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Topological Inference of the Conley Index

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Ka Man Yim, Vidit Nanda

Dynamical Systems · Submitted 21 Jun 2022

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

The authors' main claim This allows us to estimate the Conley index, and as a direct consequence, we are also able to estimate the Morse index of any critical point of a Morse function using finitely many local evaluations.

how it is stated · asserted 0.95 read the record →

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arXiv ID2206.10198 (version 1)
Pith IDIBB45E2H, Pith's permanent record of this paper and its review
CitationKa Man Yim, Vidit Nanda. "Topological Inference of the Conley Index." arXiv:2206.10198 (2022). https://pith.science/paper/IBB45E2H
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,268 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.36 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · 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 Conley index of an isolated invariant set is a fundamental object in the study of dynamical systems. Here we consider smooth functions on closed submanifolds of Euclidean space and describe a framework for inferring the Conley index of any compact, connected isolated critical set of such a function with high confidence from a sufficiently large finite point sample. The main construction of this paper is a specific index pair which is local to the critical set in question. We establish that these index pairs have positive reach and hence admit a sampling theory for robust homology inference. This allows us to estimate the Conley index, and as a direct consequence, we are also able to estimate the Morse index of any critical point of a Morse function using finitely many local evaluations.

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 Conley index of an isolated invariant set is a fundamental object in the study of dynamical systems. background 1.00 0.04 0.03 asserted 1.00
s1 Here we consider smooth functions on closed submanifolds of Euclidean space and describe a framework for inferring the Conley index of any compact, connected isolated critical set of such a function with high confidence from a sufficiently large finite point sample. contribution 0.98 0.90 0.29 asserted 0.91
s2 The main construction of this paper is a specific index pair which is local to the critical set in question. contribution 0.82 0.92 0.20 asserted 0.98
s3 We establish that these index pairs have positive reach and hence admit a sampling theory for robust homology inference. result 0.72 0.92 0.11 asserted 1.00
s4 This allows us to estimate the Conley index, and as a direct consequence, we are also able to estimate the Morse index of any critical point of a Morse function using finitely many local evaluations. result 0.65 0.93 0.54 asserted 0.95

What kind of paper the classifier reports this is: method or tool 0.90 · evidence from proof or derivation 1.00.

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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

The Conley index of an isolated invariant set is a fundamental object in the study of dynamical systems. Here we consider smooth functions on closed submanifolds of Euclidean space and describe a framework for inferring the Conley index of any compact, connected isolated critical set of such a function with high confidence from a sufficiently large finite point sample. The main construction of this paper is a specific index pair which is local to the critical set in question. We establish that these index pairs have positive reach and hence admit a sampling theory for robust homology inference. This allows us to estimate the Conley index, and as a direct consequence, we are also able to estimate the Morse index of any critical point of a Morse function using finitely many local evaluations.

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