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Record W79067861 · doi:10.30827/pna.v9i1.6109

<p>The width of a proof</p>

2014· article· es· W79067861 on OpenAlex
Gila Hanna

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

VenuePNA · 2014
Typearticle
Languagees
FieldSocial Sciences
TopicMathematics Education and Teaching Techniques
Canadian institutionsInstitute for Christian StudiesUniversity of Toronto
Fundersnot available
KeywordsHumanitiesPhilosophy

Abstract

fetched live from OpenAlex

This paper’s aim is to discuss the concept of width of a proof put forward by Timothy Gowers. It explains what this concept means and attempts to show how it relates to other concepts discussed in the existing literature on proof and proving. It also explores how the concept of width of a proof might be used productively in the mathematics curriculum and how it might fit with the various perspectives on learning to prove.La amplitud de una demostraciónEl objetivo de este artículo es discutir el concepto de amplitud de una demostración presentado por Timothy Gowers. Se explica el significado de este concepto y se trata de mostrar cómo se relaciona con otros conceptos discutidos en la literatura existente sobre prueba y demostraciones. También se explora cómo el concepto de amplitud de una demostración podría utilizarse productivamente en el currículo de matemáticas y cómo podría encajar con las diferentes perspectivas sobre el aprendizaje de la demostración.Handle: http://hdl.handle.net/10481/33233Nº de citas en SCOPUS (2017): 1 (Citas de 2º orden, 0)

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)0.002
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: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.907
Threshold uncertainty score0.412

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
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 science0.0010.000
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 head0.025
GPT teacher head0.334
Teacher spread0.308 · 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