Paper Citation Record · LEDGER

Generic simplicity for self-adjoint operators under bounded potential perturbations

As of 12 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 2 inbound Pith citation observations for arXiv:2605.31368.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2605.31368 v2

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T12:52:53.401384Z

measured 51 of 51 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T00:20:43.236281Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-06T00:20:43.500587Z

Reference resolution

49 of 49 outbound references displayed

verified exact1
verified fuzzy0
unresolved48
parse uncertain0
malformed identifier0
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External citation measurements

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Outbound references

Observation 5f9f6607-79ee-44de-8c28-ce4057795563 · outbound

This paper cites an unresolved cited work.

Generic simplicity for self-adjoint operators under bounded potential perturbations Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:46.809916Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c4b4559c-e2e8-4982-bc87-9e750444af4f · outbound

This paper cites an unresolved cited work.

Generic simplicity for self-adjoint operators under bounded potential perturbations Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:46.852655Z

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Observation 3f61c868-0c5d-46c8-b481-b9900d8148fd · outbound

This paper cites an unresolved cited work.

Generic simplicity for self-adjoint operators under bounded potential perturbations Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:46.899437Z

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Observation cf206ce2-ed2a-49fa-aa94-4039fd1a30c5 · outbound

This paper cites an unresolved cited work.

Generic simplicity for self-adjoint operators under bounded potential perturbations Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:46.983656Z

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Observation 81c73295-4691-48f5-aa73-0ecceb82db3e · outbound

This paper cites Alessandrini,On Courant’s nodal domain theorem, Forum Math.10(1998), no.

Generic simplicity for self-adjoint operators under bounded potential perturbations Alessandrini,On Courant’s nodal domain theorem, Forum Math.10(1998), no

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:47.056833Z

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Unavailable: canonical work link unavailable.

Observation 380b2379-ffda-4c8e-8133-f07d49402c92 · outbound

This paper cites A pseudodifferential calculus for maximally hypoelliptic operators and the Helffer-Nourrigat conjecture.

Generic simplicity for self-adjoint operators under bounded potential perturbations A pseudodifferential calculus for maximally hypoelliptic operators and the Helffer-Nourrigat conjecture

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:47.166027Z

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Observation 86b32b15-f2d1-4c8d-bcec-19ffab175540 · outbound

This paper cites Arendt and M.

Generic simplicity for self-adjoint operators under bounded potential perturbations Arendt and M

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:47.292512Z

Source-reported events for the cited work

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Observation 6bdd030a-2448-45ad-8ed7-364b20df30e6 · outbound

This paper cites Aronszajn,A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J.

Generic simplicity for self-adjoint operators under bounded potential perturbations Aronszajn,A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:47.413019Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 172e44c2-2e45-4079-b996-d9e29a7fec6a · outbound

This paper cites an unresolved cited work.

Generic simplicity for self-adjoint operators under bounded potential perturbations Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:47.494606Z

Source-reported events for the cited work

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Observation b2a7d3a1-0d7b-41c6-b2f9-efeffc47f475 · outbound

This paper cites somme de carr´ es.

Generic simplicity for self-adjoint operators under bounded potential perturbations somme de carr´ es

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:47.572252Z

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Unavailable: canonical work link unavailable.

Observation f87abb7d-0e22-4ffc-8536-4178a42d2daa · outbound

This paper cites Chanillo and R.

Generic simplicity for self-adjoint operators under bounded potential perturbations Chanillo and R

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:47.691315Z

Source-reported events for the cited work

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Observation a1145213-5b0f-4382-938c-4a4b96493874 · outbound

This paper cites Chatzakou and B.

Generic simplicity for self-adjoint operators under bounded potential perturbations Chatzakou and B

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:47.812406Z

Source-reported events for the cited work

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Observation 1196605d-de1f-450a-9260-d5ee5b1455d6 · outbound

This paper cites Chatzakou, J.

