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Record W2568346760 · doi:10.1016/j.crma.2007.10.033

The moduli space of germs of generic families of analytic diffeomorphisms unfolding a parabolic fixed point

2007· article· en· W2568346760 on OpenAlex
Colin Christopher, Christiane Rousseau

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

VenueComptes Rendus Mathématique · 2007
Typearticle
Languageen
FieldMathematics
TopicAdvanced Differential Equations and Dynamical Systems
Canadian institutionsUniversité de Montréal
Fundersnot available
KeywordsCodimensionModuli spaceFixed pointMathematicsPure mathematicsMathematical analysisCompatibility (geochemistry)

Abstract

fetched live from OpenAlex

We describe the moduli space of germs of generic families of analytic diffeomorphisms which unfold a parabolic fixed point of codimension 1. A complete modulus is given by unfolding the Écalle–Voronin modulus over a sector of opening greater than 2 π in the canonical parameter ϵ. In the region of overlap (Glutsyuk sector of parameter space) where the two fixed points are connected by orbits, we identify the necessary compatibility between the two representatives of the modulus. The compatibility condition implies the existence of a normalization for which the modulus is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> -summable in ϵ, non-summability occurring in the direction of real multipliers of the fixed points. We show that the compatibility condition together with the summability is sufficient for realization of the modulus.

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 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 score0.318
Threshold uncertainty score0.595

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 head0.032
GPT teacher head0.301
Teacher spread0.269 · 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