The spectral torsion for the rescaled Dirac operator

Tong Wu; Yong Wang

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The spectral torsion for the rescaled Dirac operator

Tong Wu, Yong Wang

Differential Geometry · Submitted 24 Feb 2025

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

The authors' main claim Further, based on the trilinear Clifford multiplication by functional of differential one-forms, we compute the spectral torsion for four kinds of rescaled Dirac operator on even-dimensional oriented compact spin Riemannian manifolds without boundary.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,303 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.05 · mentions code or data availability 0.02.

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

In the paper, we give four different examples of the rescaled Dirac operator by the perturbation of the function f. Further, based on the trilinear Clifford multiplication by functional of differential one-forms, we compute the spectral torsion for four kinds of rescaled Dirac operator on even-dimensional oriented compact spin Riemannian manifolds without boundary.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In the paper, we give four different examples of the rescaled Dirac operator by the perturbation of the function f.	contribution 0.91	0.93	0.08	asserted 1.00
s1	Further, based on the trilinear Clifford multiplication by functional of differential one-forms, we compute the spectral torsion for four kinds of rescaled Dirac operator on even-dimensional oriented compact spin Riemannian manifolds without boundary.	result 0.44	0.95	0.56	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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arXiv listing abstract v2

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T body sentences
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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

In the paper, we give four different examples of the rescaled Dirac operator by the perturbation of the function f. Further, based on the trilinear Clifford multiplication by functional of differential one-forms, we compute the spectral torsion for four kinds of rescaled Dirac operator on even-dimensional oriented compact spin Riemannian manifolds without boundary.

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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

What it cites · 1 sentence without a confident label

Cites as background 1 paper

Hong and Wang computed the spectral Einstein functional associated with the Dirac operator with torsion on even-dimensional spin manifolds without boundary in [ref] .

The spectral Einstein functional for the Dirac operator with torsion · Introduction · 0.90

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