The Axiomatic Foundation of Non-Commutative Set Theory: Arithmetic Topological Discontinuity and Macroscopic Contraction in ROA/STCT Framework
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2026
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| _version_ | 1866901745739759616 |
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| author | Lee, Seonggil |
| author_facet | Lee, Seonggil |
| contents | <p>This paper challenges the implicit assumption of ‘Flat Completeness’ embedded within Cantor’s diagonal argument [1] and establishes a novel set-theoretic axiomatic foundation grounded in Rough Operator Algebra (ROA) [9] and Seonggil Theory of Composite Torsion(STCT) [11]. We redefine the transfinite cardinal leap (ℵ0 → c) as a dynamic, first-order topological phase transition occurring at arithmetic resonance points. Furthermore, we prove that Russell’s Paradox [5] geometrically collapses into an open helical trajectory due to the non-zero curvature torsion tensor of non-commutative space, achieving self-regulation<br>without artificial axioms. Crucially, by introducing a non-commutative Dirac measure and a spectral delta function, we demonstrate that the topological void required for intermediate cardinal states (ℵ1) is entirely blocked, thereby resolving the Continuum Hypothesis (CH)algebraically [4]. Finally, by deriving a power-law spectral decay envelope based on the<br>explicit formulas of analytic number theory [6] and fractal scale invariance, we prove that this non-commutative framework seamlessly contracts to the classical Zermelo-Fraenkel Set Theory with the Axiom of Choice (ZFC) [2, 3] under the macroscopic flat-space limit.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20257327 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Axiomatic Foundation of Non-Commutative Set Theory: Arithmetic Topological Discontinuity and Macroscopic Contraction in ROA/STCT Framework Lee, Seonggil Non-Commutative Set Theory Rough Operator Algebra Composite Torsion Arithmetic Topological Discontinuity Continuum Hypothesis Russell'sParadox Topological Phase Transition Non-Commutative Dirac Measure Zeta-Regularization Macroscopic Contraction Limit <p>This paper challenges the implicit assumption of ‘Flat Completeness’ embedded within Cantor’s diagonal argument [1] and establishes a novel set-theoretic axiomatic foundation grounded in Rough Operator Algebra (ROA) [9] and Seonggil Theory of Composite Torsion(STCT) [11]. We redefine the transfinite cardinal leap (ℵ0 → c) as a dynamic, first-order topological phase transition occurring at arithmetic resonance points. Furthermore, we prove that Russell’s Paradox [5] geometrically collapses into an open helical trajectory due to the non-zero curvature torsion tensor of non-commutative space, achieving self-regulation<br>without artificial axioms. Crucially, by introducing a non-commutative Dirac measure and a spectral delta function, we demonstrate that the topological void required for intermediate cardinal states (ℵ1) is entirely blocked, thereby resolving the Continuum Hypothesis (CH)algebraically [4]. Finally, by deriving a power-law spectral decay envelope based on the<br>explicit formulas of analytic number theory [6] and fractal scale invariance, we prove that this non-commutative framework seamlessly contracts to the classical Zermelo-Fraenkel Set Theory with the Axiom of Choice (ZFC) [2, 3] under the macroscopic flat-space limit.</p> |
| title | The Axiomatic Foundation of Non-Commutative Set Theory: Arithmetic Topological Discontinuity and Macroscopic Contraction in ROA/STCT Framework |
| topic | Non-Commutative Set Theory Rough Operator Algebra Composite Torsion Arithmetic Topological Discontinuity Continuum Hypothesis Russell'sParadox Topological Phase Transition Non-Commutative Dirac Measure Zeta-Regularization Macroscopic Contraction Limit |
| url | https://doi.org/10.5281/zenodo.20257327 |