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Record W4321328704 · doi:10.1112/mtk.12190

Unions of lines in Rn$\mathbb {R}^n$

2023· article· en· W4321328704 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

VenueMathematika · 2023
Typearticle
Languageen
FieldMathematics
TopicAdvanced Topology and Set Theory
Canadian institutionsUniversity of British Columbia
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMathematicsMultilinear mapHausdorff dimensionConjectureDimension (graph theory)Integer (computer science)Hausdorff spaceCombinatoricsArgument (complex analysis)Set (abstract data type)Discrete mathematicsPure mathematics

Abstract

fetched live from OpenAlex

Abstract We prove a conjecture of D. Oberlin on the dimension of unions of lines in . If is an integer, , and L is a set of lines in with Hausdorff dimension at least , then the union of the lines in L has Hausdorff dimension at least . Our proof combines a refined version of the multilinear Kakeya theorem by Carbery and Valdimarsson with the multilinear → linear argument of Bourgain and Guth.

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)0.001
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 score0.020
Threshold uncertainty score0.415

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
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 head0.082
GPT teacher head0.385
Teacher spread0.303 · 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