E1P Three-Layer Zone Model: Empirical Validation of Golden Ratio Phase Transition Architecture Across 100 Complex Systems
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| Lingua: | inglese |
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2025
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| _version_ | 1866901618467799040 |
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| author | Resonant Institute |
| author_facet | Resonant Institute |
| contents | <p>We present comprehensive empirical validation of Energetic First Principles (E1P) through systematic analysis of phase transitions across 100 complex systems spanning physics, biology, computation, and social dynamics.</p> <p>Our investigation reveals a three-layer zone structure where critical transitions cluster around golden ratio (φ) derivatives:</p> <p><strong>Layer 1 (Primary φ):</strong> Theoretical zones derived from E1P's Fibonacci gradient architecture — φ⁻¹, φ⁻², φ⁻³, φ⁻⁴ and complements. Literature support: Scullard (2006) proved pc = φ⁻¹ for specific percolation geometries.</p> <p><strong>Layer 2 (Extended φ):</strong> Empirically-discovered zones at φ⁻⁵, φ⁻⁶, φ⁻¹/² and complements. Literature support: Baxter's hard hexagon model (1980) and Hardy's quantum entanglement limit (1993) both place critical phenomena at φ⁻⁵ = 0.090.</p> <p><strong>Layer 3 (Discrete Fibonacci):</strong> A distinct transition class in the [0.618, 0.667] region, centered on 2/3 = F₂/F₃. Literature support: Popkov et al. (PNAS 2015) established Fibonacci ratios as distinct universality classes.</p> <p><strong>Key Results:</strong></p> <ul> <li>98/100 systems (98%) validate within the three-layer model</li> <li>100% coverage of τ ∈ [0, 1] with 13 zones and no classification gaps</li> <li>Layer distribution: L1 52%, L2 42%, L3 4%</li> <li>Novel finding: φ⁻¹/² = 0.309 threshold (15 systems, no prior literature)</li> </ul> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18069300 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | E1P Three-Layer Zone Model: Empirical Validation of Golden Ratio Phase Transition Architecture Across 100 Complex Systems Resonant Institute Energetic First Principles E1P complex systems Phase Transition critical thresholds universality classes Statistical mechanics Fibonacci percolation <p>We present comprehensive empirical validation of Energetic First Principles (E1P) through systematic analysis of phase transitions across 100 complex systems spanning physics, biology, computation, and social dynamics.</p> <p>Our investigation reveals a three-layer zone structure where critical transitions cluster around golden ratio (φ) derivatives:</p> <p><strong>Layer 1 (Primary φ):</strong> Theoretical zones derived from E1P's Fibonacci gradient architecture — φ⁻¹, φ⁻², φ⁻³, φ⁻⁴ and complements. Literature support: Scullard (2006) proved pc = φ⁻¹ for specific percolation geometries.</p> <p><strong>Layer 2 (Extended φ):</strong> Empirically-discovered zones at φ⁻⁵, φ⁻⁶, φ⁻¹/² and complements. Literature support: Baxter's hard hexagon model (1980) and Hardy's quantum entanglement limit (1993) both place critical phenomena at φ⁻⁵ = 0.090.</p> <p><strong>Layer 3 (Discrete Fibonacci):</strong> A distinct transition class in the [0.618, 0.667] region, centered on 2/3 = F₂/F₃. Literature support: Popkov et al. (PNAS 2015) established Fibonacci ratios as distinct universality classes.</p> <p><strong>Key Results:</strong></p> <ul> <li>98/100 systems (98%) validate within the three-layer model</li> <li>100% coverage of τ ∈ [0, 1] with 13 zones and no classification gaps</li> <li>Layer distribution: L1 52%, L2 42%, L3 4%</li> <li>Novel finding: φ⁻¹/² = 0.309 threshold (15 systems, no prior literature)</li> </ul> |
| title | E1P Three-Layer Zone Model: Empirical Validation of Golden Ratio Phase Transition Architecture Across 100 Complex Systems |
| topic | Energetic First Principles E1P complex systems Phase Transition critical thresholds universality classes Statistical mechanics Fibonacci percolation |
| url | https://doi.org/10.5281/zenodo.18069300 |