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Record W2013611997 · doi:10.1016/j.anihpc.2012.08.004

Absence of robust rigidity for circle maps with breaks

2012· article· en· W2013611997 on OpenAlex
Konstantin Khanin, Saša Kocić

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.

Bibliographic record

VenueAnnales de l Institut Henri Poincaré C Analyse Non Linéaire · 2012
Typearticle
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsRigidity (electromagnetism)MathematicsStructural engineeringEngineering

Abstract

fetched live from OpenAlex

We give examples of analytic circle maps with singularities of break type with the same rotation number and the same size of the break for which no conjugacy is Lipschitz continuous. In the second part of the paper, we discuss a class of rotation numbers for which a conjugacy is C^{1} -smooth, although the numbers can be strongly non-Diophantine (Liouville). For the rotation numbers in this class, we construct examples of analytic circle maps with breaks, for which the conjugacy is not C^{1 + \alpha } smooth, for any \alpha > 0 . Résumé Nous donnons des exemples dʼapplications du cercle analytiques avec des singularités de type rupture avec le même nombre de rotation et la même taille de rupture pour lesquelles aucune conjugaison nʼest lipschitzienne. Dans la deuxième partie de lʼarticle, nous étudions une classe de nombres de rotation pour lesquels il y a une conjugaison de classe C^{1} , alors même que les nombres de rotation peuvent être fortement non-diophantiens (Liouville). Pour les nombres de rotation de cette classe, nous construisons des exemples dʼapplications du cercle analytiques avec des singularités de type rupture, pour lesquelles la conjugaison nʼest de classe C^{1 + \alpha } pour aucun \alpha > 0 .

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)0.001
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 score0.282
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
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 head0.052
GPT teacher head0.312
Teacher spread0.260 · 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