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Record W2610172741 · doi:10.1088/1361-6544/aab595

The baker’s map with a convex hole

2018· article· en· W2610172741 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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueNonlinearity · 2018
Typearticle
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsUniversity of Waterloo
FundersNatural Sciences and Engineering Research Council of CanadaCanada Foundation for Innovation
KeywordsMathematicsDisjoint setsRegular polygonCombinatoricsSet (abstract data type)Dimension (graph theory)Square (algebra)Convex setTrajectoryUnit (ring theory)GeometryConvex optimizationComputer sciencePhysics

Abstract

fetched live from OpenAlex

Abstract We consider the baker’s map B on the unit square X and an open convex set which we regard as a hole. The survivor set is defined as the set of all points in X whose B -trajectories are disjoint from H . The main purpose of this paper is to study holes H for which (dimension traps) as well as those for which any periodic trajectory of B intersects (cycle traps). We show that any H which lies in the interior of X is not a dimension trap. This means that, unlike the doubling map and other one-dimensional examples, we can have for H whose Lebesgue measure is arbitrarily close to one. Also, we describe holes which are dimension or cycle traps, critical in the sense that if we consider a strictly convex subset, then the corresponding property in question no longer holds. We also determine such that for all convex H whose Lebesgue measure is less than δ . This paper may be seen as a first extension of our work begun in Clark (2016 Discrete Continuous Dyn. Syst . A 6 1249–69; Clark 2016 PhD Dissertation The University of Manchester; Glendinning and Sidorov 2015 Ergod. Theor. Dynam. Syst . 35 1208–28; Hare and Sidorov 2014 Mon.hefte Math . 175 347–65; Sidorov 2014 Acta Math. Hung . 143 298–312) to higher dimensions.

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 score0.220
Threshold uncertainty score0.341

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 science0.0000.000
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 head0.040
GPT teacher head0.326
Teacher spread0.286 · 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