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Record W2013913731 · doi:10.2140/pjm.2002.207.393

Support sets of pairs of modules

2002· article· en· W2013913731 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.

Bibliographic record

VenuePacific Journal of Mathematics · 2002
Typearticle
Languageen
FieldMathematics
TopicCommutative Algebra and Its Applications
Canadian institutionsToronto Metropolitan University
Fundersnot available
KeywordsMathematicsCombinatoricsPure mathematics

Abstract

fetched live from OpenAlex

Let R be the quotient of a local domain (Q, n) by a proper ideal minimally generated by f 1 , . . . , f c . Assume Q/ n is algebraically closed, and let M and N be finitely generated Rmodules. We show there is an algebraic set in c-dimensional affine space, called the support set of the pair (M, N ), which describes those hypersurfaces h (f 1 , . . . , f c ) -n(f 1 , . . . , f c ) over which there are infinitely many nonzero Ext i Q/(h) (M, N ). This generalizes to arbitrary quotients of regular local rings the notion of support variety for modules over complete intersections.

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)0.001
metaresearch head score (Gemma)0.000
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 score0.190
Threshold uncertainty score0.858

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
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)0.0010.000

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 head0.075
GPT teacher head0.310
Teacher spread0.235 · 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