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bibkey: baakefrankgrimm2021three authors: Michael Baake, Natalie Priebe Frank, and Uwe Grimm year: 2021 title: Three variations on a theme by Fibonacci doi: 10.1142/S0219493721400013 claim: The Fibonacci-chain golden lattice, Minkowski embedding, star map, windows, and model sets. strata_touched:

  • D5/S1/Scale/MinkowskiModelSet license: citation-only triage: anchor

Three variations on a theme by Fibonacci

Michael Baake, Natalie Priebe Frank, and Uwe Grimm use the ring of golden integers and its standard Minkowski embedding to construct Fibonacci-chain cut-and-project sets. Their star map and window description directly attest the unlabeled model-set structure formalized here.

Search log

  • 2026-07-16: The first two NyxID/Tavily proxy attempts sent the JSON body with NyxID 0.7.1’s default application/octet-stream content type. Tavily received a JSON string and returned HTTP 422. No bibliographic conclusion was drawn from either failed request; the same query succeeded after explicitly setting Content-Type: application/json.
  • 2026-07-16: Queried Baake Grimm Aperiodic Order Volume 1 DOI Fibonacci model set Z tau star map Minkowski embedding. Cambridge front matter exposed the dedicated Minkowski-embedding and projection/model-set chapters, while an independent bibliography verified the book DOI and general construction.
  • 2026-07-16: Queried Baake Grimm Fibonacci chain Z[tau] star map window model set diagonal embedding. The results exposed the exact lattice {(x,x*) : x in Z[tau]}, identified it as the standard Minkowski embedding, and described star-map windows for Fibonacci model sets.
  • 2026-07-16: Queried Three variations on a theme by Fibonacci DOI Baake Frank Grimm 2140001. The open-access article and publisher result verified the authors, title, journal reference, and DOI 10.1142/S0219493721400013.

Verified locator

  • World Scientific: https://www.worldscientific.com/doi/10.1142/S0219493721400013
  • arXiv: https://arxiv.org/abs/1910.00988
  • Open-access article: https://pages.vassar.edu/nafrank/files/2022/07/ThreeVariationsFibonacci.pdf