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Record W1972254817 · doi:10.1016/j.jpaa.2007.05.006

The pp conjecture for the space of orderings of the field <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si34.gif" display="inline" overflow="scroll"><mml:mi mathvariant="double-struck">R</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>

2007· article· lv· W1972254817 on OpenAlexaff
Paweł Gładki, Murray Marshall

Bibliographic record

VenueJournal of Pure and Applied Algebra · 2007
Typearticle
Languagelv
FieldMathematics
TopicFunctional Equations Stability Results
Canadian institutionsUniversity of Saskatchewan
Fundersnot available
KeywordsConjectureMathematicsConic sectionSpace (punctuation)Field (mathematics)Subspace topologyCombinatoricsAlgebra over a fieldDiscrete mathematicsPure mathematicsGeometryMathematical analysisComputer science

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 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)0.001
metaresearch head score (Gemma)0.005
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: Empirical
Teacher disagreement score0.016
Threshold uncertainty score0.054

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.005
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0010.001
Science and technology studies0.0020.004
Scholarly communication0.0040.008
Open science0.0010.002
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0160.002

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 head0.016
GPT teacher head0.246
Teacher spread0.230 · 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

Citations4
Published2007
Admission routes1
Has abstractno

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