Pith. sign in

Paper Citation Record · LEDGER

Refined blow-up criteria and global solutions for triangular cross-diffusion systems

As of 16 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2607.01857.

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

pith.paper-citation-record.v1
2607.01857 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T11:50:26.030339Z

measured 32 of 32 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

32 of 32 outbound references displayed

  • verified exact24
  • verified fuzzy3
  • unresolved0
  • parse uncertain0
  • malformed identifier3
  • metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6bccba84-ceda-49a8-8655-9a991d8e5970 · outbound

This paper cites In: Proc.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems In: Proc

Reference 1

Resolution
malformed identifier
doi_truncated, observed 2026-07-03T09:57:54.992824Z

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=2026-07-03T09:55:43.232972Z digest=sha256:23b05002d6f6db55c1179f2dfabe0f0a9595e475ecf7bd08af3a6f7aedc5122f

Observation 81d12e6d-238d-44e8-a78b-983a0f99cfe7 · outbound

This paper cites an unresolved cited work.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Unresolved cited work

Reference 2

Resolution
malformed identifier
doi_truncated, observed 2026-07-03T09:57:54.985503Z

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=2026-07-03T09:55:43.232972Z digest=sha256:53f1a1c2e2c9a5f6a3ccb4c947e77504347d643349995113764faa626f7ae355

Observation 607af6df-d7a8-4f16-b42c-f5df67cf1eec · outbound

This paper cites Bahouri , J.-Y.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Bahouri , J.-Y

Reference 3

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.996881Z

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=2026-07-03T09:55:43.232972Z digest=sha256:3da980884d2c0160261f3472dc5bc63fb938774931ed4a3244631f5e85593110

Observation 0a80c830-f573-4d8a-8f87-e97b63579915 · outbound

This paper cites arXiv:2510.07138 [math].

Refined blow-up criteria and global solutions for triangular cross-diffusion systems arXiv:2510.07138 [math]

Reference 4

Resolution
verified exact
arxiv_id, observed 2026-07-03T09:57:55.006357Z

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=2026-07-03T09:55:43.232972Z digest=sha256:4d02b9830d4002dcda6c5d2f071e63af0a6adcafb74ee16a16b2647d7f20f886

Observation 4d4cd034-feea-4cd7-9457-d2efd0151f79 · outbound

This paper cites Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions

Reference 5

Resolution
verified exact
arxiv_id, observed 2026-07-03T09:57:54.936543Z

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=2026-07-03T09:55:43.232972Z digest=sha256:61c090994f1dbb706c81818d5f62164486f8451ae4a25c0b32c97c957b99278c

Observation 20adec94-056f-4f74-9218-d408090e7e04 · outbound

This paper cites On the influence of cross-diffusion in pattern formation.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems On the influence of cross-diffusion in pattern formation

Reference 6

Resolution
verified exact
arxiv_id, observed 2026-07-03T09:57:55.003168Z

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=2026-07-03T09:55:43.232972Z digest=sha256:ce02585ea51f322b77221099c1c9601123b02d552c8077a3ff12090e5928ec8c

Observation e4da3da7-a842-4151-b589-dff8995478fc · outbound

This paper cites Gagliardo-Nirenberg, composition and products in frac- tional Sobolev spaces.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Gagliardo-Nirenberg, composition and products in frac- tional Sobolev spaces

Reference 7

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.956885Z

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=2026-07-03T09:55:43.232972Z digest=sha256:355f395372f9e78ccbfa0adbf5e039e6a8a27c1f0c42bd0fc43328380e861ddd

Observation 28fd07fc-17fd-4173-ba1d-b1e6a150c209 · outbound

This paper cites Analysis of a parabolic cross-diffusion population model without self-diffusion.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Analysis of a parabolic cross-diffusion population model without self-diffusion

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-07-05T09:40:56.195801Z

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=2026-07-03T09:55:43.232972Z digest=sha256:de8bf62fd24c9c61f48d54c472bb2ed3fd9b9703e06910735bf29a835833a26c

Observation cc695cf6-605b-493d-9b44-570ec584a443 · outbound

This paper cites url: https://www.sciencedirect.com/science/ article/pii/S002203960500286X.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems url: https://www.sciencedirect.com/science/ article/pii/S002203960500286X

Reference 9

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.999254Z

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=2026-07-03T09:55:43.232972Z digest=sha256:4660010db872f29484d1b662bf2a53cf9cb87c28c2d04f3a3c9a3e4cd5ae3513

Observation 27b27da6-03b3-4ede-92ed-0be2b7ce8ec0 · outbound

This paper cites A note on the uniqueness of weak solutions to a class of cross- diffusion systems.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems A note on the uniqueness of weak solutions to a class of cross- diffusion systems

Reference 10

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.971521Z

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=2026-07-03T09:55:43.232972Z digest=sha256:8f29c8ab82cd338592c2f90b34e67d211e78056ae128433a574bdc053baa3570

Observation 30dc5e2c-54ed-4719-8ba9-3501d545e362 · outbound

This paper cites Weak–strong uniqueness of renormalized solutions to reaction–cross-diffusion systems.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Weak–strong uniqueness of renormalized solutions to reaction–cross-diffusion systems

