy ∞-natural transformations Einstein's equations black hole |
| url | https://doi.org/10.5281/zenodo.17266407 |