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Record W2986518919 · doi:10.1142/s0218216519400170

Stable Alexander polynomials of arborescent links

2019· article· en· W2986518919 on OpenAlexaff
Mikami Hirasawa, Kunio Murasugi

Bibliographic record

VenueJournal of Knot Theory and Its Ramifications · 2019
Typearticle
Languageen
FieldMathematics
TopicGraph theory and applications
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsMathematicsClass (philosophy)InterlacingPure mathematicsHahn polynomialsWilson polynomialsDiscrete orthogonal polynomialsMacdonald polynomialsDifference polynomialsOrthogonal polynomialsProperty (philosophy)Classical orthogonal polynomialsCombinatoricsGegenbauer polynomialsAlgebra over a field

Abstract

fetched live from OpenAlex

We study the zeros of Alexander polynomials of three classes of arborescent links. In the first class, the zeros are real (and negative) or modulus one. In the second class, the zeros are real (and positive). In the third class, the zeros are real or modulus one. For this purpose, we modify their Alexander polynomials into other real polynomials, with only real zeros, and use the property that two such polynomials have interlacing real zeros.

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)0.002
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 score0.008
Threshold uncertainty score0.512

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.000
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 head0.029
GPT teacher head0.301
Teacher spread0.272 · 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

Citations0
Published2019
Admission routes1
Has abstractyes

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