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Record W4390714620 · doi:10.55016/ojs/cdm.v17i1.71829

Spirals in Periodic Tilings

2022· article· en· W4390714620 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueContributions to Discrete Mathematics · 2022
Typearticle
Languageen
FieldMaterials Science
TopicQuasicrystal Structures and Properties
Canadian institutionsnot available
Fundersnot available
KeywordsSubstitution tilingHexagonal tilingPenrose tilingCombinatoricsMathematicsSpiral (railway)Tessellation (computer graphics)TileSet (abstract data type)Square tilingQuasicrystalGeometryComputer scienceMathematical analysis

Abstract

fetched live from OpenAlex

Spiral tilings, as appealing as they are for their aesthetics, have not been studied well mathematically. One of the difficulties in this area of tiling theory is providing a mathematical definition of spiral tilings. A recently published attempt at providing a formal definition distinguishes a so-called L-spiral tiling (L-tiling) and an S-spiral tiling (S-tiling), with the two types being characterized by special properties of tile set partitions. Based on these existing definitions, we investigate the spiral structure in periodic tilings. Unlike spiral tilings, periodic tilings lend themselves easily to a definition and have been well studied. We first prove that it is not possible for periodic tilings to be S-tilings. We then study a subset of periodic tilings that can be L-tilings. In particular, we demonstrate that there exist examples for each type of isohedral tilings (a subset of periodic monohedral tilings) that are L-spirable.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Bench or experimental · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.578
Threshold uncertainty score0.998

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0030.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.013
GPT teacher head0.274
Teacher spread0.261 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it