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Record W2399693043 · doi:10.1090/crmp/052/09

Nearest 𝜆_{𝑞}-multiple fractions

2010· book-chapter· en· W2399693043 on OpenAlex
Dieter Mayer, Tobias Mühlenbruch

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

VenueCRM proceedings & lecture notes · 2010
Typebook-chapter
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsMcGill University
Fundersnot available
KeywordsGeology

Abstract

fetched live from OpenAlex

We discuss the nearestq-multiple continued frac- tions and their duals forq = 2cos � π q � which are closely related to the Hecke triangle groups Gq, q = 3,4,.... They have been in- troduced in the case q = 3 by Hurwitz and for even q by Nakada. These continued fractions are generated by interval maps fq respec- tively f ⋆ q which are conjugate to subshifts over infinite alphabets. We generalize to arbitrary q a result of Hurwitz concerning the Gq- and fq-equivalence of points on the real line. The natural exten- sion of the maps fq and f ⋆ q can be used as a Poincare map for the geodesic flow on the Hecke surfaces Gq\H and allows to construct the transfer operator for this flow.

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)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Research integrity, Insufficient payload (model declined to judge)
Consensus categoriesResearch integrity
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Other · Consensus signal: none
Teacher disagreement score0.947
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.003
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0020.002
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 head0.037
GPT teacher head0.283
Teacher spread0.245 · 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