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Record W4285783060 · doi:10.5802/ahl.161

An effective weighted K-stability condition for polytopes and semisimple principal toric fibrations

2023· article· en· W4285783060 on OpenAlex
Thibaut Delcroix, Simon Jubert

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.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueAnnales Henri Lebesgue · 2023
Typearticle
Languageen
FieldMathematics
TopicGeometry and complex manifolds
Canadian institutionsUniversité du Québec à Montréal
FundersInstitut national des sciences mathématiques et de leurs interactionsUniversité Toulouse III - Paul SabatierCentre National de la Recherche ScientifiqueUniversité de ToulouseAgence Nationale de la RechercheUniversité du Québec à Montréal
KeywordsPolytopeMathematicsPrincipal (computer security)Stability (learning theory)Pure mathematicsMoment (physics)CombinatoricsAlgebra over a fieldComputer sciencePhysics

Abstract

fetched live from OpenAlex

The second author has shown that existence of extremal Kähler metrics on semisimple principal toric fibrations is equivalent to a notion of weighted uniform K-stability, read off from the moment polytope. The purpose of this article is to prove various sufficient conditions of weighted uniform K-stability which can be checked effectively and explore the low dimensional new examples of extremal Kähler metrics it provides.

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)0.000
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: Empirical
Teacher disagreement score0.180
Threshold uncertainty score0.627

Codex and Gemma teacher scores by category

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

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 head0.060
GPT teacher head0.353
Teacher spread0.293 · 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