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Record W4405308964 · doi:10.2140/agt.2024.24.3759

Spectral diameter of Liouville domains

2024· article· en· W4405308964 on OpenAlexafffund
Pierre-Alexandre Mailhot

Bibliographic record

VenueAlgebraic & Geometric Topology · 2024
Typearticle
Languageen
FieldMathematics
TopicSpectral Theory in Mathematical Physics
Canadian institutionsUniversité de Montréal
FundersCourtois FoundationUniversité de Montréal
KeywordsMathematicsPure mathematics

Abstract

fetched live from OpenAlex

The group of compactly supported Hamiltonian diffeomorphisms of a symplectic manifold is endowed with a natural bi-invariant distance, due to Viterbo, Schwarz, Oh, Frauenfelder and Schlenk, coming from spectral invariants in Hamiltonian Floer homology.This distance has found numerous applications in symplectic topology.However, its diameter is still unknown in general.In fact, for closed symplectic manifolds there is no unifying criterion for the diameter to be infinite.We prove that for any Liouville domain this diameter is infinite if and only if its symplectic cohomology does not vanish.This generalizes a result of Monzner, Vichery and Zapolsky and has applications in the setting of closed symplectic manifolds.57R17, 51F99, 53D05, 57R58 1. Introduction and results 3759 2. Liouville domains and admissible Hamiltonians 3766 3. Filtered Floer and symplectic cohomology 3773 4. Spectral invariants and spectral norm 3779 5. Cohomological barricades on Liouville domains 3781 6. Proofs of main results 3788

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)0.004
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 score0.003
Threshold uncertainty score0.009

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.004
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0030.001
Science and technology studies0.0010.003
Scholarly communication0.0020.003
Open science0.0010.002
Research integrity0.0010.001
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 head0.028
GPT teacher head0.319
Teacher spread0.291 · 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

Citations1
Published2024
Admission routes2
Has abstractyes

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