Paper Citation Record · LEDGER

Relaxation for massive particles: transport and causality

As of 19 August 2026, this Paper Citation Record lists 69 of 69 outbound references and 8 inbound Pith citation observations for arXiv:2506.15531.

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

pith.paper-citation-record.v1
2506.15531 v2

Coverage vector

measured 69 of 69 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:47:06.295509Z

measured 77 of 77 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 8 of 8 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:47:05.931275Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T21:37:24.920321Z

Reference resolution

69 of 69 outbound references displayed

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External citation measurements

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Outbound references

Observation d112d272-61d8-4027-90b1-fa19bcc8d99a · outbound

This paper cites an unresolved cited work.

Relaxation for massive particles: transport and causality Unresolved cited work

Reference 1

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Observation 489f968f-3b5a-4799-927b-aa41fa6d84dc · outbound

This paper cites Discontinuity profile, branch cuts and branch points 19.

Relaxation for massive particles: transport and causality Discontinuity profile, branch cuts and branch points 19

Reference 2

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Observation bf410eb7-c8d0-4e31-ad73-55bd475dd7d7 · outbound

This paper cites Thermoelectric transport 10 IV.

Relaxation for massive particles: transport and causality Thermoelectric transport 10 IV

Reference 3

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Observation 4ab1bb59-67cf-46c2-99cc-9f328873a5f9 · outbound

This paper cites Relaxation for massive particles: transport and causality.

Relaxation for massive particles: transport and causality Relaxation for massive particles: transport and causality

Reference 4

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Observation 1b3053b5-0237-431e-87da-1219f77acfb9 · outbound

This paper cites The simplest case is the shear diffusion channel, schematically denoted with δT 0⊥, where⊥ is one of the transverse components to our chosen axis aligned with the wave vector k.

Relaxation for massive particles: transport and causality The simplest case is the shear diffusion channel, schematically denoted with δT 0⊥, where⊥ is one of the transverse components to our chosen axis aligned with the wave vector k

Reference 5

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Observation 98f4260f-faa4-4428-8605-bf82ab24ebc0 · outbound

This paper cites the sound.

Relaxation for massive particles: transport and causality the sound

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:47:07.748906Z

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Observation 179969bc-668c-4d59-a7ce-159aaed7ff70 · outbound

This paper cites This does not induce any change in the macroscopic variables ( δT , δui), so there is no need to solve the matching conditions.

Relaxation for massive particles: transport and causality This does not induce any change in the macroscopic variables ( δT , δui), so there is no need to solve the matching conditions

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:47:07.730342Z

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Observation 69d8427e-390f-4426-96c2-3ff2739d9301 · outbound

This paper cites an unresolved cited work.

Relaxation for massive particles: transport and causality Unresolved cited work

Reference 8

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Observation 240d3bfc-525b-48d3-8073-0d4dde79f2da · outbound

This paper cites For the sake of concreteness let us pick p⊥ to be aligned along the x2 axis and denote it py in order to not confuse it with the square of the momentum.

Relaxation for massive particles: transport and causality For the sake of concreteness let us pick p⊥ to be aligned along the x2 axis and denote it py in order to not confuse it with the square of the momentum

Reference 9

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Observation 057ff761-4a48-4cf1-813b-7a4c971daa59 · outbound

This paper cites Example 1.

Relaxation for massive particles: transport and causality Example 1

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:47:07.550171Z

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Observation 1930bcb3-45e9-419e-8942-b505c6df9af2 · outbound

This paper cites Identify the ‘furthermost’ branch point ωbp, meaning the branch point that shares the branch cut with all the other branch points (when varying the integration parameter).

Relaxation for massive particles: transport and causality Identify the ‘furthermost’ branch point ωbp, meaning the branch point that shares the branch cut with all the other branch points (when varying the integration parameter)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:47:07.531892Z

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Observation 88458908-5e05-4239-b062-66701e762c43 · outbound

This paper cites In our case, the limiting value of u is given by −k q 1−u2 δ =ε =⇒uδ = r 1− δ2 k2.

Relaxation for massive particles: transport and causality In our case, the limiting value of u is given by −k q 1−u2 δ =ε =⇒uδ = r 1− δ2 k2

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:47:07.515265Z

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Observation 01984648-59d1-41fe-82ad-c6008be18423 · outbound

This paper cites (B14) The final step is a trivial transformation from δ to ω.

Relaxation for massive particles: transport and causality (B14) The final step is a trivial transformation from δ to ω

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:47:07.497824Z

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Observation e9542ecf-1811-44a7-abe7-6b20fe681e9b · outbound

This paper cites For the sake of completeness we restate the origin of the branch cut structure in RTA kinetic theory.

