שמור ב:
| מחבר ראשי: | |
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| פורמט: | Recurso digital |
| שפה: | |
| יצא לאור: |
Zenodo
2026
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| גישה מקוונת: | https://doi.org/10.5281/zenodo.19430606 |
| תגים: |
הוספת תג
אין תגיות, היה/י הראשונ/ה לתייג את הרשומה!
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תוכן הענינים:
- <p>The five topological gap families of the icosahedral quasicrystal (Z^5 ≅ H^1, Paper 8) are weakly separated in the IDS–perpendicular Fourier grading dictionary (Paper 20): the families are monotonically ordered in cumulative perpendicular Fourier grading, with non-overlapping cumulative ranges, verified on four independent approximants (L=3, V=165 and 285; L=4, V=150 and 368). Strong separation fails at finite approximant size: state-level grading ranges overlap between adjacent families. Three precommitted separation criteria — strong, weak, and failure — are defined before computation, making the paper publishable regardless of outcome. The IDS–grading correlation sharpens from ρ ≈ −0.77 at L=3 to ρ ≈ −0.96 at L=4, supporting a sharpening conjecture formulated via the family filtration sharpness ratio S_L. The conceptual consequence is that topological family structure is encoded in the spectral filtration, not in individual eigenstates — weak separation is not a weaker substitute for strong separation but the correct observable level for topological family structure in the bridge framework. This redirects the universal intertwiner programme from statewise maps to filtration-level correspondences. Twenty-third paper in a series; companion papers at DOI 10.5281/zenodo.19422381 (grading), 10.5281/zenodo.18928463 (gap labeling), 10.5281/zenodo.19424316 (inverse spectral geometry).</p>