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Record W2138675614 · doi:10.1090/s0002-9939-01-06136-6

Sums of numbers with small partial quotients

2001· article· en· W2138675614 on OpenAlexfundno aff
S. Astels

Bibliographic record

VenueProceedings of the American Mathematical Society · 2001
Typearticle
Languageen
FieldComputer Science
TopicComputability, Logic, AI Algorithms
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsQuotientMathematicsCombinatoricsDiscrete mathematics

Abstract

fetched live from OpenAlex

In a paper of James Hlavka it is stated that F ( 3 ) + F ( 2 ) + F ( 2 ) ≠ R F(3)+F(2)+F(2)\neq \mathbb {R} . In this manuscript we show that this is false by establishing that F ( 3 ) ± F ( 2 ) ± F ( 2 ) = R F(3)\pm F(2)\pm F(2)=\mathbb {R} . We also describe the corresponding products and quotients.

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.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.004
metaresearch head score (Gemma)0.017
Version: metacan-v3-hybrid-931329e0061cValidation 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: none
Teacher disagreement score0.016
Threshold uncertainty score0.052

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0040.017
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.002
Bibliometrics0.0030.003
Science and technology studies0.0020.005
Scholarly communication0.0080.011
Open science0.0010.005
Research integrity0.0010.004
Insufficient payload (model declined to judge)0.0160.006

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 head0.017
GPT teacher head0.234
Teacher spread0.217 · 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; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
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

Citations15
Published2001
Admission routes1
Has abstractyes

Explore more

Same venueProceedings of the American Mathematical SocietySame topicComputability, Logic, AI AlgorithmsFrench-language works237,207