Paper Citation Record · LEDGER

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations

As of 8 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2506.06543.

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

pith.paper-citation-record.v1
2506.06543 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T06:02:23.867104Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-18T19:07:09.519302Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-18T19:11:47.528158Z

Reference resolution

27 of 27 outbound references displayed

verified exact0
verified fuzzy17
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fd90cdb5-1a1d-4ceb-9a03-5a6accc11631 · outbound

This paper cites Basdevant, M.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Basdevant, M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:24.084104Z

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 bc8afccf-c636-4f6f-a06d-580e8250744a · outbound

This paper cites Afastdirectsolverfortheadvection-diﬀusionequationusinglow-rankapproxima- tionofthegreen’sfunction.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Afastdirectsolverfortheadvection-diﬀusionequationusinglow-rankapproxima- tionofthegreen’sfunction

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:24.077118Z

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 148206df-b62b-4913-bcb4-9dd9f3f85f4b · outbound

This paper cites Modellinguncertainties in the diﬀusion-advection equation for radon transport in soil using interval arithmetic.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Modellinguncertainties in the diﬀusion-advection equation for radon transport in soil using interval arithmetic

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:24.069790Z

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 3c7fe267-0e96-4523-9c93-e49cc886fc59 · outbound

This paper cites an unresolved cited work.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:02:24.062115Z

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 4294fc54-f0e3-44de-8453-03865299732a · outbound

This paper cites Fastexplicitoperatorsplittingmethodforconvec- tion–diﬀusion equations.International Journal for Numerical Methods in Fluids, 59(3):309–332, 2009.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Fastexplicitoperatorsplittingmethodforconvec- tion–diﬀusion equations.International Journal for Numerical Methods in Fluids, 59(3):309–332, 2009

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:24.054737Z

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 1542c312-7a25-4d78-93ef-92300b9be402 · outbound

This paper cites Asummaryofnumericalmethodsfortime-dependentadvection- dominated partial diﬀerential equations.Journal of Computational and Applied Mathematics, 128(1):423–445, 2001.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Asummaryofnumericalmethodsfortime-dependentadvection- dominated partial diﬀerential equations.Journal of Computational and Applied Mathematics, 128(1):423–445, 2001

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:24.046731Z

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 c01c2341-9b76-4779-8309-e6383f0a01aa · outbound

This paper cites Gharib, M.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Gharib, M

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:24.039216Z

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 ea06c869-80bc-478e-b3bf-28dead8ab1d7 · outbound

This paper cites an unresolved cited work.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:02:24.032136Z

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 8b217b18-8692-4735-abf9-8037865188ba · outbound

This paper cites Theoptimaldecompositionmethod(ODM) for nonlinear problems.Journal of Computational Science, 62:101690, 2022.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Theoptimaldecompositionmethod(ODM) for nonlinear problems.Journal of Computational Science, 62:101690, 2022

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:24.024876Z

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 ab170a38-dcb8-4b95-adc3-66911bf0aedf · outbound

This paper cites an unresolved cited work.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:02:24.017720Z

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 bc1319f2-58b8-4776-8a1a-da405df8e63a · outbound

This paper cites an unresolved cited work.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:02:24.010702Z

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 e6a06135-6231-49c9-8ab0-e8d15432d437 · outbound

This paper cites an unresolved cited work.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:02:24.003611Z

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 81ed3d1b-d5c1-4f36-ae7d-004b405f7324 · outbound

This paper cites an unresolved cited work.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:02:23.996450Z

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 7f2ca804-9e71-4730-966b-0955ea211f72 · outbound

This paper cites Unconditionallypositive,explicit,fourthordermethodfor the diﬀusion- and nagumo-type diﬀusion–reaction equations.J Sci Comput, 98(39), 2024.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Unconditionallypositive,explicit,fourthordermethodfor the diﬀusion- and nagumo-type diﬀusion–reaction equations.J Sci Comput, 98(39), 2024

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:23.989429Z

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 e08686f7-e7f9-4224-b985-f978ba2517bb · outbound

This paper cites Kumar, D.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Kumar, D

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:23.981329Z

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 aa737590-c0ee-4e97-bf2f-4cb71bce7c4e · outbound

This paper cites Lee and B.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Lee and B

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:23.974210Z

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 3b9333cc-7239-456c-98a1-c8a1ba1f0ae6 · outbound

This paper cites Mojtabi and M.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Mojtabi and M

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:23.966971Z

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 a5baf9d2-e34e-424d-9e21-3e17e6c4d867 · outbound

This paper cites Limitationsofananalyticalsolutionforadvection–diﬀusionwithspatiallyvariable coeﬃcients.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Limitationsofananalyticalsolutionforadvection–diﬀusionwithspatiallyvariable coeﬃcients

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:23.959698Z

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 bdcea99b-8b7a-47d4-8184-0f431537a423 · outbound

This paper cites Saleh, E.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Saleh, E

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:23.952527Z

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 8a6e3f53-8c72-4989-b322-d5457690553d · outbound

This paper cites an unresolved cited work.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:02:23.945147Z

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 7a317b8f-e018-488c-a52c-720043c8056d · outbound

This paper cites an unresolved cited work.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:02:23.938040Z

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 3326866f-72b7-4e07-875e-d21c8d59f4d2 · outbound

This paper cites PhysicsLettersA ,150(5):262– 268, 1990.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations PhysicsLettersA ,150(5):262– 268, 1990

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:23.930723Z

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 6dc384d3-edec-4b43-a5da-e441a20a9fe7 · outbound

This paper cites Zamani and F.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Zamani and F

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:23.923092Z

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 4a988468-1477-48b5-a12b-e9d2f4f84920 · outbound

This paper cites Zoppou and J.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Zoppou and J

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:23.915964Z

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 afab7de2-e0bf-448b-ba63-a349597ad0f8 · outbound

This paper cites an unresolved cited work.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:02:23.908475Z

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 82c9ee06-a532-4444-88e3-2770310f2d52 · outbound

This paper cites In this case, we initially write: ∂u ∂t − Vx ∂u ∂x = ¯d ∂2u ∂x2 , Vx := ( ∂ ¯d ∂u )( ∂u ∂x ).

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations In this case, we initially write: ∂u ∂t − Vx ∂u ∂x = ¯d ∂2u ∂x2 , Vx := ( ∂ ¯d ∂u )( ∂u ∂x )

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T06:02:23.901138Z

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 bc9b0fa8-f96f-4bf8-8760-d0425ff8ed6c · outbound

This paper cites an unresolved cited work.

A Directional-ODE Framework for Discretization of Advection-Diffusion Equations Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T06:02:23.892337Z

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.

Pith citing papers

Observation b2c5a6e9-5609-4bf0-9da9-3bac1653b6b2 · inbound

A Multi-Physics Eulerian Framework for Long-Term Contrail Evolution cites this paper.

A Multi-Physics Eulerian Framework for Long-Term Contrail Evolution A Directional-ODE Framework for Discretization of Advection-Diffusion Equations

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-05-18T19:11:47.530728Z

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.