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Record W2919459026 · doi:10.1063/1.5054897

Representation of surfaces using spinor operators

2019· article· en· W2919459026 on OpenAlex
Jayme Vaz

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

VenueJournal of Mathematical Physics · 2019
Typearticle
Languageen
FieldMathematics
TopicAlgebraic and Geometric Analysis
Canadian institutionsUniversity of Waterloo
FundersFundação de Amparo à Pesquisa do Estado de São Paulo
KeywordsSpinorDirac operatorOperator (biology)Representation (politics)MathematicsDirac equationGeneralizationSurface (topology)Algebra over a fieldQuaternionic representationClifford analysisPure mathematicsMathematical physicsReal representationMathematical analysisGeometryIrreducible representation

Abstract

fetched live from OpenAlex

We use the concept of spinor operator to study some aspects of the classical theory of surfaces in three dimensions. We show that a spinor operator representing a surface satisfies a pair of Dirac-like equations and that this spinor operator representation is a generalization of the Weierstrass representation of minimal surfaces. We also obtain spinor operator representations of a surface directly from its parameterization in terms of isothermal parameters, without the need of solving the pair of Dirac-like equations. We apply these results to minimal surfaces and their deformations and also show how they can be written in terms of quaternions and complex numbers.

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)0.001
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 score0.074
Threshold uncertainty score0.371

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
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 head0.068
GPT teacher head0.352
Teacher spread0.284 · 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