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Record W4318978771 · doi:10.5206/mt.v3i1.14322

Graphing the Remainder

2023· article· en· W4318978771 on OpenAlex

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.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueMaple Transactions · 2023
Typearticle
Languageen
FieldMathematics
TopicMathematics and Applications
Canadian institutionsnot available
Fundersnot available
KeywordsRemainderAsymptoteChinese remainder theoremFunction (biology)Computer scienceRational functionModulo operationOblique caseCalculus (dental)Computer graphics (images)MathematicsArithmeticAlgebra over a fieldAlgorithmPure mathematicsMathematical analysis

Abstract

fetched live from OpenAlex

Employing the Remainder Theorem, analytic and graphical tools, and dynamic applets, this paper investigates when the graphs of rational functions intersect horizontal, oblique, and curved asymptotes. Additionally, we consider how the respective remainder function perturbs the asymptotic function to producethe rational function. Dynamic applets assist in the development of the ideas herein. Finally, this paper endswith a significant number of student investigations.

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 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: none
Teacher disagreement score0.939
Threshold uncertainty score0.466

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
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 head0.115
GPT teacher head0.350
Teacher spread0.235 · 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