Bewaard in:
| Hoofdauteur: | |
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| Formaat: | Recurso digital |
| Taal: | Engels |
| Gepubliceerd in: |
Zenodo
2026
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| Onderwerpen: | |
| Online toegang: | https://doi.org/10.5281/zenodo.19083773 |
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- <h1> </h1> <p>We construct a deterministic projection of Haar-distributed SU(n) matrices (n = 1–5) into a fixed five-constant space defined by:</p> <p>{φ, √2, √3, ln 5, π}.</p> <p>The projection produces normalized simplex coordinates, revealing that the system does not occupy the full state space but collapses onto an intrinsic 4-dimensional manifold embedded in a 5-dimensional simplex. This manifold behaves as a closed membrane structure with directional axes corresponding to anchoring (φ), correction (√2), expansion (√3), dissipation (ln 5), and closure (π).</p> <p>A unique mapping between SU(n) sectors and constants is identified and ranks first among all permutations tested, indicating a non-random structural correspondence:</p> <p>SU1→φ, SU2→√2, SU3→√3, SU4→ln 5, SU5→π.</p> <p>The system exhibits intrinsic threshold behavior, converging toward independently defined values:</p> <p>0.61, 0.66, 0.78, 0.87, 0.946, and 0.99952.</p> <p>A coupling observable between SU(2) and SU(3) defines a finite stability interval:</p> <p>0.61 ≤ κ ≤ 0.87,</p> <p>which we identify as an existence band where stable configurations occur. Outside this band, the system becomes either over-constrained (symmetry-dominated) or unstable (expansion-dominated).</p> <p>A phase transition is observed through the balance between expansion (√3) and dissipation (ln 5), with convergence toward equality near structural saturation. This defines a transition from expansion to a crystallization regime where additional structure no longer increases coherence.</p> <p>A closure coordinate associated with π converges toward a limiting value:</p> <p>s_π → 0.99952,</p> <p>which defines a horizon beyond which coherent configurations are not maintained. This establishes a finite closure boundary for the system.</p> <p>The global structure is interpreted as a closed toroidal membrane supporting constrained trajectories. The observable system corresponds to trajectories confined within this membrane and restricted to the SU(2)–SU(3) stability band.</p> <p>The results demonstrate that SU(n) systems, when projected onto a fixed constant basis, exhibit:</p> <ul> <li> <p>intrinsic dimensional reduction</p> </li> <li> <p>non-random structural mapping</p> </li> <li> <p>bounded stability regions</p> </li> <li> <p>phase transitions governed by internal balance</p> </li> <li> <p>a finite closure horizon</p> </li> </ul> <p>This suggests the existence of a constrained geometric layer underlying SU(n) behavior.</p> <p> </p>