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Record W4395050863 · doi:10.1515/crelle-2024-0022

On κ-solutions and\break canonical neighborhoods in 4d Ricci flow

2024· article· en· W4395050863 on OpenAlexaff
Robert Haslhofer

Bibliographic record

VenueJournal für die reine und angewandte Mathematik (Crelles Journal) · 2024
Typearticle
Languageen
FieldMathematics
TopicGeometric Analysis and Curvature Flows
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsRicci flowFlow (mathematics)MathematicsRicci curvatureGeometry

Abstract

fetched live from OpenAlex

Abstract We introduce a classification conjecture for κ-solutions in 4d Ricci flow. Our conjectured list includes known examples from the literature, but also a new one-parameter family of ℤ 2 2 × O 3 {\mathbb{Z}_{2}^{2}\times\mathrm{O}_{3}} -symmetric bubble-sheet ovals that we construct. We observe that some special cases of the conjecture follow from recent results in the literature. We also introduce a stronger variant of the classification conjecture for ancient asymptotically cylindrical 4d Ricci flows, which does not assume smoothness and nonnegative curvature operator a priori. Assuming this stronger variant holds true, we establish a canonical neighborhood theorem for 4d Ricci flow through cylindrical singularities, which shares some elements in common with Perelman’s canonical neighborhood theorem for 3d Ricci flow as well as the mean-convex neighborhood theorem for mean curvature flow through neck-singularities. Finally, we argue that quotient-necks lead to new phenomena, and sketch an example of non-uniqueness for 4d Ricci flow through singularities.

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 machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.002
Version: metacan-v3-hybrid-931329e0061cValidation 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 score0.006
Threshold uncertainty score0.021

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.000
Science and technology studies0.0020.002
Scholarly communication0.0020.002
Open science0.0010.002
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0060.001

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 head0.036
GPT teacher head0.336
Teacher spread0.301 · 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; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
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

Citations4
Published2024
Admission routes1
Has abstractyes

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Same venueJournal für die reine und angewandte Mathematik (Crelles Journal)Same topicGeometric Analysis and Curvature FlowsFrench-language works237,207