Fermat's Last Theorem: Fully Constructive Proof by Absolute Dynamic Residual Exhaustion Descent (ADRED) — Proof-Theoretic Minimalization
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| Format: | Recurso digital |
| Langue: | anglais |
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2025
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| _version_ | 1866902052229087232 |
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| author | Onodera, Hiroaki |
| author_facet | Onodera, Hiroaki |
| contents | <p>This paper presents a fully constructive proof of Fermat’s Last Theorem using the Absolute Dynamic Residual Exhaustion Descent (ADRED) method. Unlike previous proofs relying on higher-order mathematics, the ADRED method operates entirely within first-order Peano Arithmetic (PA), utilizing bounded descent, coprimality extraction, and residual absorption dynamics. Moreover, the proof-theoretic strength is reduced to Primitive Recursive Arithmetic (PRA), establishing one of the minimal formalizations of FLT to date. This version includes a complete proof-theoretic formalization as an additional chapter.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15661595 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Fermat's Last Theorem: Fully Constructive Proof by Absolute Dynamic Residual Exhaustion Descent (ADRED) — Proof-Theoretic Minimalization Onodera, Hiroaki Fermat's Last Theorem, Constructive Proof, Primitive Recursive Arithmetic, Peano Arithmetic, Proof Theory, ADRED, Residual Descent, Formal Verification Mathematics, Number Theory, Logic, Proof Theory, Mathematical Logic <p>This paper presents a fully constructive proof of Fermat’s Last Theorem using the Absolute Dynamic Residual Exhaustion Descent (ADRED) method. Unlike previous proofs relying on higher-order mathematics, the ADRED method operates entirely within first-order Peano Arithmetic (PA), utilizing bounded descent, coprimality extraction, and residual absorption dynamics. Moreover, the proof-theoretic strength is reduced to Primitive Recursive Arithmetic (PRA), establishing one of the minimal formalizations of FLT to date. This version includes a complete proof-theoretic formalization as an additional chapter.</p> |
| title | Fermat's Last Theorem: Fully Constructive Proof by Absolute Dynamic Residual Exhaustion Descent (ADRED) — Proof-Theoretic Minimalization |
| topic | Fermat's Last Theorem, Constructive Proof, Primitive Recursive Arithmetic, Peano Arithmetic, Proof Theory, ADRED, Residual Descent, Formal Verification Mathematics, Number Theory, Logic, Proof Theory, Mathematical Logic |
| url | https://doi.org/10.5281/zenodo.15661595 |