Paper Citation Record · LEDGER

Shock-type singularity of the hyperbolic-parabolic chemotaxis system

As of 14 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2501.09656.

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

pith.paper-citation-record.v1
2501.09656 v1

Coverage vector

measured 26 of 26 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-10T19:55:24.389779Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

26 of 26 outbound references displayed

verified exact0
verified fuzzy24
unresolved2
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 40db0b9f-8ccf-48ff-8e8d-c3582e8ab78e · outbound

This paper cites A review of vasculogenesis models.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system A review of vasculogenesis models

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.813943Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cb946f9b-e5d4-49be-be00-4603f1979037 · outbound

This paper cites Structure of singularities for the Euler-Poisson system of ion dynamics.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Structure of singularities for the Euler-Poisson system of ion dynamics

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-10T19:55:24.298697Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11719a7e-92b3-4059-805f-8002ac23e7fc · outbound

This paper cites Fourier Analysis and Nonlinear Partial Diﬀerential Eq ua- tions.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Fourier Analysis and Nonlinear Partial Diﬀerential Eq ua- tions

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.803246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2a8a3d3e-64e3-4297-ba25-73d52c831f7d · outbound

This paper cites Formation of point shocks for 3D compressible Euler Communi- cations on Pure and Applied Mathematics , 76(9):2073–2191, 2023.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Formation of point shocks for 3D compressible Euler Communi- cations on Pure and Applied Mathematics , 76(9):2073–2191, 2023

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.792739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 09b71b6a-058d-48c1-87e0-43f974c05477 · outbound

This paper cites Formation of shocks for 2D isentropic compressible Euler.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Formation of shocks for 2D isentropic compressible Euler

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.781162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 89035864-d743-49b5-b88c-31c50db61579 · outbound

This paper cites Shock formation and vorticity creation for 3d Euler, Communi- cations on Pure and Applied Mathematics , 76(9):1965–2072, 2023.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Shock formation and vorticity creation for 3d Euler, Communi- cations on Pure and Applied Mathematics , 76(9):1965–2072, 2023

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.770175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a2c6ce0a-916d-474a-a0ff-5256c5677e00 · outbound

This paper cites The onset of inst ability in unsteady boundary-layer separation.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system The onset of inst ability in unsteady boundary-layer separation

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.758893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1631be0e-2267-4e40-ac3c-8174ee2fe785 · outbound

This paper cites Kinetic and hydrodynamic models of chemotactic aggregation.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Kinetic and hydrodynamic models of chemotactic aggregation

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.748244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0acbfaae-8b63-4b3b-b303-3d51e59e329d · outbound

This paper cites Singularity formation for Burgers equation with transverse viscosity.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Singularity formation for Burgers equation with transverse viscosity

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-10T19:55:24.327247Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42282aa6-a256-4ed1-b7f4-aa98dd4b3d45 · outbound

This paper cites The Hyperbolic-Parabolic Chemotaxis System for Vascul o- genesis: Global Dynamics and Relaxation Limit Toward a Kell er–Segel Model.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system The Hyperbolic-Parabolic Chemotaxis System for Vascul o- genesis: Global Dynamics and Relaxation Limit Toward a Kell er–Segel Model

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.737587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 06628d7d-500d-4ba3-865b-2c643f71afda · outbound

This paper cites The role of self-sim ilarity in singularities of partial diﬀerential equations.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system The role of self-sim ilarity in singularities of partial diﬀerential equations

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.726787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation fe46508b-36b7-4819-968f-ffe2e628db2b · outbound

This paper cites Partial diﬀerential equations.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Partial diﬀerential equations

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.716531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 54222cfb-0cd4-422a-8e54-da43f5f3c466 · outbound

This paper cites Derivation of hyperbolic models for chemosensitive move- ment.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Derivation of hyperbolic models for chemosensitive move- ment

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.705770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b857cc07-8d9b-4e0b-bde5-d5cb37429736 · outbound

This paper cites Approximation of hy perbolic models for chemosensitive movement.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Approximation of hy perbolic models for chemosensitive movement

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.694768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4ad28d37-723e-4035-a5b1-3e0b256426f8 · outbound

This paper cites Percola tion, morphogenesis, and Burgers dynamics in blood vessels formation.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Percola tion, morphogenesis, and Burgers dynamics in blood vessels formation

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.682844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2e5ba8f5-bedb-46e0-8afe-64647853a2f3 · outbound

This paper cites Nonlinear stability of phase transition steady states to a hyperbolic–parabolic system modeling va scular networks.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Nonlinear stability of phase transition steady states to a hyperbolic–parabolic system modeling va scular networks

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.670962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0afcd205-abaa-46d8-9f8a-56d99fca28dc · outbound

This paper cites Asymp totic stability of diﬀusion waves of a quasi-linear hyperbo lic- parabolic model for vasculogenesis.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Asymp totic stability of diﬀusion waves of a quasi-linear hyperbo lic- parabolic model for vasculogenesis

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.659632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 37fcdee5-7935-4688-8f00-bc7c7cc40589 · outbound

This paper cites Conve rgence to nonlinear diﬀusion waves for a hyperbolic-parabo lic chemotaxis system modelling vasculogenesis.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Conve rgence to nonlinear diﬀusion waves for a hyperbolic-parabo lic chemotaxis system modelling vasculogenesis

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.647866Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a3975451-d300-4eb1-958a-d284635a7df2 · outbound

This paper cites Vort icity and incompressible ﬂow.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Vort icity and incompressible ﬂow

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.535064Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 390ae695-f01e-4e9d-94e9-d30530008c4f · outbound

This paper cites Asymptotics for L2 minimal blow-up solutions of critical nonlinear Schr¨ odinger equation.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Asymptotics for L2 minimal blow-up solutions of critical nonlinear Schr¨ odinger equation

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.523385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 72c58e68-b626-400d-9665-95444cb64674 · outbound

This paper cites The blow-up dynamic a nd upper bound on the blow-up rate for critical nonlinear Schr¨ odinger equation.Annals of mathematics , 157–222, 2005.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system The blow-up dynamic a nd upper bound on the blow-up rate for critical nonlinear Schr¨ odinger equation.Annals of mathematics , 157–222, 2005

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.509731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation dc9ad089-a0da-4916-abc7-7aff01b35451 · outbound

This paper cites On strongly anisotropic type I blowup.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system On strongly anisotropic type I blowup

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.495284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 667eca2f-9825-44b5-8ca4-a3d086243f69 · outbound

This paper cites Stability of the blow-up p roﬁle for equations of the type ut = ∆ u + |u|p− 1u.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Stability of the blow-up p roﬁle for equations of the type ut = ∆ u + |u|p− 1u

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.481803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7298e662-4881-49c9-955a-c87748aa3fb2 · outbound

This paper cites Gradient blow -up for dispersive and dissipative perturbations of the Bur gers equation.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Gradient blow -up for dispersive and dissipative perturbations of the Bur gers equation

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.468206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f0cf3399-73f8-468d-a38f-0b579213a966 · outbound

This paper cites Existence and asym ptotic behavior of solutions to a quasi-linear hyperbolic- parabolic model of vasculogenesis.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Existence and asym ptotic behavior of solutions to a quasi-linear hyperbolic- parabolic model of vasculogenesis

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.456542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1d069d72-d642-4f09-960a-57aa9b1b3a62 · outbound

This paper cites Shock Formation of the Burgers–Hilbert Equation.

Shock-type singularity of the hyperbolic-parabolic chemotaxis system Shock Formation of the Burgers–Hilbert Equation

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T19:55:24.444103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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