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Spectral determinant on graphs with generalized boundary conditions

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Jean Desbois

Mesoscale and Nanoscale Physics · Submitted 20 Sep 2001

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

The authors' main claim The spectral determinant of the Schr\"odinger operator ($ - \Delta + V(x) $) on a graph is computed for general boundary conditions.

how it is stated · asserted 1.00 read the record →

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arXiv IDcond-mat/0109366 (version 1)
Pith IDUYB4QDQD, Pith's permanent record of this paper and its review
CitationJean DESBOIS. "Spectral determinant on graphs with generalized boundary conditions." arXiv:cond-mat/0109366 (2001). https://pith.science/paper/UYB4QDQD
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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,838 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The spectral determinant of the Schr\"odinger operator ($ - \Delta + V(x) $) on a graph is computed for general boundary conditions. ($\Delta$ is the Laplacian and $V(x)$ is some potential defined on the graph). Applications to restricted random walks on graphs are discussed.

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 The spectral determinant of the Schr\"odinger operator ($ - \Delta + V(x) $) on a graph is computed for general boundary conditions. contribution 0.71 0.90 0.72 asserted 1.00
s1 ($\Delta$ is the Laplacian and $V(x)$ is some potential defined on the graph). background 0.96 0.11 0.04 asserted 0.82
s2 Applications to restricted random walks on graphs are discussed. contribution 0.66 0.68 0.10 asserted 0.94

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

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  • references and citing sentences
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  • P abstract
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  • 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

The spectral determinant of the Schr\"odinger operator ($ - \Delta + V(x) $) on a graph is computed for general boundary conditions. ($\Delta$ is the Laplacian and $V(x)$ is some potential defined on the graph). Applications to restricted random walks on graphs are discussed.

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