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Record W1541686930 · doi:10.1090/conm/625/12489

Plank theorems via successive inradii

2014· preprint· en· W1541686930 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.

Bibliographic record

VenueContemporary mathematics - American Mathematical Society · 2014
Typepreprint
Languageen
FieldMathematics
TopicMathematics and Applications
Canadian institutionsUniversity of Calgary
Fundersnot available
KeywordsHyperplanePlankConjectureRegular polygonMathematicsAffine transformationDiscrete geometryField (mathematics)CombinatoricsPure mathematicsDiscrete mathematicsGeometryEngineering

Abstract

fetched live from OpenAlex

In the 1930’s, Tarski introduced his plank problem at a time when the field discrete geometry was about to born. It is quite remarkable that Tarski’s question and its variants continue to generate interest in the geometric as well as analytic aspects of coverings by planks in the present time as well. Besides giving a short survey on the status of the affine plank conjecture of Bang (1950) we prove some new partial results for the successive inradii of the convex bodies involved. The underlying geometric structures are successive hyperplane cuts introduced several years ago by Conway and inductive tilings introduced recently by Akopyan and Karasev.

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)0.003
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Research integrity
Consensus categoriesMeta-epidemiology (narrow)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.515
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.002
Meta-epidemiology (narrow)0.0020.002
Meta-epidemiology (broad)0.0050.002
Bibliometrics0.0000.001
Science and technology studies0.0010.002
Scholarly communication0.0010.000
Open science0.0030.003
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0010.001

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 head0.058
GPT teacher head0.332
Teacher spread0.274 · 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