Generic simplicity for self-adjoint operators under bounded potential perturbations Chatzakou, J

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:47.933436Z

Source-reported events for the cited work

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Observation 83aece5f-8696-44bb-bcdd-d4a08fcc4fe0 · outbound

This paper cites Engel and R.

Generic simplicity for self-adjoint operators under bounded potential perturbations Engel and R

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:48.010085Z

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Observation 6f787c98-1e8a-4476-8e21-a81ac15c6ada · outbound

This paper cites Eswarathasan and C.

Generic simplicity for self-adjoint operators under bounded potential perturbations Eswarathasan and C

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:48.136482Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6c1ebce-65c2-46f8-90f6-8bd109618fc7 · outbound

This paper cites Di Fazio, M.

Generic simplicity for self-adjoint operators under bounded potential perturbations Di Fazio, M

Reference 16

Resolution: verified exact; doi, observed 2026-08-02T12:54:01.857186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 550d0de8-33fc-43a6-88b4-404a0415ed21 · outbound

This paper cites an unresolved cited work.

Generic simplicity for self-adjoint operators under bounded potential perturbations Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:48.521296Z

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Observation 981d7c1f-f6ac-4f2d-bc8b-103312574cbd · outbound

This paper cites an unresolved cited work.

Generic simplicity for self-adjoint operators under bounded potential perturbations Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:48.652876Z

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Observation e7b710d5-0009-4bc4-b4fd-d33ffd7dffbf · outbound

This paper cites Gilbarg and N.

Generic simplicity for self-adjoint operators under bounded potential perturbations Gilbarg and N

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:48.863846Z

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Observation 45f287f9-1173-4a3b-9868-69b922b2c587 · outbound

This paper cites Guibourg,In´ egalit´ es maximales pour l’op´ erateur de Schr¨ odinger, C.

Generic simplicity for self-adjoint operators under bounded potential perturbations Guibourg,In´ egalit´ es maximales pour l’op´ erateur de Schr¨ odinger, C

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:49.093873Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5992e7c6-8e67-4184-a344-b3440a46da33 · outbound

This paper cites Harakeh and L.

Generic simplicity for self-adjoint operators under bounded potential perturbations Harakeh and L

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:49.257877Z

Source-reported events for the cited work

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Observation 5a590b68-e9dd-42a7-899f-e860496a7d46 · outbound

This paper cites Helffer, T.

Generic simplicity for self-adjoint operators under bounded potential perturbations Helffer, T

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:49.329989Z

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Observation e6e250a7-0069-4b82-9adf-34190f3f2965 · outbound

This paper cites Helffer and J.

Generic simplicity for self-adjoint operators under bounded potential perturbations Helffer and J

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:49.414218Z

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Observation 607cd87d-09e2-49c7-b21f-387c38c2790a · outbound

This paper cites Helffer and J.

Generic simplicity for self-adjoint operators under bounded potential perturbations Helffer and J

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:49.509290Z

Source-reported events for the cited work

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Observation d726b3ca-b13c-4b4d-9127-e22a2d315971 · outbound

This paper cites Helffer and A.

Generic simplicity for self-adjoint operators under bounded potential perturbations Helffer and A

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:49.595978Z

Source-reported events for the cited work

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Observation 03d0b4af-d947-4921-ae7b-1de60757aad6 · outbound

This paper cites Helffer,Introduction to semi-classical methods for the Schr¨ odinger operator with magnetic fields, in: A.

Generic simplicity for self-adjoint operators under bounded potential perturbations Helffer,Introduction to semi-classical methods for the Schr¨ odinger operator with magnetic fields, in: A

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:49.695861Z

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Observation d4b0899e-cbf1-4804-81f0-cac5e1ff6c8d · outbound

This paper cites Helffer,Spectral Theory and its Applications, Cambridge Studies in Advanced Mathematics, vol.

Generic simplicity for self-adjoint operators under bounded potential perturbations Helffer,Spectral Theory and its Applications, Cambridge Studies in Advanced Mathematics, vol

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:49.789818Z

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Unavailable: canonical work link unavailable.

Observation ef3dea45-86d4-42a9-99ef-74a51af50ff6 · outbound

This paper cites Helffer and J.

