Pith. Sign in

RECORD

Dixmier traces on noncompact isospectral deformations

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Victor Gayral, Bruno Iochum, Joseph C. Varilly

High Energy Physics - Theory · Submitted 21 Jul 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that this relation persists for actions of $R^l$, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDhep-th/0507206 (version 2)
Pith IDX6VFWMEB, Pith's permanent record of this paper and its review
CitationBruno Iochum, Joseph C. Varilly, Victor Gayral. "Dixmier traces on noncompact isospectral deformations." arXiv:hep-th/0507206 (2005). https://pith.science/paper/X6VFWMEB
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,000 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.83 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.84 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group $R^l$. Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals of functions on the manifold. We show that this relation persists for actions of $R^l$, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group $R^l$. contribution 1.00 0.92 0.10 asserted 1.00
s1 Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals of functions on the manifold. background 1.00 0.08 0.06 asserted 1.00
s2 We show that this relation persists for actions of $R^l$, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators. result 0.89 0.95 0.82 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group $R^l$. Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals of functions on the manifold. We show that this relation persists for actions of $R^l$, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators.

Human review

How Pith checks papers → · Full audit of this paper →

References
How the literature uses it

1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.