MétaCan
Menu
Back to cohort
Record W4381436529 · doi:10.3336/gm.58.1.06

Equivalent topologies on the contracting boundary

2023· article· en· W4381436529 on OpenAlexafffund
Vivian He

Bibliographic record

VenueGlasnik Matematicki · 2023
Typearticle
Languageen
FieldMathematics
TopicGeometric and Algebraic Topology
Canadian institutionsUniversity of Toronto
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMathematicsBoundary (topology)GeodesicMathematical analysisMorse theorySublinear functionBounded functionPure mathematicsTopology (electrical circuits)Combinatorics

Abstract

fetched live from OpenAlex

The contracting boundary of a proper geodesic metric space generalizes the Gromov boundary of a hyperbolic space. It consists of contracting geodesics up to bounded Hausdorff distances. Another generalization of the Gromov boundary is the \(\kappa\)–Morse boundary with a sublinear function \(\kappa\). The two generalizations model the Gromov boundary based on different characteristics of geodesics in Gromov hyperbolic spaces. It was suspected that the \(\kappa\)–Morse boundary contains the contracting boundary. We will prove this conjecture: when \(\kappa =1\) is the constant function, the 1-Morse boundary and the contracting boundary are equivalent as topological spaces.

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.

How this classification was reachedexpand

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)0.005
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
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 score0.090
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.005
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.003

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 head0.130
GPT teacher head0.352
Teacher spread0.222 · 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

Classification

machine, unvalidated

Machine predicted; both teacher heads agree on what is shown here.

Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations1
Published2023
Admission routes2
Has abstractyes

Explore more

Same venueGlasnik MatematickiSame topicGeometric and Algebraic TopologyFrench-language works237,207