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Record W4383820584 · doi:10.1002/mana.202200214

Envelopes and classifying spaces

2023· article· en· W4383820584 on OpenAlexaff
Nikita A. Karpenko

Bibliographic record

VenueMathematische Nachrichten · 2023
Typearticle
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsUniversity of Alberta
Fundersnot available
KeywordsMathematicsHomomorphismTorusConstraint (computer-aided design)Algebraic numberPure mathematicsImage (mathematics)Group (periodic table)Spin (aerodynamics)Reductive groupAlgebra over a fieldDiscrete mathematicsGroup theoryMathematical analysisGeometryArtificial intelligence

Abstract

fetched live from OpenAlex

Abstract For a split semisimple algebraic group H with its split maximal torus S , let be the restriction homomorphism of the Chow rings of the classifying spaces of H and S , where W is the Weyl group. A constraint on the image of f , given by the Steenrod operations, has been applied to the spin groups in a previous paper. Here, we describe and apply to the spin groups another constraint, which is given by the reductive envelopes of H . We also recover in this way some older results on orthogonal groups.

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)0.000
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 score0.015
Threshold uncertainty score0.670

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
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)0.0000.000

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 head0.074
GPT teacher head0.327
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.

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

Citations2
Published2023
Admission routes1
Has abstractyes

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