Generic simplicity for self-adjoint operators under bounded potential perturbations Helffer and J

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:49.883984Z

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Observation 3366f149-640b-4bcd-a035-708ebcdebdcc · outbound

This paper cites H¨ ormander,Hypoelliptic second order differential equations, Acta Math.119(1967), 147–171.

Generic simplicity for self-adjoint operators under bounded potential perturbations H¨ ormander,Hypoelliptic second order differential equations, Acta Math.119(1967), 147–171

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:50.059699Z

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Unavailable: canonical work link unavailable.

Observation 97533f6a-4e7a-490d-8221-d1c3105f71c0 · outbound

This paper cites Iwatsuka,Magnetic Schr¨ odinger operators with compact resolvent, J.

Generic simplicity for self-adjoint operators under bounded potential perturbations Iwatsuka,Magnetic Schr¨ odinger operators with compact resolvent, J

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:50.211681Z

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Observation 45ab0100-4fad-467b-8c1d-539e18725b75 · outbound

This paper cites Kato,Perturbation Theory for Linear Operators, Classics in Mathematics, Springer, Berlin, 1995.

Generic simplicity for self-adjoint operators under bounded potential perturbations Kato,Perturbation Theory for Linear Operators, Classics in Mathematics, Springer, Berlin, 1995

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:50.311769Z

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Unavailable: canonical work link unavailable.

Observation 18d220e8-96e1-45e0-a1b3-528f595c39c3 · outbound

This paper cites Kondratiev and M.

Generic simplicity for self-adjoint operators under bounded potential perturbations Kondratiev and M

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:50.407682Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dcf91cc7-2cd2-4285-b6c9-55160b3d78b1 · outbound

This paper cites Laurent and M.

Generic simplicity for self-adjoint operators under bounded potential perturbations Laurent and M

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:50.506956Z

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Observation 67637db8-aa0e-409d-a9f3-2a2a04403d38 · outbound

This paper cites an unresolved cited work.

Generic simplicity for self-adjoint operators under bounded potential perturbations Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:50.706944Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f249fb6-846b-466f-84fb-d6011cf8ee54 · outbound

This paper cites Lu,Weighted Poincar´ e and Sobolev inequalities for vector fields satisfying H¨ ormander’s con- dition and applications, Rev.

Generic simplicity for self-adjoint operators under bounded potential perturbations Lu,Weighted Poincar´ e and Sobolev inequalities for vector fields satisfying H¨ ormander’s con- dition and applications, Rev

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:50.864976Z

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Unavailable: canonical work link unavailable.

Observation 6c788486-1d2a-4a70-ba26-d293004b23b2 · outbound

This paper cites Lu, On Harnack’s inequality for a class of strongly degenerate Schr¨ odinger operators formed by vector fields, Differ.

Generic simplicity for self-adjoint operators under bounded potential perturbations Lu, On Harnack’s inequality for a class of strongly degenerate Schr¨ odinger operators formed by vector fields, Differ

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:50.999536Z

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Observation 2b458181-e906-4a4c-a218-588b85369f6d · outbound

This paper cites Mohsen,Abstract maximal hypoellipticity and applications, arXiv:2601.13741 [math.OA], 2026.

Generic simplicity for self-adjoint operators under bounded potential perturbations Mohsen,Abstract maximal hypoellipticity and applications, arXiv:2601.13741 [math.OA], 2026

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:51.088947Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8660d304-009c-483a-b157-691c65dbf344 · outbound

This paper cites Persson,Bounds for the discrete part of the spectrum of a semi-bounded Schr¨ odinger operator, Math.

Generic simplicity for self-adjoint operators under bounded potential perturbations Persson,Bounds for the discrete part of the spectrum of a semi-bounded Schr¨ odinger operator, Math

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:51.181822Z

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Unavailable: canonical work link unavailable.

Observation da99ed08-f816-46e3-aa7b-093d65e51eec · outbound

This paper cites Pleijel,Remarks on Courant’s nodal line theorem, Comm.

