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Record W2029149643 · doi:10.1088/0951-7715/19/7/007

Domain of analyticity of normalizing transformations

2006· article· en· W2029149643 on OpenAlex
Maria Saprykina

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

VenueNonlinearity · 2006
Typearticle
Languageen
FieldChemistry
TopicMolecular spectroscopy and chirality
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsPolydiscMathematicsHolomorphic functionSymplectic geometryPure mathematicsTransformation (genetics)Legendre transformationAnalytic functionMathematical analysisQuadratic equationHamiltonian systemDomain (mathematical analysis)Complex planeGeometry

Abstract

fetched live from OpenAlex

We investigate questions of divergence or local convergence of (formal) normalizing transformations associated with the Birkhoff normal form (BNF) at the origin of a holomorphic Hamiltonian system. These questions are addressed for systems for which the BNF is a quadratic function , Λ := (λ1, ..., λd) being a non-resonant, either real or purely imaginary, vector. We prove that for a generic or one can define Hamiltonians satisfying the following properties: (i) H is real-analytic, holomorphic in the unit polydisc , and H is defined arbitrarily close to HΛ, (ii) the BNF of H equals HΛ and (iii) any symplectic normalizing transformation diverges, or given any 0 < ρ < 1 any normalizing transformation diverges outside the polydisc of radius ρ, and there is a real-analytic normalizing transformation (converging in a smaller domain).

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: Bench or experimental · Consensus signal: Bench or experimental
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.071
Threshold uncertainty score0.389

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 head0.007
GPT teacher head0.245
Teacher spread0.238 · 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