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Record W4367163627 · doi:10.4310/arkiv.2023.v61.n1.a1

Yagita’s counter-examples and beyond

2023· article· sv· W4367163627 on OpenAlex
Sanghoon Baek, Nikita A. Karpenko

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

VenueArkiv för matematik · 2023
Typearticle
Languagesv
FieldMathematics
TopicAlgebraic Geometry and Number Theory
Canadian institutionsUniversity of Alberta
FundersSamsungSamsung Science and Technology Foundation
KeywordsPolitical science

Abstract

fetched live from OpenAlex

A conjecture on a relationship between the Chow and Grothendieck rings for the generically twisted variety of Borel subgroups in a split semisimple group G, stated by the second author, has been disproved by Nobuaki Yagita in characteristic 0 for G=Spin(2n+1) with n=8 and n=9.For n=8, the second author provided an alternative simpler proof of Yagita's result, working in any characteristic, but failed to do so for n=9.This gap is filled here by involving a new ingredient -Pieri type K-theoretic formulas for highest orthogonal grassmannians.Besides, a similar counter-example for n=10 is produced.Note that the conjecture on Spin(2n+1) holds for n up to 5; it remains open for n=6, n=7, and every n≥11.

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)0.002
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 categoriesInsufficient payload (model declined to judge)
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 score0.149
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.001
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0030.008

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 head0.031
GPT teacher head0.277
Teacher spread0.247 · 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