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Record W4417233078 · doi:10.4171/dm/1039

The topological form is the Pfaffian form

2025· article· W4417233078 on OpenAlex
Paul‐Hermann Balduf, Simone Hu

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.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueDocumenta Mathematica · 2025
Typearticle
Language
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of CanadaInstitut Périmètre de physique théorique
KeywordsPfaffianCohomologyDifferential formTopological quantum field theoryEquivalence (formal languages)Commutative propertyGraphQuantum field theoryTopological algebra

Abstract

fetched live from OpenAlex

For a given graph G , Budzik, Gaiotto, Kulp, Wang, Williams, Wu, Yu, and the first author studied a ‘topological’ differential form \alpha_{G} , which expresses violations of BRST-closedness of a quantum field theory along a single topological direction. In a seemingly unrelated context, Brown, Panzer, and the second author studied a ‘Pfaffian’ differential form \phi_{G} , which is used to construct cohomology classes of the odd commutative graph complex and of \mathsf{GL}_{2n}(\Z) . We give an explicit combinatorial proof that \alpha_{G} coincides with \phi_{G} . We also discuss the equivalence of several properties of these forms which had been established independently for both contexts in previous work.

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)0.003
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies, Insufficient payload (model declined to judge)
Consensus categoriesScience and technology studies, Insufficient payload (model declined to judge)
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 score0.714
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.001
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0000.001
Science and technology studies0.0040.003
Scholarly communication0.0010.000
Open science0.0030.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0090.002

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 head0.021
GPT teacher head0.330
Teacher spread0.309 · 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