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| 格式: | Recurso digital |
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Zenodo
2025
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| 主題: | |
| 在線閱讀: | https://doi.org/10.5281/zenodo.17917543 |
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- <p>This work presents empirical evidence for a universal geometric coherence pattern appearing across physical systems spanning more than fifteen orders of magnitude in energy scale. Within the Relational Thermodynamic Layered Index (RTLI) framework, we identify a closed three-angle cycle—θc ≈ 20.2°, 90° − θc ≈ 69.8°, and 2θc ≈ 40.4°—that governs dominant variance directions in quantum, thermodynamic, galactic, and cosmological datasets.</p> <p>Using principal component analysis applied to six independent public datasets, we show that observed variance orientations consistently align with one of the predicted RTLI coherence angles, with a combined probability of ≲10⁻³ under random alignment. The long-standing cosmic microwave background low-ℓ anomaly corridor coincides precisely with the interval [θc, 2θc], while non-cosmic systems exhibit stable hardness ratios clustering near 1/√e. In representative cases, a four-sphere variance constraint is preserved to numerical precision, indicating an underlying symplectic structure.</p> <p>The results support a cyclic, rather than monotonic, recursion across physical scales. Coherence does not propagate indefinitely toward higher-order structures but instead traces a closed loop consistent with toroidal topology, wherein each scale selects a complementary angle from the same geometric basis. These findings suggest that invariant geometric constraints on variance flow may serve as a scale-independent organizing principle underlying diverse physical phenomena.</p>