Reference 11

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.986856Z

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=2026-07-03T09:55:43.232972Z digest=sha256:624295d5e358c0dd648e3ce19eab181126396b5a7315780a78572e7afdea18d4

Observation 21b8fa26-ea41-4609-99ac-9aa0ed287656 · outbound

This paper cites Existence of global solutions for the Shigesada- Kawasaki-Teramoto model with weak cross-diffusion.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Existence of global solutions for the Shigesada- Kawasaki-Teramoto model with weak cross-diffusion

Reference 12

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.967052Z

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=2026-07-03T09:55:43.232972Z digest=sha256:c4c602f8c17d5d89891ef4e44dc6ca98d76491ee8200eb404b360480a045e85e

Observation a4e90a8e-0f4f-4ba5-bade-d45172cb1b23 · outbound

This paper cites Bonnet-BenDhia, L.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Bonnet-BenDhia, L

Reference 13

Resolution
metadata mismatch
arxiv_id, observed 2026-07-03T09:57:54.960003Z

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=2026-07-03T09:55:43.232972Z digest=sha256:1c35dfc5bf084c4a21ac89a03f44511740ee69f3757dd39669a7a0777438e417

Observation ef867dfc-4108-45c8-8fe5-9806cd60980b · outbound

This paper cites Persisting entropy structure for nonlocal cross-diffusion systems.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Persisting entropy structure for nonlocal cross-diffusion systems

Reference 14

Resolution
malformed identifier
doi_truncated, observed 2026-07-03T09:57:54.964735Z

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=2026-07-03T09:55:43.232972Z digest=sha256:675bbdd7eaecd9e1aa1ad539974ef0f30dab4be01de66166a92ad1f37bf71312

Observation 80e237c1-0554-43cd-95dd-c2049fe94f80 · outbound

This paper cites Partial Differential Equations.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Partial Differential Equations

Reference 15

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.978251Z

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=2026-07-03T09:55:43.232972Z digest=sha256:80b7593c06ffc1639f9fbdf99bb019ce2e1c2f84b1b9a3bd5e878ca2f45fb0b0

Observation a48972e3-2f6e-4328-b8d6-cdfa4045c287 · outbound

This paper cites Transference on certain multilinear multiplier operators.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Transference on certain multilinear multiplier operators

Reference 16

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.979592Z

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=2026-07-03T09:55:43.232972Z digest=sha256:21e6f4af297484e35de2709957ad5c590ef6988fcf14e919c1a5d2dfdc0d0106

Observation f6bd8670-2666-482b-8edb-0218f6a5752c · outbound

This paper cites an unresolved cited work.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Unresolved cited work

Reference 17

Resolution
verified exact
arxiv_id, observed 2026-07-03T09:57:55.003696Z

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=2026-07-03T09:55:43.232972Z digest=sha256:2f1c4151001ece62e1157e92abc130b9ae8b068fc71f360cb3c8b1e143bcab9a

Observation 5689e8b5-86e6-4824-9679-a247c5cd506e · outbound

This paper cites Global smooth solutions for triangular reaction-cross diffusion systems.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Global smooth solutions for triangular reaction-cross diffusion systems

Reference 18

Resolution
verified exact
arxiv_id, observed 2026-07-03T09:57:54.988787Z

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=2026-07-03T09:55:43.232972Z digest=sha256:d8f5bde22f82e6130ae4eef024164eef343ba9c5b535051a2f33d698e5ac0a0e

Observation c4974ec2-63ae-41d6-8370-83e2b79b9d38 · outbound

This paper cites Gradient Estimates and Global Existence of Smooth Solutions to a Cross-Diffusion System.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Gradient Estimates and Global Existence of Smooth Solutions to a Cross-Diffusion System

Reference 19

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.980391Z

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=2026-07-03T09:55:43.232972Z digest=sha256:c462173bdc5e6fd52eae0e37332b9365419b6cd8591c84e626934fc0a78dde97

Observation 8cc00cbb-48d9-462c-811e-19891d0360d5 · outbound

This paper cites Coexistence-segregation dichotomy in the full cross-diffusion limit of the stationary SKT model.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Coexistence-segregation dichotomy in the full cross-diffusion limit of the stationary SKT model

Reference 20

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.950689Z

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=2026-07-03T09:55:43.232972Z digest=sha256:3286da9841944e588be1895c04fc80e027b10d69bbccb65831c2a8d8dfb936ff

Observation 002641b3-5378-4dd9-8fdb-4966daf74318 · outbound

This paper cites Smooth solutions to a quasi-linear system of diffusion equations for a certain population model.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Smooth solutions to a quasi-linear system of diffusion equations for a certain population model

Reference 21

Resolution
verified exact
doi, observed 2026-07-03T09:57:55.001067Z

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=2026-07-03T09:55:43.232972Z digest=sha256:30e3dfa452fd05f27fbc710942d7f9727a84a9461236185a9479bd5f72ffb92f

Observation 421f1b96-e484-40cd-87f3-065f152eb71c · outbound

This paper cites Entropic structure and duality for multiple species cross-diffusion systems.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Entropic structure and duality for multiple species cross-diffusion systems

