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| Formato: | Recurso digital |
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Zenodo
2026
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| Acceso en línea: | https://doi.org/10.5281/zenodo.19520669 |
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- <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>