Generic simplicity for self-adjoint operators under bounded potential perturbations Pleijel,Remarks on Courant’s nodal line theorem, Comm

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:51.253317Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 978e2393-6ec9-47e3-be71-cf48db512cf2 · outbound

This paper cites Reed and B.

Generic simplicity for self-adjoint operators under bounded potential perturbations Reed and B

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:51.323531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4e4e2751-6d59-4098-9ff8-fa1d73745a70 · outbound

This paper cites Reed and B.

Generic simplicity for self-adjoint operators under bounded potential perturbations Reed and B

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:51.398028Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a3d6b1d-6426-4222-84e5-dd3351ed8f3e · outbound

This paper cites an unresolved cited work.

Generic simplicity for self-adjoint operators under bounded potential perturbations Unresolved cited work

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:51.528780Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b3b2150-66ce-4b44-a0b0-77b1a6331d71 · outbound

This paper cites Shen,L p estimates for Schr¨ odinger operators with certain potentials, Ann.

Generic simplicity for self-adjoint operators under bounded potential perturbations Shen,L p estimates for Schr¨ odinger operators with certain potentials, Ann

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:51.636456Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 533d7685-49ab-45dc-9017-41c6a992b1eb · outbound

This paper cites Simon,Schr¨ odinger operators with purely discrete spectrum, Methods Funct.

Generic simplicity for self-adjoint operators under bounded potential perturbations Simon,Schr¨ odinger operators with purely discrete spectrum, Methods Funct

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:51.713684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 642589bd-a76a-4e60-980c-1c157d1cdc77 · outbound

This paper cites Simon,Some quantum operators with discrete spectrum but classically continuous spectrum, Ann.

Generic simplicity for self-adjoint operators under bounded potential perturbations Simon,Some quantum operators with discrete spectrum but classically continuous spectrum, Ann

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:51.872010Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb2528b3-c665-402a-93f0-36357c723a62 · outbound

This paper cites Teschl,Mathematical Methods in Quantum Mechanics: With Applications to Schr¨ odinger Op- erators, Graduate Studies in Mathematics, vol.

Generic simplicity for self-adjoint operators under bounded potential perturbations Teschl,Mathematical Methods in Quantum Mechanics: With Applications to Schr¨ odinger Op- erators, Graduate Studies in Mathematics, vol

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:52.258686Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95ad634d-d967-4771-b34c-cdb9b4e50c42 · outbound

This paper cites Tralli,Double Ball Property for non-divergence horizontally elliptic operators on step two Carnot groups, Rend.

Generic simplicity for self-adjoint operators under bounded potential perturbations Tralli,Double Ball Property for non-divergence horizontally elliptic operators on step two Carnot groups, Rend

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:53.166173Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 61a25d8c-aa16-4347-972c-f5e63072529c · outbound

This paper cites Uhlenbeck,Generic properties of eigenfunctions, Amer.

Generic simplicity for self-adjoint operators under bounded potential perturbations Uhlenbeck,Generic properties of eigenfunctions, Amer

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:53.301774Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b401530-0a38-4191-aa73-018259b68559 · outbound

This paper cites Some Key Properties of Eigenfunctions Linked to Degenerate Elliptic Differential Operators.

Generic simplicity for self-adjoint operators under bounded potential perturbations Some Key Properties of Eigenfunctions Linked to Degenerate Elliptic Differential Operators

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-02T12:52:53.401384Z

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Unavailable: canonical work link unavailable.

Pith citing papers

Observation 83bffa64-e8dd-430e-8b07-9a589aefa53d · inbound

Coarse nodal counts on sub-Riemannian manifolds cites this paper.

Coarse nodal counts on sub-Riemannian manifolds Generic simplicity for self-adjoint operators under bounded potential perturbations

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-06T00:20:43.504562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d5d4572f-cabb-4847-b3d3-3524cb41f303 · inbound

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities cites this paper.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Generic simplicity for self-adjoint operators under bounded potential perturbations

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.124463Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.