Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:13:36.029823Z
Paper Citation Record · LEDGER
As of 8 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:2507.06716.
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 2026-08-06T19:13:36.029823Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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
54 of 54 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation e3d048a8-59ce-4298-9430-b5f74c862d60 · outbound
An optimal fractional Hardy inequality on the discrete half-line Stegun.Handbook of mathematical functions with formulas, graphs, and mathematical tables
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6f4eb0d9-af54-4eaf-9439-bc0119e17e66 · outbound
An optimal fractional Hardy inequality on the discrete half-line FractionalboundaryHardyinequalityforthecritical cases, arXiv:2308.11956, 2024
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 04e2e892-0b0e-4ae3-923a-d81f704e36ec · outbound
An optimal fractional Hardy inequality on the discrete half-line Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions ofN-body Schrödinger operators, volume 29 ofMathematical Notes
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation dc480e54-b38f-4bb8-82eb-ee78e4f95999 · outbound
An optimal fractional Hardy inequality on the discrete half-line Askey and Ranjan Roy
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 486e743a-cdb8-43e1-8fd1-4dd3e022d644 · outbound
An optimal fractional Hardy inequality on the discrete half-line Balinsky, W
Reference 5
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4de62ee0-8290-4965-93fd-b38c521d5c64 · outbound
An optimal fractional Hardy inequality on the discrete half-line Sharp Poincaré-Hardy and Poincaré- Rellich inequalities on the hyperbolic space.J
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 706ac49b-05ba-4e0a-a44f-421f93163fd8 · outbound
An optimal fractional Hardy inequality on the discrete half-line On the spectrum of singular boundary-value problems.Mat
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 43277f0e-358a-4398-977a-d07b0e8c9417 · outbound
An optimal fractional Hardy inequality on the discrete half-line The best constant in a fractional Hardy inequality
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c6e142e5-603a-4089-8240-05ac3baf9994 · outbound
An optimal fractional Hardy inequality on the discrete half-line Hardy’s inequality and Green function on metric measure spaces.J
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a58ca1cb-5cc5-46f2-aeba-4941d588ef28 · outbound
An optimal fractional Hardy inequality on the discrete half-line Hardy’s inequality for the fractional powers of a discrete Lapla- cian
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8285b7fe-8665-4dfb-9016-e22173e1e04e · outbound
An optimal fractional Hardy inequality on the discrete half-line On Landis conjecture for positive Schrödinger operators on graphs.Int
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 06acdabb-c1d6-4148-9df7-c65e50e0bace · outbound
An optimal fractional Hardy inequality on the discrete half-line The space of Hardy-weights for quasilinear operators on discrete graphs
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7a56be24-537c-41b8-a78c-9a8b3bb50bf2 · outbound
An optimal fractional Hardy inequality on the discrete half-line The Landis conjecture via Liouville comparison principle and criticality theory
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d9118d4e-6656-4620-846d-8b8d4930d2fb · outbound
An optimal fractional Hardy inequality on the discrete half-line On existence of minimizers for weighted $L^p$-Hardy inequalities on $C^{1,\gamma}$-domains with compact boundary
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1b27123d-4ffb-403f-9949-5aa4ebac6e09 · outbound
An optimal fractional Hardy inequality on the discrete half-line Optimal Hardy weight for second-order elliptic operator: an answer to a problem of Agmon.J
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1cdf5db1-8628-4e6a-972d-752bac5f5bf7 · outbound
An optimal fractional Hardy inequality on the discrete half-line OptimalLp Hardy-type inequalities
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ba5e9513-eb0f-4199-b129-d8cd3a05ac5f · outbound
An optimal fractional Hardy inequality on the discrete half-line Fractional and non-fractional Hardy inequality on a lattice $\Z^d$
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ae6081df-c14b-48bc-b90b-317bd9f783b2 · outbound
An optimal fractional Hardy inequality on the discrete half-line On(global)uniquecontinuation properties of the fractional discrete Laplacian.J
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 22858bda-1eb4-4220-b758-d98cf47669ff · outbound
An optimal fractional Hardy inequality on the discrete half-line Landis' conjecture: a survey
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e04dfda3-ea17-41f0-ba1c-8e6988ccafe3 · outbound
An optimal fractional Hardy inequality on the discrete half-line On the optimality and decay ofp-Hardy weights on graphs.Calc
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 0bc3ca9b-aa78-42ad-8a36-70b0e900d1a1 · outbound
An optimal fractional Hardy inequality on the discrete half-line Quasi-Linear Criticality Theory and Green's Functions on Graphs
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 05fe2f86-85f6-4047-87ac-3f5e66fe1c67 · outbound
An optimal fractional Hardy inequality on the discrete half-line An improved discretep-Hardy inequal- ity
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d480df2e-3a4f-4105-9a81-2fb7d466ccdf · outbound
An optimal fractional Hardy inequality on the discrete half-line Sharp Hardy-type inequalities for non-compact har- monic manifolds and Damek–Ricci spaces.Israel J
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 0f3f34bd-06be-40a2-9843-af39f42de05c · outbound
An optimal fractional Hardy inequality on the discrete half-line Optimal Poincar\'e-Hardy-type Inequalities on Manifolds and Graphs
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation aa7e367d-9744-48f1-91fb-1e82c6fc1cd8 · outbound
An optimal fractional Hardy inequality on the discrete half-line Unresolved cited work
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1ca6dc54-a9f3-443b-9bc0-9b1bfbf406ff · outbound
An optimal fractional Hardy inequality on the discrete half-line Frank, Elliott H
