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Record W127451680

Prequantum transfer operator for Anosov diffeomorphism. (Preliminary Version).

2012· preprint· en· W127451680 on OpenAlexaff
Fréderic Faure, Masato Tsujii

Bibliographic record

VenuearXiv (Cornell University) · 2012
Typepreprint
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsToronto Metropolitan University
Fundersnot available
KeywordsDiffeomorphismTransfer operatorOperator (biology)Symplectic geometrySpectrum (functional analysis)Fourier integral operatorMathematicsTransfer (computing)Extension (predicate logic)Fourier transformPure mathematicsConnection (principal bundle)Mathematical analysisOperator theoryPhysicsComputer scienceGeometryQuantum mechanics
DOInot available

Abstract

fetched live from OpenAlex

This is a preliminary version and some other results will appear in the next version. We define the prequantization of a symplectic Anosov diffeomorphism, which is a U(1) extension of the diffeomorphism preserving an associated specific connection. We study the spectrum of the associated transfer operator, called prequantum transfer operator, restricted to the N-th Fourier mode with respect to the U(1) action on P. We investigate the spectral property in the limit N to infinity, regarding the transfer operator as a Fourier integral operator and using semi-classical analysis. In the main result, we show a band structure of the spectrum, that is, the spectrum is contained in a few separated annuli and a disk concentric at the origin.

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)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
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 score0.383
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0010.000

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 head0.136
GPT teacher head0.229
Teacher spread0.093 · 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

Citations5
Published2012
Admission routes1
Has abstractyes

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