Structural Constraints of Cohesive ∞-Toposes on Physical Modeling: A Meta-Theoretical Analysis of Axioms, Models, and Predictive Power
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2026
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| _version_ | 1866901755569111040 |
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| author | Benamara, Djilali |
| author_facet | Benamara, Djilali |
| contents | <p><span>We present a comprehensive analysis of an axiomatic framework proposing that physical theories be formulated within cohesive </span><span>∞</span><span>-toposes. Through systematic examination of seven foundational axioms, we demonstrate that this framework provides rigorous mathematical foundations for gauge theories, quantum field theories, and gravity, while remaining fundamentally distinct from empirical physical theories. Our analysis reveals that the framework functions as a </span><span>universal test engine</span><span>: given hypothetical or empirical data, it computes the minimal mathematical structures required and enforces consistency constraints, but does not generate physical predictions </span><span>ab initio</span><span>. We evaluate specific instantiations including electromagnetism, Yang-Mills theory, and M-theory, and identify the precise boundary between structural derivation and phenomenological input.</span> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18733650 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Structural Constraints of Cohesive ∞-Toposes on Physical Modeling: A Meta-Theoretical Analysis of Axioms, Models, and Predictive Power Benamara, Djilali <p><span>We present a comprehensive analysis of an axiomatic framework proposing that physical theories be formulated within cohesive </span><span>∞</span><span>-toposes. Through systematic examination of seven foundational axioms, we demonstrate that this framework provides rigorous mathematical foundations for gauge theories, quantum field theories, and gravity, while remaining fundamentally distinct from empirical physical theories. Our analysis reveals that the framework functions as a </span><span>universal test engine</span><span>: given hypothetical or empirical data, it computes the minimal mathematical structures required and enforces consistency constraints, but does not generate physical predictions </span><span>ab initio</span><span>. We evaluate specific instantiations including electromagnetism, Yang-Mills theory, and M-theory, and identify the precise boundary between structural derivation and phenomenological input.</span> </p> |
| title | Structural Constraints of Cohesive ∞-Toposes on Physical Modeling: A Meta-Theoretical Analysis of Axioms, Models, and Predictive Power |
| url | https://doi.org/10.5281/zenodo.18733650 |