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Record W4401307383 · doi:10.48550/arxiv.2408.00522

Relative Helicity and Tiling Twist

2024· preprint· en· W4401307383 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.

fundA Canadian funder is recorded on the work.
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

VenuearXiv (Cornell University) · 2024
Typepreprint
Languageen
FieldMaterials Science
TopicQuasicrystal Structures and Properties
Canadian institutionsnot available
FundersPontifícia Universidade Católica do Rio de JaneiroFundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de JaneiroConselho Nacional de Desenvolvimento Científico e TecnológicoNatural Sciences and Engineering Research Council of CanadaCoordenação de Aperfeiçoamento de Pessoal de Nível Superior
KeywordsHelicityTwistPhysicsMathematicsGeometryParticle physics

Abstract

fetched live from OpenAlex

We consider domino tilings of 3D cubiculated regions. The tilings have two invariants, flux and twist, often integer-valued, which are given in purely combinatorial terms. These invariants allow one to classify the tilings with respect to certain elementary moves, flips and trits. In this paper we present a construction associating a divergence-free vector field $ξ_t$ to any domino tiling $t$, such that the flux of the tiling $t$ can be interpreted as the (relative) rotation class of the field $ξ_t$, while the twist of $t$ is proved to be the relative helicity of the field $ξ_t$.

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)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.201
Threshold uncertainty score0.858

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
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 science0.0000.002
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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 head0.063
GPT teacher head0.182
Teacher spread0.120 · 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