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Record W2963850835 · doi:10.1002/cpa.21812

Finite Morse Index Implies Finite Ends

2019· article· en· W2963850835 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

VenueCommunications on Pure and Applied Mathematics · 2019
Typearticle
Languageen
FieldMathematics
TopicGeometric Analysis and Curvature Flows
Canadian institutionsUniversity of British Columbia
Fundersnot available
KeywordsMorse codeMathematicsCurvatureIndex (typography)Order (exchange)Mathematical analysisFinite element methodCluster analysisPure mathematicsGeometryStatisticsPhysicsComputer science

Abstract

fetched live from OpenAlex

Abstract We prove that finite Morse index solutions to the Allen‐Cahn equation in ℝ 2 have finitely many ends and linear energy growth . The main tool is a curvature decay estimate on level sets of these finite Morse index solutions, which in turn is reduced to a problem on the uniform second‐order regularity of clustering interfaces for the singularly perturbed Allen‐Cahn equation. Using an indirect blowup technique, in the spirit of the classical Colding‐Minicozzi theory in minimal surfaces, we show that the obstruction to the uniform second‐order regularity of clustering interfaces in ℝ n is associated to the existence of nontrivial entire solutions to a (finite or infinite) Toda system in ℝ n –1 . For finite Morse index solutions in ℝ 2 , we show that this obstruction does not exist by using information on stable solutions of the Toda system. © 2019 Wiley Periodicals, Inc.

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)0.000
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: none
Teacher disagreement score0.681
Threshold uncertainty score0.920

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.001
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 head0.044
GPT teacher head0.295
Teacher spread0.251 · 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