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 632b056b-35e4-4f4b-ba58-6e52f4cf51aa · outbound
An optimal fractional Hardy inequality on the discrete half-line Criticality transition for positive powers of the discrete Laplacian on the half line.Rev
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d86b64b5-cb32-4600-a6c2-4b4554b2a927 · outbound
An optimal fractional Hardy inequality on the discrete half-line An improved discrete Rellich inequality on the half-line
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 04088e08-8ee5-470a-87a8-b0e584557a09 · outbound
An optimal fractional Hardy inequality on the discrete half-line Hardy and Rellich inequality on lattices
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 9ece4995-2b9e-44aa-a86e-5f2a7f212e62 · outbound
An optimal fractional Hardy inequality on the discrete half-line One-dimensional discrete Hardy and Rellich inequalities on integers
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 64552b91-cbf9-4bc7-9796-dca416319e7c · outbound
An optimal fractional Hardy inequality on the discrete half-line Unresolved cited work
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bc1958b8-2ba0-4f91-b61c-f909ae887931 · outbound
An optimal fractional Hardy inequality on the discrete half-line Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation f1c500d9-f2aa-40cf-9a3a-6c65bd9c3e01 · outbound
An optimal fractional Hardy inequality on the discrete half-line Wojciechowski.Graphs and discrete Dirichlet spaces
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 895e8cc1-c0ef-4349-a84f-0c7a1da7213f · outbound
An optimal fractional Hardy inequality on the discrete half-line Optimal Hardy inequality for fractional Laplacians on the integers.Ann
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3443c2c9-b62f-4cab-a2dc-ce5c09326f58 · outbound
An optimal fractional Hardy inequality on the discrete half-line An improved discrete Hardy in- equality
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c1ac30a8-433a-4e89-a874-49a301ce25d9 · outbound
An optimal fractional Hardy inequality on the discrete half-line Optimal Hardy inequalities for Schrödinger operators on graphs.Comm
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2ffe1db3-3419-438a-beec-ab0c51714791 · outbound
An optimal fractional Hardy inequality on the discrete half-line Criticality theory for Schrödinger operators on graphs.J
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7daa7e33-9a03-419f-90c6-cd813bbc286a · outbound
An optimal fractional Hardy inequality on the discrete half-line From Hardy to Rellich inequalities on graphs
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4a77a96c-67dc-473c-a5f1-226b9e608208 · outbound
An optimal fractional Hardy inequality on the discrete half-line Unresolved cited work
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 34a72ea6-22a2-4f79-9743-b248dda5d46f · outbound
An optimal fractional Hardy inequality on the discrete half-line Geometrical aspects of spectral theory
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 0aa027e1-4dec-46c4-82c0-304df6c09d40 · outbound
An optimal fractional Hardy inequality on the discrete half-line A sharp form of the discrete Hardy inequality and the Keller-Pinchover-Pogorzelski inequality.Amer
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 9c78fc55-ab16-46fc-adee-25dcc982d827 · outbound
An optimal fractional Hardy inequality on the discrete half-line Spectral enclosures and stability for non- self-adjoint discrete Schrödinger operators on the half-line.Bull
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 25c9489d-8966-46fb-b07b-2278b99203ae · outbound
An optimal fractional Hardy inequality on the discrete half-line The prehistory of the Hardy inequality
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 79ea6c32-754a-4c01-81cd-73d93037bb48 · outbound
An optimal fractional Hardy inequality on the discrete half-line Hölder-Lebesgue regularity and almost periodicity for semidis- crete equations with a fractional Laplacian
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 07ff939b-d9f1-4640-a615-b5cc1a98d714 · outbound
An optimal fractional Hardy inequality on the discrete half-line Cambridge Series in Statistical and Proba- bilistic Mathematics
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b036d28e-b541-4e37-9770-f2dde9c642fd · outbound
An optimal fractional Hardy inequality on the discrete half-line A Liouville-type theorem for Schrödinger operators.Comm
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 79208bc4-a08f-4a6c-85f8-9a455c689853 · outbound
An optimal fractional Hardy inequality on the discrete half-line On positive solutions of the(p, A)-Laplacian with potential in Morrey space.Anal
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 70a816e7-fa85-4712-92a0-fa5ca83693ff · outbound
An optimal fractional Hardy inequality on the discrete half-line Ground state alternative forp-Laplacian with potential term
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 13f2bb16-154c-427a-a345-af7773d82698 · outbound
An optimal fractional Hardy inequality on the discrete half-line ImprovementofthediscreteHardyinequality
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 9958a3e7-2ffa-40dc-a722-e32cd8c79735 · outbound
An optimal fractional Hardy inequality on the discrete half-line (Weak) Hardy and Poincaré inequalities and criticality theory
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c9bd9f10-cc75-4790-af82-3babb52267a4 · outbound
An optimal fractional Hardy inequality on the discrete half-line Orthogonal polynomials, volume Vol
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 9f89ee1e-5b34-49b8-8ff1-ca50bff3b4b4 · outbound
An optimal fractional Hardy inequality on the discrete half-line Criticality for Schrödinger type operators based on recurrent symmetric stable processes
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 96b98785-c12e-4432-a05f-a4814aa33758 · outbound
An optimal fractional Hardy inequality on the discrete half-line Optimal Hardy-weights for the (p, A)-Laplacian with a potential term
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7e1d5bde-20b3-455c-b618-b79f7a8379bb · outbound
An optimal fractional Hardy inequality on the discrete half-line Nauk SSSR, Vsesoyuz
Reference 220
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
No inbound Pith citation observations are available.