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Record W2017328220 · doi:10.1093/imrn/rnp115

Conformal Dimension: Cantor Sets and Fuglede Modulus

2009· article· en· W2017328220 on OpenAlex
Hayk Hakobyan

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

VenueInternational Mathematics Research Notices · 2009
Typearticle
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsUniversity of Toronto
FundersStony Brook University
KeywordsMathematicsConformal mapDimension (graph theory)Zero (linguistics)Measure (data warehouse)Space (punctuation)ModulusCombinatoricsPure mathematicsMathematical analysisGeometryComputer science

Abstract

fetched live from OpenAlex

In this paper, we give several conditions for a space to be minimal for conformal dimension. We show that there are sets of zero length and conformal dimension 1, thus answering a question of Bishop and Tyson. Another sufficient condition for minimality is given in terms of a modulus of a system of measures in the sense of Fuglede [7]. It implies in particular that if is minimal for conformal dimension and supports a measure λ such that for every ε > 0 there is a constant 0 < C < ∞ such that C−1r1+ε ≤ λ (E∩ B(x, r)) ≤ C r1−ε, then X × Y is minimal for conformal dimension for every compact Y.

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)0.002
metaresearch head score (Gemma)0.003
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 score0.182
Threshold uncertainty score0.737

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.003
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 science0.0010.000
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 head0.142
GPT teacher head0.457
Teacher spread0.316 · 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