Relaxation for massive particles: transport and causality For the sake of completeness we restate the origin of the branch cut structure in RTA kinetic theory

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:47:07.481208Z

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Observation 4cdb5752-f2e2-4f92-9734-b287fe4d2822 · outbound

This paper cites Pitaevskii and E.

Relaxation for massive particles: transport and causality Pitaevskii and E

Reference 15

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Observation 441be1ce-391d-431e-98ba-471d199f00ac · outbound

This paper cites de Groot, W.

Relaxation for massive particles: transport and causality de Groot, W

Reference 16

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Observation f19690fa-f649-4956-9f39-cfae160836b2 · outbound

This paper cites Anderson and H.

Relaxation for massive particles: transport and causality Anderson and H

Reference 17

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Observation d0fe5730-d60b-4280-8553-c24f56df58d1 · outbound

This paper cites Liboff, Kinetic Theory (Springer-Verlag, New York, USA, 2003).

Relaxation for massive particles: transport and causality Liboff, Kinetic Theory (Springer-Verlag, New York, USA, 2003)

Reference 18

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Observation 3e6d827d-00b5-4bdb-88ab-925bcec12983 · outbound

This paper cites From strong to weak coupling in holographic models of thermalization.

Relaxation for massive particles: transport and causality From strong to weak coupling in holographic models of thermalization

Reference 19

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Observation 155a6628-7ed8-4c40-8147-8a6454ad67ed · outbound

This paper cites Retarded Correlators in Kinetic Theory: Branch Cuts, Poles and Hydrodynamic Onset Transitions.

Relaxation for massive particles: transport and causality Retarded Correlators in Kinetic Theory: Branch Cuts, Poles and Hydrodynamic Onset Transitions

Reference 20

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Observation d3a609b3-0fbb-49ed-8923-549336a6b255 · outbound

This paper cites Anisotropic Hydrodynamics for Rapidly Expanding Systems.

Relaxation for massive particles: transport and causality Anisotropic Hydrodynamics for Rapidly Expanding Systems

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.036078Z

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Observation 97db435b-a09f-4679-96fc-f30c1882fa64 · outbound

This paper cites Testing viscous and anisotropic hydrodynamics in an exactly solvable case.

Relaxation for massive particles: transport and causality Testing viscous and anisotropic hydrodynamics in an exactly solvable case

Reference 22

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This paper cites Exact solution of the (0+1)-dimensional Boltzmann equation for a massive gas.

Relaxation for massive particles: transport and causality Exact solution of the (0+1)-dimensional Boltzmann equation for a massive gas

Reference 23

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This paper cites Analytic structure of nonhydrodynamic modes in kinetic theory.

Relaxation for massive particles: transport and causality Analytic structure of nonhydrodynamic modes in kinetic theory

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.052768Z

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This paper cites Flow in AA and pA as an interplay of fluid-like and non-fluid like excitations.

Relaxation for massive particles: transport and causality Flow in AA and pA as an interplay of fluid-like and non-fluid like excitations

Reference 25

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Observation b4a11c43-e7f4-4b39-b600-830a946d1b7e · outbound

This paper cites Extended relaxation time approximation and relativistic dissipative hydrodynamics.

Relaxation for massive particles: transport and causality Extended relaxation time approximation and relativistic dissipative hydrodynamics

Reference 26

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This paper cites Opacity dependence of transverse flow, pre-equilibrium and applicability of hydrodynamics in heavy-ion collisions.

Relaxation for massive particles: transport and causality Opacity dependence of transverse flow, pre-equilibrium and applicability of hydrodynamics in heavy-ion collisions

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.070217Z

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This paper cites New insights into the analytic structure of correlation functions via kinetic theory.

Relaxation for massive particles: transport and causality New insights into the analytic structure of correlation functions via kinetic theory

Reference 28

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This paper cites Hu, (2024), arXiv:2409.05131 [hep-ph].

Relaxation for massive particles: transport and causality Hu, (2024), arXiv:2409.05131 [hep-ph]

Reference 29

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This paper cites Particle number diffusion in second-order relativistic dissipative hydrodynamics with momentum-dependent relaxation time.

Relaxation for massive particles: transport and causality Particle number diffusion in second-order relativistic dissipative hydrodynamics with momentum-dependent relaxation time

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.088336Z

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Observation 382766e2-d61a-4a29-a67d-5fd457175b4b · outbound

This paper cites Quasi-particle hydrodynamics with momentum-dependent relaxation time.

