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Record W2769852147 · doi:10.1007/s00208-019-01810-x

Extreme biases in prime number races with many contestants

2019· preprint· en· W2769852147 on OpenAlexafffund
Adam J. Harper, Youness Lamzouri

Bibliographic record

VenueMathematische Annalen · 2019
Typepreprint
Languageen
FieldMathematics
TopicAnalytic Number Theory Research
Canadian institutionsYork University
FundersJesus College, University of CambridgeNatural Sciences and Engineering Research Council of CanadaDirectorate for Mathematical and Physical Sciences
KeywordsModuloMathematicsPrime (order theory)CombinatoricsMathematical proofGaussianPrime numberRange (aeronautics)Discrete mathematicsPhysics

Abstract

fetched live from OpenAlex
No abstract in any covered source. Its absence is recorded, not treated as a negative.

No abstract. This is not a gap in this database; OpenAlex has none either. 23.3% of the frame is in this state, and the screen finds HALF as much metaresearch here, so the absence is a measured bias rather than a missing field.

How this classification was reachedexpand

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)0.002
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
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 score0.478
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.001
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0030.002

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 head0.195
GPT teacher head0.385
Teacher spread0.189 · 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

Classification

machine, unvalidated

Machine predicted; both teacher heads agree on what is shown here.

Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations1
Published2019
Admission routes2
Has abstractno

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