MétaCan
Menu
Back to cohort
Record W3100187951

[no title]

2009· article· en· W3100187951 on OpenAlex

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.
fundA Canadian funder is recorded on the work.

Bibliographic record

Venuenot available
Typearticle
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsUniversity of Waterloo
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMathematicsBernoulli's principleBETA (programming language)CombinatoricsUpper and lower boundsEntropy (arrow of time)Discrete mathematicsMathematical analysisPhysicsThermodynamicsComputer science
DOInot available

Abstract

fetched live from OpenAlex

ABSTRACT. Let β ∈ (1, 2) be a Pisot number and let Hβ denote Garsia’s entropy for the Bernoulli convolution associated with β. It is well known that Hβ < 1 for any Pisot β (see [5]); for the Pisot numbers which satisfy x m = x m−1 + x m−2 + · · · + x + 1 (with m ≥ 2) Garsia’s entropy has been evaluated with high precision, and it proves to be close to 1 – see [1, 6]. No other numerical values for Hβ are known. In the present paper we show that Hβ> 0.81 for all Pisot β and improve this lower bound for certain ranges of β. Our method is based on finding a good upper bound for the maximal growth exponent for the expansions in base β.

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)0.001
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 score0.179
Threshold uncertainty score0.451

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.001
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 head0.050
GPT teacher head0.348
Teacher spread0.298 · 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

Quick stats

Citations14
Published2009
Admission routes2
Has abstractyes

Explore more

Same topicMathematical Dynamics and FractalsFrench-language works237,207