Reference 22

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.993982Z

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=2026-07-03T09:55:43.232972Z digest=sha256:e894328a28e63705967cf8a05920ab05f1f2276e13575f45ac01f8897bc62b85

Observation c30e0b56-9ca0-4d39-9ead-c7c75fc82747 · outbound

This paper cites On Kato-Ponce and fractional Leibniz.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems On Kato-Ponce and fractional Leibniz

Reference 23

Resolution
verified exact
local_arxiv, observed 2026-07-03T09:57:54.983431Z

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=2026-07-11T11:50:26.030339Z digest=sha256:7878ffc0e42a52ca9e71c7cfa23c1e39b4b781fba35fde27ce78e2a7da017aa6

Observation 6209c0cc-9ca9-4dc2-9a64-ff072893fd60 · outbound

This paper cites On the global existence of a cross-diffusion system.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems On the global existence of a cross-diffusion system

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-07-05T09:40:56.197582Z

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=2026-07-03T09:55:43.232972Z digest=sha256:4b8c1d46b2f686f76d5b7818ece2a12cdfc6c35991b26ab5251dbddb0425d690

Observation bbe028b2-6095-4d6b-a9c6-d8477d88bade · outbound

This paper cites url: https://www.aimsciences.org/en/article/ doi/10.3934/dcds.1998.4.193.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems url: https://www.aimsciences.org/en/article/ doi/10.3934/dcds.1998.4.193

Reference 25

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.990735Z

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=2026-07-03T09:55:43.232972Z digest=sha256:bd8210648894962038ac1cf04aa608daa338cd8d9b81b71d850e09c653e459d5

Observation 69f30b47-254b-4d6c-a940-0c74a06280e7 · outbound

This paper cites From non-local to classical SKT systems: triangular case with bounded coefficients.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems From non-local to classical SKT systems: triangular case with bounded coefficients

Reference 26

Resolution
verified exact
local_arxiv, observed 2026-07-03T09:57:54.982402Z

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=2026-07-03T09:55:43.232972Z digest=sha256:a28a3134897ead52ed734abc14452b5f276afa8efbd05182b456e5b7a7ed4d2e

Observation 64ce07a8-d5d4-4daa-86e2-b8d8b9eeb049 · outbound

This paper cites Hitchhiker's guide to the fractional Sobolev spaces.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Hitchhiker's guide to the fractional Sobolev spaces

Reference 27

Resolution
metadata mismatch
local_arxiv, observed 2026-07-03T09:57:54.975933Z

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=2026-07-03T09:55:43.232972Z digest=sha256:1f8d0ce3b237ae06e6dd2904973e2c7260875aa0d6b060bf63a8b728a9ccac74

Observation bf86c2dc-7e5c-413d-8594-c8576fc2a0b8 · outbound

This paper cites Hitchhiker's guide to the fractional Sobolev spaces.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Hitchhiker's guide to the fractional Sobolev spaces

Reference 28

Resolution
verified exact
local_arxiv, observed 2026-07-03T09:57:55.768512Z

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=2026-07-03T09:55:43.232972Z digest=sha256:952e29b4cf1caf5c5b82c5ba22b272a9cbc659bf91801da3fb46ff21dcce8df8

Observation 32e1e64e-02be-42cc-ac53-047d796fce25 · outbound

This paper cites Global existence of solutions for a strongly coupled quasilinear parabolic system.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Global existence of solutions for a strongly coupled quasilinear parabolic system

Reference 29

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.994924Z

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=2026-07-03T09:55:43.232972Z digest=sha256:86f9f9b6dd42089fe812f868aacfee74efd2607be2014c81e1703347b591c3b5

Observation 9c9751e5-1e27-41b1-a29d-79f6f31aad71 · outbound

This paper cites Parabolic Lp - Lq estimates.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Parabolic Lp - Lq estimates

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-07-05T09:40:56.193675Z

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=2026-07-03T09:55:43.232972Z digest=sha256:97e556f2baded48de8e4ef4eb86cf2d332d2152af30f5537ba6f662cd94282a0

Observation f5ba25cc-1929-4235-bd46-4a8017439e0d · outbound

This paper cites Spatial segregation of interacting species.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Spatial segregation of interacting species

Reference 31

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.963342Z

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=2026-07-03T09:55:43.232972Z digest=sha256:7446d07c9a7fb3598d62e32b9f9f2d9e0d67b257c995fdcda9a29a071efaa58b

Observation 2dcf4d3f-b57e-44ce-9c2a-2cfe9d503492 · outbound

This paper cites Regularity for a class of non-lin ear elliptic systems.

Refined blow-up criteria and global solutions for triangular cross-diffusion systems Regularity for a class of non-lin ear elliptic systems

Reference 32

Resolution
verified exact
doi, observed 2026-07-03T09:57:54.969252Z

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=2026-07-03T09:55:43.232972Z digest=sha256:9ac6216320f3c3f2f3f0cb70fcaa6e0572241210b375ff854a7cf476ceea2c0b

Pith citing papers

No inbound Pith citation observations are available.