Paper Citation Record · LEDGER

Differential invariants for a class of diffusion equations

As of 16 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:1909.00477.

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

pith.paper-citation-record.v1
1909.00477 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T05:59:55.855924Z

measured 35 of 35 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.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

35 of 35 outbound references displayed

verified exact8
verified fuzzy23
unresolved4
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ea1acf20-7c91-4e5c-941b-d3d9f4a45e2d · outbound

This paper cites Invariant parameterization of geostrophic eddies in the ocean.

Differential invariants for a class of diffusion equations Invariant parameterization of geostrophic eddies in the ocean

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:59:55.995144Z

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.

Observation 6dd55654-9926-4514-95c8-c60cc71afb34 · outbound

This paper cites Invariant parameterization and turbulence modeling on the beta-plane.

Differential invariants for a class of diffusion equations Invariant parameterization and turbulence modeling on the beta-plane

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:59:55.981030Z

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.

Observation 29951302-e19e-49a6-b7d4-50db6d4006de · outbound

This paper cites Invariant discretization schemes for the shallow-water equations.

Differential invariants for a class of diffusion equations Invariant discretization schemes for the shallow-water equations

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:59:55.966098Z

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.

Observation fc98b23e-1e9e-41ce-b1fd-96d64abb32fe · outbound

This paper cites Group classification of linear evolution equations.

Differential invariants for a class of diffusion equations Group classification of linear evolution equations

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:59:55.951698Z

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.

Observation a7dcf2e5-b61a-4699-8950-f1830b0fbe0b · outbound

This paper cites and Valiquette F., Symmetry-preserving numeri cal schemes, in Symmetries and Integrability of Diﬀerence Equations , Springer, 2017, pp.

Differential invariants for a class of diffusion equations and Valiquette F., Symmetry-preserving numeri cal schemes, in Symmetries and Integrability of Diﬀerence Equations , Springer, 2017, pp

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.304429Z

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.

Observation bb38d84d-99e7-402b-b6fd-7df63b34f966 · outbound

This paper cites and Pohjanpelto J., Algorithms for di ﬀerential invariants of symmetry groups of diﬀer- ential equations, Found.

Differential invariants for a class of diffusion equations and Pohjanpelto J., Algorithms for di ﬀerential invariants of symmetry groups of diﬀer- ential equations, Found

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.293988Z

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.

Observation 801e0ae2-ec43-4f15-a2ba-c04afaa32ea4 · outbound

This paper cites 8 of Diﬀerential and integral equa- tions and their applications , Chapman & Hall/CRC, Boca Raton, FL, 2011.

Differential invariants for a class of diffusion equations 8 of Diﬀerential and integral equa- tions and their applications , Chapman & Hall/CRC, Boca Raton, FL, 2011

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.282338Z

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.

Observation 0f35a6b9-e34a-4f23-8869-dfe8541a3ba9 · outbound

This paper cites Group Analysis of Diﬀerential E quations & Integrable Systems.

Differential invariants for a class of diffusion equations Group Analysis of Diﬀerential E quations & Integrable Systems

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.270502Z

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.

Observation 0bfc3cf1-4479-4e67-893d-a47fb5622cfb · outbound

This paper cites and Olver P.J., Moving coframes: I.

Differential invariants for a class of diffusion equations and Olver P.J., Moving coframes: I

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.258846Z

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.

Observation 313efa03-8c3a-4c63-824c-4504d9e89a46 · outbound

This paper cites and Olver P.J., Moving coframes.

Differential invariants for a class of diffusion equations and Olver P.J., Moving coframes

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.246417Z

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.

Observation 3b1b6a84-8bd2-4242-aedd-85320a0c5c07 · outbound

This paper cites and Tracina R., On some diﬀer ential invariants for a family of diﬀusion equations, J.

Differential invariants for a class of diffusion equations and Tracina R., On some diﬀer ential invariants for a family of diﬀusion equations, J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.236127Z

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.

Observation ffbc6b7f-32ce-4c2d-bcc1-9f7da91777ab · outbound

This paper cites an unresolved cited work.

Differential invariants for a class of diffusion equations Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:59:56.224460Z

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.

Observation d12f8de0-7c35-4b08-94aa-9547ac0ec578 · outbound

This paper cites and Thailert E., Invaria nts of linear parabolic diﬀerential equations, Commun.

Differential invariants for a class of diffusion equations and Thailert E., Invaria nts of linear parabolic diﬀerential equations, Commun

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.212549Z

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.

Observation a01662d9-fe2e-4321-918c-815c8dc8621f · outbound

This paper cites and Sophocleous C., Diﬀerential invari ants of the one-dimensional quasi-linear second-order evolution equation, Commun.

Differential invariants for a class of diffusion equations and Sophocleous C., Diﬀerential invari ants of the one-dimensional quasi-linear second-order evolution equation, Commun

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.200682Z

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.

Observation f968c686-e91e-4f23-b674-3f5dcb01225b · outbound

This paper cites and Valenti A., Diﬀerential invariants of nonlinear equations vtt = f (x, vx)vxx + g(x, vx), Commun.

Differential invariants for a class of diffusion equations and Valenti A., Diﬀerential invariants of nonlinear equations vtt = f (x, vx)vxx + g(x, vx), Commun

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.188667Z

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.

Observation 07ed67ec-1ed7-4644-8961-9532b05a1d69 · outbound

This paper cites and Sophocleous C., Group a nalysis of variable coeﬃcient diﬀusion-convection equations.

Differential invariants for a class of diffusion equations and Sophocleous C., Group a nalysis of variable coeﬃcient diﬀusion-convection equations

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.176516Z

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.

