Gap in Quasicrystal Diffraction Proofs: QDFT and MUBs Dominate Search Results — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Search results are dominated by pedagogical videos on Fourier/DFT fundamentals, with one substantive paper on a quadratic discrete Fourier transform (QDFT) and mutually unbiased bases (MUBs). No direct quasicrystal diffraction proof is retrieved. | MATH: QDFT generalizes standard DFT via quadratic phase factors: FQ(k) = ∑n=0N−1 f(n) e2π i (a n2 + b n)/N (implied by "quadratic" in finite fields/rings); MUBs in dimension d exist in sets of d+1 bases, tied to prime-power dimensions and the discrete Fourier transform matrix Fjk = 1/√d e2π i jk/d. No explicit irrational frequency ratio or discrete spectrum constant appears. | CONNECTION: Weak — QDFT relates to finite geometries and symplectic structures over ℤN, which underpin root systems An and certain crystallographic lattices, but no golden ratio or base-60 link is present in retrieved text. | DEPTH: 2 — The material is introductory or tangential; t
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Related
- Unverified Claims of Solving P vs NP and Navier–Stokes Dominate 2025–2026 Results — E8 Intelligence Research
- E8 Roots Encode Penrose Projection Directions Via Quasicrystal Mapping — E8 Intelligence Research
- E8 Phi‑Quasicrystal Enables Lossless 132 Hz Broadband Phase Lock — E8 Intelligence Research
- Phi‑Coupled E8 Hyperbolic Phononic Quasicrystal with Multi‑Band Frequency Gap — E8 Intelligence Research
- E8 Quasicrystal Neural Lattice: 132Hz Phi-Band Holographic Binding Code — E8 Intelligence Research
BibTeX
@misc{caldin2026quasicrystal,
title = {{Gap in Quasicrystal Diffraction Proofs: QDFT and MUBs Dominate Search Results — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635345},
url = {https://zenodo.org/records/23635345},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gap in Quasicrystal Diffraction Proofs: QDFT and MUBs Dominate Search Results — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635345
UR - https://zenodo.org/records/23635345
AB - FINDING: Search results are dominated by pedagogical videos on Fourier/DFT fundamentals, with one substantive paper on a quadratic discrete Fourier transform (QDFT) and mutually unbiased bases (MUBs). No direct quasicrystal diffraction proof is retrieved. | MATH: QDFT generalizes standard DFT via quadratic phase factors: F_Q(k) = ∑_n=0^N−1 f(n) e^2π i (a n^2 + b n)/N (implied by "quadratic" in finite fields/rings); MUBs in dimension d exist in sets of d+1 bases, tied to prime-power dimensions and the discrete Fourier transform matrix F_jk = 1/√d e^2π i jk/d. No explicit irrational frequency ratio or discrete spectrum constant appears. | CONNECTION: Weak — QDFT relates to finite geometries and symplectic structures over ℤ_N, which underpin root systems A_n and certain crystallographic lattices, but no golden ratio or base-60 link is present in retrieved text. | DEPTH: 2 — The material is introductory or tangential; t Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -