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Record W4405639020 · doi:10.1112/blms.13212

Associahedra as moment polytopes

2024· article· en· W4405639020 on OpenAlexafffund
Michael Gekhtman, Hugh Thomas

Bibliographic record

VenueBulletin of the London Mathematical Society · 2024
Typearticle
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsUniversité du Québec à Montréal
FundersNatural Sciences and Engineering Research Council of CanadaNational Science Foundation
KeywordsPolytopeMathematicsCluster algebraQuotientCombinatoricsMoment mapMoment (physics)Symplectic geometryTorusPure mathematicsTriangulationAlgebra over a fieldGeometryPhysics

Abstract

fetched live from OpenAlex

Abstract Generalized associahedra are a well‐studied family of polytopes associated with a finite‐type cluster algebra and a choice of starting cluster. We show that the generalized associahedra constructed by Padrol, Palu, Pilaud, and Plamondon, building on ideas from Arkani‐Hamed, Bai, He, and Yan, can be naturally viewed as moment polytopes for an open patch of the quotient of the cluster ‐variety with universal coefficients by its maximal natural torus action. We prove our result by showing that the construction of Padrol, Palu, Pilaud, and Plamondon can be understood on the basis of the way that moment polytopes behave under symplectic reduction.

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)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
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 score0.115
Threshold uncertainty score0.998

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
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)0.0030.000

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 head0.017
GPT teacher head0.279
Teacher spread0.262 · 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 teacher head, not a consensus.

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

Citations0
Published2024
Admission routes2
Has abstractyes

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