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Record W2513146802 · doi:10.4310/mrl.2018.v25.n1.a1

Relative K-stability and extremal Sasaki metrics

2018· preprint· en· W2513146802 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.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueMathematical Research Letters · 2018
Typepreprint
Languageen
FieldMathematics
TopicGeometry and complex manifolds
Canadian institutionsnot available
FundersUniversité du Québec à Montréal
KeywordsMathematicsAutomorphismTorusInvariant (physics)Pure mathematicsCone (formal languages)Manifold (fluid mechanics)HomogeneousMathematical analysisCombinatoricsGeometryMathematical physics

Abstract

fetched live from OpenAlex

We define K-stability of a polarized Sasakian manifold relative to a maximal torus of automorphisms. The existence of a Sasaki-extremal metric in the polarization is shown to imply that the polarization is K-semistable. Computing this invariant for the deformation to the normal cone gives an extention of the Lichnerowicz obstruction, due to Gauntlett, Martelli, Sparks, and Yau, to an obstruction of Sasaki-extremal metrics. We use this to give a list of examples of Sasakian manifolds whose Sasaki cone contains no extremal representatives. These give the first examples of Sasaki cones of dimension greater than one that contain no extremal Sasaki metrics whatsoever. In the process we compute the unreduced Sasaki cone for an arbitrary smooth link of a weighted homogeneous polynomial.

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)0.010
metaresearch head score (Gemma)0.021
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMetaresearch, Meta-epidemiology (narrow), Research integrity, Insufficient 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 score0.081
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0100.021
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0010.001
Science and technology studies0.0000.002
Scholarly communication0.0000.000
Open science0.0010.004
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0020.000

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 head0.356
GPT teacher head0.440
Teacher spread0.085 · 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