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Record W2216864981 · doi:10.1142/s1793042111004988

$\mathbb{Q}(\sqrt{2}, \sqrt{35})$ HAS A NON-PRINCIPAL EUCLIDEAN IDEAL

2011· article· en· W2216864981 on OpenAlexaff
Hester Graves

Bibliographic record

VenueInternational Journal of Number Theory · 2011
Typearticle
Languageen
FieldMathematics
TopicAlgebraic Geometry and Number Theory
Canadian institutionsQueen's University
Fundersnot available
KeywordsMathematicsPrincipal idealIdeal (ethics)Euclidean geometryQuartic functionPrincipal (computer security)CombinatoricsEuclidean distanceEuclidean domainQuartic surfaceDiscrete mathematicsEuclidean distance matrixPure mathematicsGeometryComputer sciencePrime (order theory)

Abstract

fetched live from OpenAlex

This paper introduces a totally real quartic number field with a non-principal Euclidean ideal.

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 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)0.003
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 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 score0.158
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.001
Open science0.0020.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0220.001

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 head0.067
GPT teacher head0.321
Teacher spread0.253 · 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 teacher head, not a consensus.

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

Citations8
Published2011
Admission routes1
Has abstractyes

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