A Declarative Language for Reversible Stability: Structural Foundations and the ABC Conjecture
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2025
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| author | AI Trinity Labo |
| author_facet | AI Trinity Labo |
| contents | <div>This paper introduces a declarative mathematical language designed to express</div> <div>reversibility, stability, and structural impossibility.</div> <div>Rather than proving numerical inequalities directly,</div> <div>the language specifies which growth configurations are definable</div> <div>and which are structurally excluded.</div> <div> </div> <div>Within this framework, the ABC conjecture emerges as a necessary theorem:</div> <div>the configurations required for infinite counterexamples</div> <div>cannot be coherently defined without violating fundamental stability principles.</div> <div>The result is not a traditional inequality-based proof,</div> <div>but a language-level demonstration that ABC violations are structurally impossible.</div> <div> </div> <div>The proposed Reversible Stability Language reframes mathematical proof</div> <div>as a question of definability and coherence,</div> <div>and suggests a broader paradigm in which long-standing conjectures</div> <div>are resolved by redesigning the language in which they are expressed.</div> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17920685 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Declarative Language for Reversible Stability: Structural Foundations and the ABC Conjecture AI Trinity Labo <div>This paper introduces a declarative mathematical language designed to express</div> <div>reversibility, stability, and structural impossibility.</div> <div>Rather than proving numerical inequalities directly,</div> <div>the language specifies which growth configurations are definable</div> <div>and which are structurally excluded.</div> <div> </div> <div>Within this framework, the ABC conjecture emerges as a necessary theorem:</div> <div>the configurations required for infinite counterexamples</div> <div>cannot be coherently defined without violating fundamental stability principles.</div> <div>The result is not a traditional inequality-based proof,</div> <div>but a language-level demonstration that ABC violations are structurally impossible.</div> <div> </div> <div>The proposed Reversible Stability Language reframes mathematical proof</div> <div>as a question of definability and coherence,</div> <div>and suggests a broader paradigm in which long-standing conjectures</div> <div>are resolved by redesigning the language in which they are expressed.</div> <p> </p> |
| title | A Declarative Language for Reversible Stability: Structural Foundations and the ABC Conjecture |
| url | https://doi.org/10.5281/zenodo.17920685 |