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Record W4394846876 · doi:10.4171/qt/206

A perturbed-Alexander invariant

2024· article· en· W4394846876 on OpenAlex
Dror Bar-Natan, Roland van der Veen

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

VenueQuantum Topology · 2024
Typearticle
Languageen
FieldMathematics
TopicAdvanced Topics in Algebra
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsMathematicsInvariant (physics)Pure mathematicsMathematical physics

Abstract

fetched live from OpenAlex

In this note, we give concise formulas, which lead to a simple and fast computer program that computes a powerful knot invariant. This invariant \rho_{1} is not new; yet our formulas are by far the simplest and fastest. Given a knot, we write one of the standard matrices, A , whose determinant is its Alexander polynomial; yet instead of computing the determinant, we consider a certain quadratic expression in the entries of A^{-1} . The proximity of our formulas to the Alexander polynomial suggests that they should have a topological explanation, which we do not have yet.

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)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient 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 score0.557
Threshold uncertainty score0.999

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)0.0020.000

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 head0.064
GPT teacher head0.363
Teacher spread0.299 · 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