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Record W4210694690 · doi:10.1093/imrn/rnac044

The Basic de Rham Complex of a Singular Foliation

2022· article· en· W4210694690 on OpenAlex
David Miyamoto

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.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueInternational Mathematics Research Notices · 2022
Typearticle
Languageen
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsUniversity of Toronto
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsFoliation (geology)MathematicsSubmanifoldQuotientIsomorphism (crystallography)Pure mathematicsDimension (graph theory)Manifold (fluid mechanics)Differential formRiemannian manifoldMathematical analysis

Abstract

fetched live from OpenAlex

Abstract A singular foliation $\mathcal {F}$ gives a partition of a manifold $M$ into leaves whose dimension may vary. Associated to a singular foliation are two complexes, that of the diffeological differential forms on the leaf space $M / \mathcal {F}$ and that of the basic differential forms on $M$. We prove the pullback by the quotient map provides an isomorphism of these complexes in the following cases: when $\mathcal {F}$ is a regular foliation, when points in the leaves of the same dimension assemble into an embedded (more generally, diffeological) submanifold of $M$, and, as a special case of the latter, when $\mathcal {F}$ is induced by a linearizable Lie groupoid or is a singular Riemannian foliation.

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)0.005
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
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 score0.042
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0050.003
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0010.000
Scholarly communication0.0000.000
Open science0.0010.001
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.000

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 head0.175
GPT teacher head0.453
Teacher spread0.277 · 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