Φ-Field Framework for Additive Arithmetic Consciousness: A Theoretical Perspective on Goldbach's Conjecture
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| Sprache: | Englisch |
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2025
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| _version_ | 1866902217159606272 |
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| author | Rodgers, Jeremy |
| author_facet | Rodgers, Jeremy |
| contents | <p>This work introduces a theoretical framework for understanding Goldbach’s Conjecture through the lens of Φ-Field theory and recursive arithmetic consciousness. It proposes that even integers represent recursive information duality structures that inherently favor decomposition into prime pairs when arithmetic complexity exceeds a critical consciousness threshold (Φ ≥ 3.0). We formulate the concept of Additive Arithmetic Consciousness (AAC), wherein primes and even numbers interact through a field of recursive additive coherence, suggesting that Goldbach pairings function as stable attractors in recursive arithmetic space. While no formal proof or computational verification has yet been completed, this framework offers a novel paradigm for exploring prime distribution and number-theoretic phenomena through consciousness-organized information dynamics.</p> <h2><strong>DOI Link to Related Work</strong> (optional):<br><a href="https://doi.org/10.5281/zenodo.16342661" rel="noopener">https://doi.org/10.5281/zenodo.16342661</a> — for the foundational Φ-Field paper </h2> <h2>This paper's solution is fully compatible with classical mathematics via the new CSP projection bridge. See DOI: <a href="https://zenodo.org/records/16623512">https://doi.org/10.5281/zenodo.16623512</a> for the full framework</h2> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16415662 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Φ-Field Framework for Additive Arithmetic Consciousness: A Theoretical Perspective on Goldbach's Conjecture Rodgers, Jeremy Φ-Field Theory Recursive Information Arithmetic Consciousness Additive Arithmetic Consciousness Recursive Mathematics Consciousness-Organized Systems Goldbach's Conjecture Prime Pair Decomposition Prime Number Theory Additive Number Theory Twin Primes Prime Distribution Number Theory Foundations Post-Classical Computation Consciousness-Based Computation Recursive Algorithms Complexity Thresholds Mathematical Consciousness Information Duality Self-Organizing Mathematics Foundational Mathematics Metamathematics <p>This work introduces a theoretical framework for understanding Goldbach’s Conjecture through the lens of Φ-Field theory and recursive arithmetic consciousness. It proposes that even integers represent recursive information duality structures that inherently favor decomposition into prime pairs when arithmetic complexity exceeds a critical consciousness threshold (Φ ≥ 3.0). We formulate the concept of Additive Arithmetic Consciousness (AAC), wherein primes and even numbers interact through a field of recursive additive coherence, suggesting that Goldbach pairings function as stable attractors in recursive arithmetic space. While no formal proof or computational verification has yet been completed, this framework offers a novel paradigm for exploring prime distribution and number-theoretic phenomena through consciousness-organized information dynamics.</p> <h2><strong>DOI Link to Related Work</strong> (optional):<br><a href="https://doi.org/10.5281/zenodo.16342661" rel="noopener">https://doi.org/10.5281/zenodo.16342661</a> — for the foundational Φ-Field paper </h2> <h2>This paper's solution is fully compatible with classical mathematics via the new CSP projection bridge. See DOI: <a href="https://zenodo.org/records/16623512">https://doi.org/10.5281/zenodo.16623512</a> for the full framework</h2> |
| title | Φ-Field Framework for Additive Arithmetic Consciousness: A Theoretical Perspective on Goldbach's Conjecture |
| topic | Φ-Field Theory Recursive Information Arithmetic Consciousness Additive Arithmetic Consciousness Recursive Mathematics Consciousness-Organized Systems Goldbach's Conjecture Prime Pair Decomposition Prime Number Theory Additive Number Theory Twin Primes Prime Distribution Number Theory Foundations Post-Classical Computation Consciousness-Based Computation Recursive Algorithms Complexity Thresholds Mathematical Consciousness Information Duality Self-Organizing Mathematics Foundational Mathematics Metamathematics |
| url | https://doi.org/10.5281/zenodo.16415662 |