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Record W2990587881 · doi:10.1090/tran/8046

D-FINITENESS, RATIONALITY, and HEIGHT

2020· article· en· W2990587881 on OpenAlex
Jason P. Bell, Khoa D. Nguyen, Umberto Zannier

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.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueScuola Normale Superiore di Pisa · 2020
Typearticle
Languageen
FieldMathematics
TopicAdvanced Combinatorial Mathematics
Canadian institutionsUniversity of CalgaryUniversity of Waterloo
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMathematicsPower seriesSeries (stratigraphy)UnivariateFormal power seriesRational functionFunction (biology)Discrete mathematicsPure mathematicsMultivariate statisticsStatisticsMathematical analysis

Abstract

fetched live from OpenAlex

Motivated by a result of van der Poorten and Shparlinski for univariate power series, Bell and Chen prove that if a multivariate power series over a field of characteristic 0 is D-finite and its coefficients belong to a finite set, then it is a rational function. We extend and strengthen their results to certain power series whose coefficients may form an infinite set. We also prove that if the coefficients of a univariate D-finite power series “look like” the coefficients of a rational function, then the power series is rational. Our work relies on the theory of Weil heights, the Manin–Mumford theorem for tori, an application of the Subspace Theorem, and various combinatorial arguments involving heights, power series, and linear recurrence sequences.

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)0.001
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 score0.018
Threshold uncertainty score0.971

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.001
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 head0.078
GPT teacher head0.305
Teacher spread0.227 · 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