Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Sprache: | |
| Veröffentlicht: |
Zenodo
2026
|
| Online-Zugang: | https://doi.org/10.5281/zenodo.19520669 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866901900319784960 |
|---|---|
| author | Way, J.J. |
| author_facet | Way, J.J. |
| contents | <p>Conditional inverse spectral theorem for cut-and-project quasicrystals: the equivariant spectral datum determines embedding dimension N, point-group symmetry G, and acceptance-window class [W], up to lattice automorphism. The reconstruction proceeds through a four-step pipeline — N from band combinatorics, G from irrep content, gap-family count from K-theoretic labeling, window class from Z[φ⁻²] gap-label fine structure. Steps (R2)–(R3) are unconditional theorems; steps (R1) and (R4) are conditional on the Binomial Band Conjecture and Window Injectivity, both verified for N = 2, 4, 5, 6. Every step assembles a proved result from a 26-paper programme. Central insight: spectral gaps carry the most rigid structural data — the memory of the embedding geometry is stored more faithfully in the absences than in the bands. Twenty-seventh paper in a series; companion papers at DOI 10.5281/zenodo.18793518 and 10.5281/zenodo.19515992.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19520669 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Hearing the Shape of a Quasicrystal: Inverse Spectral Reconstruction from Gap Labels Way, J.J. <p>Conditional inverse spectral theorem for cut-and-project quasicrystals: the equivariant spectral datum determines embedding dimension N, point-group symmetry G, and acceptance-window class [W], up to lattice automorphism. The reconstruction proceeds through a four-step pipeline — N from band combinatorics, G from irrep content, gap-family count from K-theoretic labeling, window class from Z[φ⁻²] gap-label fine structure. Steps (R2)–(R3) are unconditional theorems; steps (R1) and (R4) are conditional on the Binomial Band Conjecture and Window Injectivity, both verified for N = 2, 4, 5, 6. Every step assembles a proved result from a 26-paper programme. Central insight: spectral gaps carry the most rigid structural data — the memory of the embedding geometry is stored more faithfully in the absences than in the bands. Twenty-seventh paper in a series; companion papers at DOI 10.5281/zenodo.18793518 and 10.5281/zenodo.19515992.</p> |
| title | Hearing the Shape of a Quasicrystal: Inverse Spectral Reconstruction from Gap Labels |
| url | https://doi.org/10.5281/zenodo.19520669 |