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Multiple quadrature

2000· book-chapter· en· W4388319155 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

Venuenot available
Typebook-chapter
Languageen
FieldMathematics
TopicIterative Methods for Nonlinear Equations
Canadian institutionsSimon Fraser University
Fundersnot available
KeywordsQuadrature (astronomy)Unit circleNumerical integrationClenshaw–Curtis quadratureMathematicsGauss–Laguerre quadratureTanh-sinh quadratureGauss–Kronrod quadrature formulaGauss–Hermite quadratureMathematical analysisCalculus (dental)GeometryGaussian quadratureNyström methodPhysicsOpticsIntegral equation

Abstract

fetched live from OpenAlex

Abstract Methods of approximate integration based on quadrature are historically the oldest of the integration techniques. In fact, the term quadrature stems from the ancient Greek problem of “squaring the circle”. The squaring of a circle is the process of inscribing or circumscribing a circle with rectangles (or polygons) of known area for the purpose of estimating n (i.e. the area of a circle with unit radius). Engels (1980) provides a brief history of the development of quadrature.

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 categoriesMeta-epidemiology (narrow), Insufficient 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: Other · Consensus signal: Other
Teacher disagreement score0.421
Threshold uncertainty score1.000

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 integrity0.0000.001
Insufficient payload (model declined to judge)0.0170.002

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 head0.122
GPT teacher head0.366
Teacher spread0.244 · 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