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Record W2342796914 · doi:10.48550/arxiv.1602.01715

Loop equations from differential systems

2016· preprint· en· W2342796914 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

VenuearXiv (Cornell University) · 2016
Typepreprint
Languageen
FieldMathematics
TopicAdvanced Topics in Algebra
Canadian institutionsUniversité de Montréal
Fundersnot available
KeywordsMathematicsPrincipal bundleLoop (graph theory)Riemann surfacePure mathematicsLie algebraLoop algebraAlgebra over a fieldFiber bundleDifferential equationVirasoro algebraMathematical physicsBundleMathematical analysisCombinatoricsCurrent algebraAlgebra representationLine bundle

Abstract

fetched live from OpenAlex

To any differential system $dΨ=ΦΨ$ where $Ψ$ belongs to a Lie group (a fiber of a principal bundle) and $Φ$ is a Lie algebra $\mathfrak g$ valued 1-form on a Riemann surface $Σ$, is associated an infinite sequence of "correlators" $W_n$ that are symmetric $n$-forms on $Σ^n$. The goal of this article is to prove that these correlators always satisfy "loop equations", the same equations satisfied by correlation functions in random matrix models, or the same equations as Virasoro or W-algebra constraints in CFT.

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)
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 score0.645
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 science0.0010.001
Research integrity0.0000.001
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 head0.152
GPT teacher head0.239
Teacher spread0.087 · 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