Observation 76ef3294-1ffc-4832-90cf-e86a48c64211 · outbound

This paper cites and Mahomed F.M., Singular invariant e quation for the (1 + 1) Fokker–Planck equation, J.

Differential invariants for a class of diffusion equations and Mahomed F.M., Singular invariant e quation for the (1 + 1) Fokker–Planck equation, J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.165004Z

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.

Observation 2949119b-5dd5-4d70-a7f8-5c3166d494c4 · outbound

This paper cites and Sophocleous C., On form-preserving p oint transformations of partial diﬀerential equations, J.

Differential invariants for a class of diffusion equations and Sophocleous C., On form-preserving p oint transformations of partial diﬀerential equations, J

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.153024Z

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.

Observation bac13a99-bb0b-4748-adaf-84b9645e1584 · outbound

This paper cites and Bluman G.W., When nonlinear diﬀerential eq uations are equivalent to linear diﬀerential equations, SIAM J.

Differential invariants for a class of diffusion equations and Bluman G.W., When nonlinear diﬀerential eq uations are equivalent to linear diﬀerential equations, SIAM J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.141908Z

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.

Observation 751fa6eb-7081-48d3-a8d1-0824739cc0af · outbound

This paper cites Algebraic method for group classification of (1+1)-dimensional linear Schr\"odinger equations.

Differential invariants for a class of diffusion equations Algebraic method for group classification of (1+1)-dimensional linear Schr\"odinger equations

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:59:55.936892Z

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.

Observation c8894a1f-96ce-4509-afd2-31c85e0f8fd7 · outbound

This paper cites Petersburg Math.

Differential invariants for a class of diffusion equations Petersburg Math

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.130730Z

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.

Observation a4a8621b-cec7-49d2-bdac-e6ac8eef017c · outbound

This paper cites an unresolved cited work.

Differential invariants for a class of diffusion equations Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:59:56.119832Z

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.

Observation b059e8b7-fd2c-441d-a114-d76a6c0f08bc · outbound

This paper cites an unresolved cited work.

Differential invariants for a class of diffusion equations Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:59:56.108238Z

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.

Observation ab0c10cb-667e-4015-8c41-ae3808d97119 · outbound

This paper cites an unresolved cited work.

Differential invariants for a class of diffusion equations Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-14T05:59:56.096442Z

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.

Observation c85acebc-3847-4891-9c42-28c62fbd46ff · outbound

This paper cites and Pohjanpelto J., Moving frames for Lie pse udo-groups, Canadian J.

Differential invariants for a class of diffusion equations and Pohjanpelto J., Moving frames for Lie pse udo-groups, Canadian J

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.084416Z

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.

Observation 605718d4-1100-433f-b0f5-448c0d11165f · outbound

This paper cites and Pohjanpelto J., Diﬀerential invariant a lgebras of Lie pseudo-groups, Adv.

Differential invariants for a class of diffusion equations and Pohjanpelto J., Diﬀerential invariant a lgebras of Lie pseudo-groups, Adv

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.072705Z

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.

Observation 46e0163a-d25a-4352-a925-833f14ac7240 · outbound

This paper cites Group analysis of general Burgers-Korteweg-de Vries equations.

Differential invariants for a class of diffusion equations Group analysis of general Burgers-Korteweg-de Vries equations

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:59:55.922818Z

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.

Observation 4106737d-6090-4c12-a29b-cd5df0423b43 · outbound

This paper cites Press, New York, 1982.

Differential invariants for a class of diffusion equations Press, New York, 1982

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.060498Z

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.

Observation 99c888a8-4ec7-4cf7-ac95-492e09d19555 · outbound

This paper cites 3, Institute of Mathematics, Kyiv, 2006, pp.

Differential invariants for a class of diffusion equations 3, Institute of Mathematics, Kyiv, 2006, pp

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.048782Z

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.

Observation 188a9726-c5f4-457e-a87a-7a6777269b58 · outbound

This paper cites Symmetry preserving parameterization schemes.

Differential invariants for a class of diffusion equations Symmetry preserving parameterization schemes

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:59:55.907931Z

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.

Observation 4130bdbd-0ff2-46e2-8520-d83639cf981f · outbound

This paper cites Admissible Transformations and Normalized Classes of Nonlinear Schroedinger Equations.

Differential invariants for a class of diffusion equations Admissible Transformations and Normalized Classes of Nonlinear Schroedinger Equations

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-14T05:59:55.892209Z

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.

Observation 641defff-9197-47b7-95f2-06ab3ae7ce8e · outbound

This paper cites and Tracina R., Second-order diﬀerential in variants of a family of diﬀusion equations, J.

Differential invariants for a class of diffusion equations and Tracina R., Second-order diﬀerential in variants of a family of diﬀusion equations, J

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.038633Z

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.

Observation 145ce86d-926b-443c-bc17-11afa4ba6e6c · outbound

This paper cites and Valenti A., On the linearizat ion of semilinear wave equations, Nonlin.

Differential invariants for a class of diffusion equations and Valenti A., On the linearizat ion of semilinear wave equations, Nonlin

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.027817Z

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

Observation 472d758d-ecab-4463-81d1-6bed56b744dd · outbound

This paper cites Nonlinear Sci.

Differential invariants for a class of diffusion equations Nonlinear Sci

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.016815Z

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.

Observation 4dbd4555-6c10-4774-b485-70b4981f6e93 · outbound

This paper cites and Tracina R., Invariants o f two-and three-dimensional hyperbolic equations, J.

Differential invariants for a class of diffusion equations and Tracina R., Invariants o f two-and three-dimensional hyperbolic equations, J

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T05:59:56.005669Z

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.

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