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Paper Citation Record · LEDGER

Analytical calculation of the inverse nabla Laplace transform

As of 16 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:1909.02655.

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

pith.paper-citation-record.v1
1909.02655 v2

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:41:09.301144Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

19 of 19 outbound references displayed

  • verified exact3
  • verified fuzzy6
  • unresolved10
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 854fc031-2232-4476-ba72-d253344e7ef2 · outbound

This paper cites an unresolved cited work.

Analytical calculation of the inverse nabla Laplace transform Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:09.522193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.235594Z digest=sha256:eb4af4b43db3884ddc54111a9e84f9d78cdca34f6c01f35e52aca4ca74f2eb68

Observation e8472ef0-60bd-4ab6-86d5-f7ee1e7bf859 · outbound

This paper cites Jarad, B.

Analytical calculation of the inverse nabla Laplace transform Jarad, B

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:09.513515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.239976Z digest=sha256:1f3a8e71b7bc6d4936049e73c903abc3b4c7bb54280d50717f38b79e31b286c7

Observation 20fe231f-3cf5-40e7-82b3-5ee291463c9d · outbound

This paper cites an unresolved cited work.

Analytical calculation of the inverse nabla Laplace transform Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:09.504524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.243654Z digest=sha256:549a52a03e2b9273781eb147540a608a53a082408cf9c3d1624f1683b95efd0d

Observation 04f3ded8-da88-4966-8deb-75c4dcbbb51b · outbound

This paper cites an unresolved cited work.

Analytical calculation of the inverse nabla Laplace transform Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:09.495156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.247203Z digest=sha256:caee7b3853aa6bae259856a2de8cc11ddd566f8c4ff129dcf2f0a4504e39187c

Observation 4862d4fa-6eb4-41eb-a030-3a8d98d48629 · outbound

This paper cites Abdeljawad, F.

Analytical calculation of the inverse nabla Laplace transform Abdeljawad, F

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:09.486013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.250929Z digest=sha256:ee6b3054af6ba5e8ccf16c2ba090f611f9198f992bc56e2c42ed21954b17ef76

Observation 65f8e34d-0ab5-4073-a79b-f07b6522a0c5 · outbound

This paper cites an unresolved cited work.

Analytical calculation of the inverse nabla Laplace transform Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:09.476533Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.254719Z digest=sha256:3f6c413fbe45c717e3a2a6f275e8f3163a98764b4f5fa869e1271db85b4a7d87

Observation 6b11c849-977c-44ed-8f83-6aad879a204d · outbound

This paper cites Abdeljawad, and D.

Analytical calculation of the inverse nabla Laplace transform Abdeljawad, and D

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:09.465174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.258717Z digest=sha256:59b7882b621ba4f5d536da735d62a7987bd5bbd408b6a2fb12996162c3bfe57c

Observation 9e6ea810-f684-4064-97e0-30ed4a1bab89 · outbound

This paper cites Bohner, and A.

Analytical calculation of the inverse nabla Laplace transform Bohner, and A

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:09.453357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.261693Z digest=sha256:a63e7cfcdb3a7692c2f0abc4d34ea450e7a24f8ea1d0bafde2692781de84d1c9

Observation 1780f905-ad1d-4c3e-9abb-fdc46e7b1814 · outbound

This paper cites an unresolved cited work.

Analytical calculation of the inverse nabla Laplace transform Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:09.442646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.265045Z digest=sha256:8352f502310d7e39378bc1425aa04e537f346b5e56d5b2588a57029d21d84e90

Observation e90b6327-a250-45cd-90fb-527b79d59fb5 · outbound

This paper cites Cheng, Theory of Fractional Difference Equations, Xiamen: Xiamen University Press, 2011.

Analytical calculation of the inverse nabla Laplace transform Cheng, Theory of Fractional Difference Equations, Xiamen: Xiamen University Press, 2011

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:09.433143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.269042Z digest=sha256:a1f6bc36402e6df16ef1a9c3bf5103be3e70e46bc09a77f0fb400d850db0e823

Observation a7e205c5-a6d4-452f-91c2-d1ab26d33d4e · outbound

This paper cites an unresolved cited work.

Analytical calculation of the inverse nabla Laplace transform Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:09.423352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.272928Z digest=sha256:8664939de11a30856248eee6a1c0bca2854ee47f7ea9eae7ad6ca7a25b7570ba

Observation 4ba881e9-ca6e-4df6-a1c4-ec28304e64cc · outbound

This paper cites Goodrich, and A.

Analytical calculation of the inverse nabla Laplace transform Goodrich, and A

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:09.413969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.277362Z digest=sha256:b37008ce9a3676d3e8f8311da1e052cb254be3b969b3861adfcb1a8128f143f1

Observation ccc5d62f-9008-41a3-bf54-93d4a7f98edf · outbound

This paper cites Time-domain response of nabla discrete fractional order systems.

Analytical calculation of the inverse nabla Laplace transform Time-domain response of nabla discrete fractional order systems

Reference 13

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:41:09.359838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.280542Z digest=sha256:3e3dc9b3d7a9144384680856978d74a77c3dfa813568c21d643aaa357bc1c514

Observation 816676f4-f2eb-442a-aa01-62bc5b528d5c · outbound

This paper cites an unresolved cited work.

Analytical calculation of the inverse nabla Laplace transform Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:09.404651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.284357Z digest=sha256:cddf2954d09240cadccc4dcd71c6250b2f7647953f1050756e95eb94eafa3c5b

Observation 311f098a-4f3b-4c56-abf8-257a60fc1bdd · outbound

This paper cites an unresolved cited work.

Analytical calculation of the inverse nabla Laplace transform Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:09.394108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.287993Z digest=sha256:22321ecfd688b9f8edbbba1c13bca69870e768e5649be9f4eadadd69cd695ed3

Observation 328cd680-e484-407e-aee4-e103d3f0572e · outbound

This paper cites an unresolved cited work.

Analytical calculation of the inverse nabla Laplace transform Unresolved cited work

Reference 16

Resolution
verified exact
doi, observed 2026-08-14T11:41:09.329951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.291239Z digest=sha256:90529fc4d95354300cef69ac4598e33e09e10653b3bbc8899d0cd3a75058554f

Observation 84494830-09ca-4130-80cc-b59e610164e6 · outbound

This paper cites an unresolved cited work.

Analytical calculation of the inverse nabla Laplace transform Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:09.382924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.294277Z digest=sha256:f131c75f6ef22ba67d70d65f6ca46a4b48f575b39a024a89ae62a342914c0560

Observation fb1a369a-1a8a-41a9-a7e3-9556ba830ed7 · outbound

This paper cites Lyapunov functions for nabla discrete fractional order systems.

Analytical calculation of the inverse nabla Laplace transform Lyapunov functions for nabla discrete fractional order systems

Reference 18

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:41:09.345101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.297532Z digest=sha256:5da74dcfb8ef74d70315c99312f5a212942633f71140cc563c2a03aa5df9e7cb

Observation a4033a12-91aa-45aa-ae05-12d37aa30f43 · outbound

This paper cites an unresolved cited work.

Analytical calculation of the inverse nabla Laplace transform Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:09.372682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:09.301144Z digest=sha256:1d5abaa46b08b97b2c221f2fd0491aae2adf4966072f474767ec50856c5e1f74

Pith citing papers

No inbound Pith citation observations are available.