Paper Citation Record · LEDGER

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations

As of 22 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2505.23002.

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

pith.paper-citation-record.v1
2505.23002 v2

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:01:27.974518Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

38 of 38 outbound references displayed

verified exact2
verified fuzzy23
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 47214878-8568-47d0-8335-78270ffe48e6 · outbound

This paper cites Ainsworth and J.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Ainsworth and J

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:35.798960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 439c02e6-18de-4281-95dd-d4388d9c58e9 · outbound

This paper cites Ainsworth and J.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Ainsworth and J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:35.575991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8c23f8ef-0c44-4a08-a45a-c14b1661b61b · outbound

This paper cites Arzani, K.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Arzani, K

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:35.328681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4d4ddffd-8ff1-4acd-a552-5dc3e945dd73 · outbound

This paper cites Blum and R.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Blum and R

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:35.071789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4804d958-5e79-46aa-bccf-6cf85a6bd450 · outbound

This paper cites Bottou and O.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Bottou and O

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:34.804595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3ceb4dda-28ef-4d3d-a94e-7fc93780f976 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:34.437987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0c083288-6142-49da-a2eb-00739a55c318 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:34.426217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 49d93816-0766-4ca9-95de-006e409553d8 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:34.258472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 461215bb-2be3-467c-a3a2-560aeb786a14 · outbound

This paper cites Chaikovskii, A.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Chaikovskii, A

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:34.007966Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c625c4bb-5521-4bcc-bc98-d00c3c0125d5 · outbound

This paper cites Chaikovskii and Y.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Chaikovskii and Y

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:33.715310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2d419458-d9d0-4a68-9072-5e436741074d · outbound

This paper cites Chaikovskii and Y.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Chaikovskii and Y

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:33.435811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bb1930b2-6015-43de-85a1-b06ea5e69869 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:33.177632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 819419c3-56d9-4276-a036-a835f41a7882 · outbound

This paper cites F ang, S.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations F ang, S

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:33.026851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 18f68799-a0ae-4261-a052-0b7c93463c56 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:32.899527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ae4724ba-fa41-42cf-8fd0-983f9b78ba63 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:32.738882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f24e6e59-1f48-4288-b52e-7b1b1334bf80 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:32.623579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 95b2257f-99da-47e0-858f-528f9125ae1b · outbound

This paper cites Hornik,Approximation capabilities of multilayer feedforward networks, Neural Netw., 4 (1991), pp.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Hornik,Approximation capabilities of multilayer feedforward networks, Neural Netw., 4 (1991), pp

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:32.481742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b4dac956-0e8f-4731-a7a2-e96c8d42faaa · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 18

Resolution: verified exact; doi, observed 2026-08-07T13:01:28.305216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ce37ba16-f3c6-4c26-90ab-0d05f23b9331 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 19

Resolution: verified exact; doi, observed 2026-08-07T13:01:28.145957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 322d8e40-2eda-441f-b1d9-2199d8478288 · outbound

This paper cites Levashova, A.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Levashova, A

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:32.293288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7c4eb9f6-05b8-4084-b09c-c9ce154053bb · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:32.135954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 12072d36-2599-4415-bb8d-d20feaf0facd · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:31.985641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 275fddfc-88dd-48e2-bcc9-41ed52877af1 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:31.833367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8e455106-ccb6-4bde-ba42-2328b2d5ab19 · outbound

This paper cites Nefedov,The existence and asymptotic stability of periodic solutions with an interior layer of burgers type equations with modular advection, Math.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Nefedov,The existence and asymptotic stability of periodic solutions with an interior layer of burgers type equations with modular advection, Math

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:31.651659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f87a9693-1afe-4f70-a243-63e83ad95150 · outbound

This paper cites Olchev, K.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Olchev, K

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:31.434211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 92eecc89-e058-4b05-b570-0e9bdc00b15d · outbound

This paper cites Orlov, N.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Orlov, N

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:31.087031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation be70e8eb-f3bc-486b-9281-dfaf8a359947 · outbound

This paper cites Raissi, P.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Raissi, P

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:30.872150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 81ff1d0b-67be-47a3-9810-b1587ff28a13 · outbound

This paper cites Rudenko,Inhomogeneous Burgers equation with modular nonlinearity: excitation and evolution of high-intensity waves, Dokl.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Rudenko,Inhomogeneous Burgers equation with modular nonlinearity: excitation and evolution of high-intensity waves, Dokl

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:30.671355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cd9953fa-fa56-4c20-a0cf-d99c7788f600 · outbound

This paper cites Sidorova, N.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Sidorova, N

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:30.409369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 620e7c3f-100e-4b80-bae0-9c4319390564 · outbound

This paper cites Sirignano and K.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Sirignano and K

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:30.187254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation fbacc393-f4cb-4203-bd00-b94361a24813 · outbound

This paper cites Sogachev and O.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Sogachev and O

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:30.014727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a4d2d9ba-e417-480d-849f-81ef011cf7f0 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:29.787885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e9c29696-8abf-423c-86fa-a11faea30e35 · outbound

This paper cites W ang, L.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations W ang, L

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:29.547715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 72a7342e-03c7-4f52-8beb-922a30a5cbdf · outbound

This paper cites W ang, Y.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations W ang, Y

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:29.280784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c2d2d976-0fe3-452c-bbc2-076d791ca973 · outbound

This paper cites W ang, C.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations W ang, C

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:29.033771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1a9125a5-f808-40e7-a3b3-0375fec8aec7 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:28.763037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b30f4de1-be87-4ffa-9554-6c175d1fae30 · outbound

This paper cites an unresolved cited work.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:01:28.615907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 98955564-217b-4ddc-a9a2-0c6b01178e25 · outbound

This paper cites Zhang and G.

Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations Zhang and G

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:01:28.428935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.