Where Δμ Begins, Gödel Ends
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| Format: | Recurso digital |
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2025
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| _version_ | 1866902247848280064 |
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| author | Ednyashev, Sanal |
| author_facet | Ednyashev, Sanal |
| contents | <p>This work reconstructs the foundational structure of mathematics using the Theory of Ontological Conflicts (TOC). </p> <p>It introduces a new invariant — Δμ — to quantify ontological transitions between formal statements, logic systems, and computational structures.</p> <p> </p> <p>Key results:</p> <p>- Formalization of Gödel incompleteness as Δμ-barriers across μ-levels </p> <p>- Reformulation of P ≠ NP as ontological non-collapse </p> <p>- Δμ-theoretic analysis of the Riemann Hypothesis and Goldbach Conjecture </p> <p>- Construction of the TOCₖ logic hierarchy and universal system TOC∞ </p> <p>- Application to AI, cryptography, category theory, and computability</p> <p> </p> <p>This document provides the first axiomatic structure where truth, proof, and semantic depth are unified via ontological lifts. </p> <p>All formal systems are shown to be open with respect to Δμ. </p> <p>The framework is purely structural, free of interpretation or philosophical dependency.</p> <p> </p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15514222 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Where Δμ Begins, Gödel Ends Ednyashev, Sanal <p>This work reconstructs the foundational structure of mathematics using the Theory of Ontological Conflicts (TOC). </p> <p>It introduces a new invariant — Δμ — to quantify ontological transitions between formal statements, logic systems, and computational structures.</p> <p> </p> <p>Key results:</p> <p>- Formalization of Gödel incompleteness as Δμ-barriers across μ-levels </p> <p>- Reformulation of P ≠ NP as ontological non-collapse </p> <p>- Δμ-theoretic analysis of the Riemann Hypothesis and Goldbach Conjecture </p> <p>- Construction of the TOCₖ logic hierarchy and universal system TOC∞ </p> <p>- Application to AI, cryptography, category theory, and computability</p> <p> </p> <p>This document provides the first axiomatic structure where truth, proof, and semantic depth are unified via ontological lifts. </p> <p>All formal systems are shown to be open with respect to Δμ. </p> <p>The framework is purely structural, free of interpretation or philosophical dependency.</p> <p> </p> <p> </p> |
| title | Where Δμ Begins, Gödel Ends |
| url | https://doi.org/10.5281/zenodo.15514222 |