Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T10:24:56.579969Z
Paper Citation Record · LEDGER
As of 23 August 2026, this Paper Citation Record lists 66 of 66 outbound references and 0 inbound Pith citation observations for arXiv:2412.16752.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T10:24:56.579969Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
66 of 66 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation dbd7a6ef-919a-49f7-a303-5a1ce0cbae3f · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 610f08ca-fd6c-4f0c-b38b-0cf3346c495e · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7b1f4df8-45d6-4a86-8578-765fa9d53249 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 295dce54-4bdd-4e90-aa9e-5f0d9cd8df5c · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Asahi, Spectral theory of the difference equations , Progr
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2ec1bc45-fd7e-40d6-9bf5-44ec19b7271d · outbound
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 16f02c3e-d08e-459c-aa65-addf841d9e6f · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation fc6a509a-cb6e-4a72-8293-753509ef0b1a · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d23ef0d1-f964-4a85-9193-28c3e48b1b5a · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 58e0357e-3c6c-411f-aaf4-24414c648aca · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation bf0147da-aedb-4064-8270-64f8f76ddf8c · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation dadce278-2c79-4161-aa0c-a669e84d705f · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 97e7fd2b-e836-4b9c-a23f-ec05504cf7a0 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 70195316-236f-4143-b2b8-cfeba677aeca · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Bohner and O
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e77db4f6-a488-4a7f-a409-bb2e9ef47660 · outbound
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2ca13486-39f5-4f2a-8c30-0e76aeb42814 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Bohner and S
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation df0140dc-f978-496a-91dd-933f71c36d05 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Bruce, Discrete time in quantum mechanics , Phys
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b1da1e5f-7a3b-4e5e-bb52-f5bb6ad6c874 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 58aa33a4-1c0a-4e79-b9d4-09433abc7cc5 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 00d290b6-6d51-4675-853e-c8b686952864 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c538d60c-27f4-4eaa-8c64-04f841342d75 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 25d26cce-4709-4669-b6b3-328df82d594c · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3b1492d6-b556-4c50-b723-c98eb52be753 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation a8e71238-6858-409c-9d2f-7bd103be15e8 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Advances in Discrete Dynam- ical Systems
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 209a24ae-4ab0-45b5-be44-bc046ac23b5e · outbound
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 08af3c23-60bc-4134-b5f0-8f1a82ed61ea · outbound
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation cca08f0f-11c0-413f-b0a9-2b93561df8bd · outbound
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e47ba449-e3f6-43f9-bcec-6cd9460e7744 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d34f87e0-e663-4bff-8817-e46d33e7a83c · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 6ccb3687-d2f8-4760-87b6-5e1e8133be2f · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 396fcaa0-d5d9-4217-87dc-822c38ac29d1 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 0546cb2c-2b04-427a-8952-04905bc0c043 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Gesztesy and E
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c99b41b1-84ab-4332-b11e-b503587104cd · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 65c3efc1-a9d9-4742-8ce9-b6d75e876a05 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation a6794ad0-a8b5-428b-967a-d8df726f0c98 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8a115867-35c6-441d-b883-c21ee430fe42 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 145b677a-d895-4b2c-835d-ba6316d5434e · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5cd14031-b6b1-4717-9e58-c4fe8f9740de · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Huseynov and E
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 6d72fcda-ea69-4f8c-a722-f1a0d86209c7 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Jirari, Second-Order Sturm–Liouville Difference Equations and Or thogonal Polynomials , Memoirs of the American Mathematical Society, V ol
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 85a25457-2412-4083-8084-53ebbc6f545d · outbound
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b7f37f2f-dda9-440f-ba4d-a609c9c0a9ae · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 90e63e85-2213-4168-a9bb-ddcab129efa9 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Kratz, An oscillation theorem for self-adjoint differential syst ems and the Rayleigh principle for quadratic functionals , J
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 15a30deb-581c-4a25-b930-072bd2659161 · outbound
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 82292db6-4dac-49e5-9114-0435664f63bf · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation cf7b4df8-29c2-46d3-bb09-7dfd9b4f2387 · outbound
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation ab62ccd4-2722-4385-8682-b62122ebc458 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 104230c2-df4f-4e7a-a2fe-01583f32b584 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e027c02c-2fcc-44dd-8da9-0dc13c26ee59 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c1fb8984-5cd1-4773-9260-71dd56934478 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e8527111-10f5-4a0b-a872-fa14e56e8a4d · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c2843d70-b320-4369-8281-f621c8130e2f · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Operator Theor y: Advances and Applications
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2749a987-b6df-434c-a226-b65addc50b84 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Schur, Zur Entwicklung willkürlicher Funktionen nach Lösungen vo n Systemen linearer Dif- ferentialgleichungen (in German), Math
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9e13c41c-5a94-4d20-8e15-3e51230cd7a3 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Shi, Weyl–Titchmarsh theory for a class of discrete linear Hamil tonian systems, Linear Alge- bra Appl
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e39550ee-ce20-49d7-82ad-d3d9c1f8ee5b · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Simon, Loewner’s Theorem on Monotone Matrix Functions , Grundlehren der Mathematis- chen Wissenschaften [Fundamental Principles of Mathemati cal Sciences], V ol
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b77d2d51-fe64-4945-9fb8-71c12a726b84 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Šimon Hilscher and V
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e9aaa2cf-3f15-44fb-beb3-02bc3a8b3f12 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Šimon Hilscher and P
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9aa9eff3-a57a-461f-a8d7-fee0386bc81e · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Šimon Hilscher and P
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c0aa06ba-3cff-4f7a-9c37-ef61172e907f · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d63d28c1-369d-4394-9b79-d7551486407f · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5b6545bb-a598-48cd-8574-dfabda18f3ff · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8ce68413-293c-4385-bf60-65bfa3375dbd · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Unresolved cited work
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c1dc5e2e-4bc7-4fcf-b17a-3e4a173d2e21 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Teschl, Jacobi Operators and Completely Integrable Nonlinear Latt ices, Mathematical Sur- veys and Monographs, V ol
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation edf3a8e6-ffd6-45d4-9e85-4bf62a564191 · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Tuna, Completeness theorem for the dissipative Sturm–Liouville operator on bounded time scales, Indian J
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 30bd6305-f7ce-42fa-8845-26b1c490a73a · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Viglialoro and J
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e03c4b05-179c-4d57-874e-25b97937d92a · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Progress on Difference Equations and Discrete Dynamic al Systems
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c15ea2c0-8b19-44d4-83d9-2b63d73fc80c · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Zemánek and S
Reference 65
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7f5119a5-553b-498e-836b-a532a5f99cbc · outbound
Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter Zemánek and S
Reference 66
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
No inbound Pith citation observations are available.