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Roll Models

2013· article· en· W4237689020 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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueAmerican Mathematical Monthly · 2013
Typearticle
Languageen
FieldPhysics and Astronomy
TopicExperimental and Theoretical Physics Studies
Canadian institutionsTrinity College
Fundersnot available
KeywordsMotion (physics)Diversity (politics)Computer scienceMathematics educationCalculus (dental)MathematicsArtificial intelligenceSociology

Abstract

fetched live from OpenAlex

These notes attempt a case study of applied mathematics for beginning students via problems of rolling. They do so by pointing out diverse surprising phenomena, many of which the reader can try at home, modeling them, and testing the limits of these models. One message is that rolling, because it tightly coordinates different modes of motion, tends to be more exactly solvable than meets the eye. Another message is that the thrill of applied mathematics is not in how difficult the mathematics is, but rather in what diversity of surprises in one's own experience one can discover, then understand.

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.

Direct model labels (unvalidated)

Per-model category and study-design labels from the labeling rounds. They are machine output, unvalidated, and the disagreement between models ships as data. No study design here is MEDLINE-validated yet.

Model armCategoriesStudy designConfidence
gemmano category
Domain: not available · Genre: Empirical
About the Canadian research system: no · About a Canadian topic: no
Theoretical or conceptuallow
gptno category
Domain: not available · Genre: Other
About the Canadian research system: no · About a Canadian topic: no
Theoretical or conceptuallow
models agreeAgreement compares identical category sets and study designs across arms.

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 categoriesInsufficient 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: none
Teacher disagreement score0.985
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)0.0020.002

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 head0.007
GPT teacher head0.226
Teacher spread0.219 · 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