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Record W4226028291 · doi:10.2140/agt.2024.24.3363

Bounding the Kirby–Thompson invariant ofspun knots

2024· preprint· en· W4226028291 on OpenAlex
Román Aranda, Puttipong Pongtanapaisan, Scott A. Taylor, Suixin Zhang

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

VenueAlgebraic & Geometric Topology · 2024
Typepreprint
Languageen
FieldMathematics
TopicGeometric and Algebraic Topology
Canadian institutionsUniversity of Saskatchewan
FundersDivision of Mathematical SciencesColby CollegeNational Science Foundation
KeywordsInvariant (physics)MathematicsBounding overwatchPure mathematicsCombinatoricsArtificial intelligenceComputer scienceMathematical physics

Abstract

fetched live from OpenAlex

A bridge trisection of a smooth surface in $S^4$ is a decomposition analogous to a bridge splitting of a link in $S^3$. The Kirby-Thompson invariant of a bridge trisection measures its complexity in terms of distances between disc sets in the pants complex of the trisection surface. We give the first significant bounds for the Kirby-Thompson invariant of spun knots. In particular, we show that the Kirby-Thompson invariant of the spun trefoil is 15.

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)0.003
metaresearch head score (Gemma)0.008
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Research integrity, Insufficient payload (model declined to judge)
Consensus categoriesMeta-epidemiology (narrow), Research integrity, Insufficient 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 score0.199
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.008
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.001
Bibliometrics0.0050.007
Science and technology studies0.0010.001
Scholarly communication0.0000.000
Open science0.0030.007
Research integrity0.0020.005
Insufficient payload (model declined to judge)0.0040.002

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 head0.054
GPT teacher head0.327
Teacher spread0.273 · 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