Relaxation for massive particles: transport and causality Quasi-particle hydrodynamics with momentum-dependent relaxation time

Reference 31

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This paper cites On attractor and fixed points in Bjorken flows.

Relaxation for massive particles: transport and causality On attractor and fixed points in Bjorken flows

Reference 32

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This paper cites An analytic approach to the RTA Boltzmann attractor.

Relaxation for massive particles: transport and causality An analytic approach to the RTA Boltzmann attractor

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.104283Z

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This paper cites Transport coefficients of second-order relativistic fluid dynamics in the relaxation-time approximation.

Relaxation for massive particles: transport and causality Transport coefficients of second-order relativistic fluid dynamics in the relaxation-time approximation

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.110502Z

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This paper cites From moments of the distribution function to hydrodynamics: The non-conformal case.

Relaxation for massive particles: transport and causality From moments of the distribution function to hydrodynamics: The non-conformal case

Reference 35

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This paper cites Relativistic second-order dissipative and anisotropic fluid dynamics in the relaxation-time approximation for an ideal gas of massive particles.

Relaxation for massive particles: transport and causality Relativistic second-order dissipative and anisotropic fluid dynamics in the relaxation-time approximation for an ideal gas of massive particles

Reference 36

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This paper cites Hydrodynamic and Non-hydrodynamic Excitations in Kinetic Theory -- A Numerical Analysis in Scalar Field Theory.

Relaxation for massive particles: transport and causality Hydrodynamic and Non-hydrodynamic Excitations in Kinetic Theory -- A Numerical Analysis in Scalar Field Theory

Reference 37

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This paper cites Spectra of correlators in the relaxation time approximation of kinetic theory.

Relaxation for massive particles: transport and causality Spectra of correlators in the relaxation time approximation of kinetic theory

Reference 38

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This paper cites Three-point functions from a Schwinger-Keldysh effective action, resummed in derivatives.

Relaxation for massive particles: transport and causality Three-point functions from a Schwinger-Keldysh effective action, resummed in derivatives

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.136513Z

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Relaxation for massive particles: transport and causality Unresolved cited work

Reference 40

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This paper cites Bulk viscosity, particle spectra and flow in heavy-ion collisions.

Relaxation for massive particles: transport and causality Bulk viscosity, particle spectra and flow in heavy-ion collisions

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.147826Z

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This paper cites Magneto-Seebeck coefficient and Nernst coefficient of hot and dense hadron gas.

Relaxation for massive particles: transport and causality Magneto-Seebeck coefficient and Nernst coefficient of hot and dense hadron gas

Reference 42

Resolution: verified exact; local_arxiv, observed 2026-08-15T19:47:06.715885Z

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Observation 708cb32a-0a34-4f25-b5f6-8b40f363ad54 · outbound

This paper cites Zebarjadi, S.

Relaxation for massive particles: transport and causality Zebarjadi, S

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:47:07.402494Z

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This paper cites Relativistic (Lattice) Boltzmann Equation with Non-Ideal Equation of State.

Relaxation for massive particles: transport and causality Relativistic (Lattice) Boltzmann Equation with Non-Ideal Equation of State

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.163657Z

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This paper cites Kinetic Theory of Quasiparticles, Retarded Correlators and Hydrodynamics.

Relaxation for massive particles: transport and causality Kinetic Theory of Quasiparticles, Retarded Correlators and Hydrodynamics

Reference 45

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This paper cites Normal mode analysis within relativistic massive transport.

Relaxation for massive particles: transport and causality Normal mode analysis within relativistic massive transport

Reference 46

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This paper cites Holography and hydrodynamics with weakly broken symmetries.

Relaxation for massive particles: transport and causality Holography and hydrodynamics with weakly broken symmetries

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.179657Z

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This paper cites Rigorous bounds on transport from causality.

Relaxation for massive particles: transport and causality Rigorous bounds on transport from causality

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.184649Z

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This paper cites The Hydrohedron: Bootstrapping Relativistic Hydrodynamics.

Relaxation for massive particles: transport and causality The Hydrohedron: Bootstrapping Relativistic Hydrodynamics

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.190129Z

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This paper cites Dispersion relations alone cannot guarantee causality.

Relaxation for massive particles: transport and causality Dispersion relations alone cannot guarantee causality

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.195412Z

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Observation 466e7d35-3a4a-4c6c-b996-a7b737bcb305 · outbound

This paper cites AdS black holes and thermal Yang-Mills correlators.

Relaxation for massive particles: transport and causality AdS black holes and thermal Yang-Mills correlators

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.200659Z

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Observation 8b853e6c-4a1d-4f7e-9132-bde68c8fc450 · outbound

This paper cites Branch-cut in the shear-stress response function of massless $\lambda \varphi^4$ with Boltzmann statistics.

Relaxation for massive particles: transport and causality Branch-cut in the shear-stress response function of massless $\lambda \varphi^4$ with Boltzmann statistics

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.205776Z

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Observation 5387a476-694f-4c3c-8bb3-01d53a053443 · outbound

This paper cites Transport peak in thermal spectral function of ${\cal N}=4$ supersymmetric Yang-Mills plasma at intermediate coupling.

Relaxation for massive particles: transport and causality Transport peak in thermal spectral function of ${\cal N}=4$ supersymmetric Yang-Mills plasma at intermediate coupling

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.210620Z

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This paper cites Adding new branches to the "Christmas tree" of the quasinormal spectrum of black branes.

Relaxation for massive particles: transport and causality Adding new branches to the "Christmas tree" of the quasinormal spectrum of black branes

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.216412Z

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Observation acca13a6-9ea7-4169-952b-330835890a0f · outbound

This paper cites Exploring improved holographic theories for QCD: Part I.

Relaxation for massive particles: transport and causality Exploring improved holographic theories for QCD: Part I

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.222435Z

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This paper cites Exploring improved holographic theories for QCD: Part II.

Relaxation for massive particles: transport and causality Exploring improved holographic theories for QCD: Part II

Reference 56

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This paper cites Quasi-normal modes of a strongly coupled non-conformal plasma and approach to criticality.

Relaxation for massive particles: transport and causality Quasi-normal modes of a strongly coupled non-conformal plasma and approach to criticality

Reference 57

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Relaxation for massive particles: transport and causality Unresolved cited work

Reference 58

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Observation 6c3f85f7-df87-431a-9f3e-fa56f84c9463 · outbound

This paper cites Lectures on hydrodynamic fluctuations in relativistic theories.

Relaxation for massive particles: transport and causality Lectures on hydrodynamic fluctuations in relativistic theories

Reference 59

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This paper cites New developments in relativistic magnetohydrodynamics.

Relaxation for massive particles: transport and causality New developments in relativistic magnetohydrodynamics

Reference 60

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Observation 886e2fea-295c-4a03-8e8d-aac2d5f45ba7 · outbound

This paper cites Cercignani and G.

Relaxation for massive particles: transport and causality Cercignani and G

Reference 61

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This paper cites Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes.

Relaxation for massive particles: transport and causality Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes

Reference 62

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Observation 78a41be8-974d-4385-b050-f033d7cacc5c · outbound

This paper cites Holographic quantum matter.

Relaxation for massive particles: transport and causality Holographic quantum matter

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.264469Z

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This paper cites Opacity dependence of elliptic flow in kinetic theory.

Relaxation for massive particles: transport and causality Opacity dependence of elliptic flow in kinetic theory

Reference 64

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Observation c7c5cb0c-9cf8-41f5-a2e7-8a90a6dc1d45 · outbound

This paper cites Towards the BBGKY hierarchy: a scheme beyond the Boltzmann equation and application to a weakly confined QCD gas.

Relaxation for massive particles: transport and causality Towards the BBGKY hierarchy: a scheme beyond the Boltzmann equation and application to a weakly confined QCD gas

Reference 65

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Observation c8368ab3-5771-410b-881b-f22520da745f · outbound

This paper cites Bazow, G.

Relaxation for massive particles: transport and causality Bazow, G

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.280238Z

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Observation 4c7e0102-a869-4ffb-8df9-a3ed1bd8c931 · outbound

This paper cites Hybrid Fluid Models from Mutual Effective Metric Couplings.

Relaxation for massive particles: transport and causality Hybrid Fluid Models from Mutual Effective Metric Couplings

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-15T19:47:06.284849Z

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Observation 220e6e2f-0bb2-4344-9758-5ca42c9bebf6 · outbound

This paper cites Abramowitz and I.

Relaxation for massive particles: transport and causality Abramowitz and I

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:47:07.340689Z

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Observation db5aa93a-f8f3-4e78-b6dd-22430f7d3a36 · outbound

This paper cites an unresolved cited work.

Relaxation for massive particles: transport and causality Unresolved cited work

Reference 69

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:47:07.323354Z

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Pith citing papers

Observation 73fd8888-c7f6-4c93-828e-7c2e7684a787 · inbound

Normal mode analysis within relativistic massive transport cites this paper.

Normal mode analysis within relativistic massive transport Relaxation for massive particles: transport and causality

Reference 57

Resolution: verified exact; arxiv_id, observed 2026-05-22T16:31:47.375187Z

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