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Source: paper_references, paper_reference_links, observed 2026-08-15T15:13:46.536185Z
Paper Citation Record · LEDGER
As of 15 August 2026, this Paper Citation Record lists 100 of 123 outbound references and 0 inbound Pith citation observations for arXiv:2608.01900.
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Source: paper_references, paper_reference_links, observed 2026-08-15T15:13:46.536185Z
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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00
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100 of 123 outbound references displayed
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Observation a05c3d3e-be3d-42d5-8c8c-768bde7ed5c7 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
Reference 1
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics (15) Dividing both sides of equation (14) by ( a2 1 + a2 2 + a2 3)2, v4 c + [Γ⊥ ⊥(ˆa2 1 + ˆa2
Reference 2
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Observation a0a9cd47-8d8e-461a-b84a-b59a52c958e3 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics (16) 2 It should be noted that each component of this matrix is Loren tz vector as shown in Appendix A
Reference 3
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Observation 0e435b2c-8bf6-40c8-8a0b-aa4ae792f4f5 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
Reference 4
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Observation 208512c4-3754-4bfa-b0b5-3e8b0bef7fcf · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics (20) Equation (17) can be solved straightforwardly
Reference 5
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
Reference 6
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics We derive the conditions that satisfy these four require- ments one by one
Reference 7
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
Reference 8
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Substituting this into Eq
Reference 9
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Observation 89fed2b4-3cad-4acf-987e-e7666a568cfc · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
Reference 10
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
Reference 11
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
Reference 12
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Observation 11868e4f-9d2b-4c22-8ceb-1e1ea83658ed · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Substituting v2 c = 0 into f (v2 c ), we obtain f (0) = (Γ L z Γ⊥ ⊥ − ΓL ⊥Γ⊥ z )(1 − ˆa2 3)ˆa2
Reference 13
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Observation 8a2a4fcb-0e2c-44d3-9ad8-d961a1175c15 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics (B5) Therefore, the condition for satisfying (a) is as follows: ΓL ⊥Γ⊥ z ≤ ΓL z Γ⊥ ⊥
Reference 14
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Observation faa03edf-db5f-425d-b53a-2df60b3a859f · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Substituting v2 c = 1 into f (v2 c ) and rearranging in terms of ˆa2 3, we obtain f (1) = −(ΓL z Γ⊥ ⊥ − ΓL ⊥Γ⊥ z )(ˆa2 3)2 + (ΓL z − Γ⊥ ⊥ + ΓL z Γ⊥ ⊥ − ΓL ⊥Γ⊥ z )ˆa2 3 + Γ⊥ ⊥ + 1
Reference 15
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Then, in order to satisfy f (v2 c = 1) ≥ 0, it suffices that g(ˆa2
Reference 16
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Observation 52b06af5-65cd-4e75-ad95-1aa81f42f54f · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Substituting ˆa2 3 = 0 into g(ˆa2 3), we obtain g(0) = Γ ⊥ ⊥ + 1
Reference 17
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics The symmetry axis of f (v2 c ) is given by v2 c = − 1 2 [Γ⊥ ⊥(1 − ˆa2
Reference 18
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Observation 40c555bc-aa72-4f24-b1a6-4d50a726c688 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics (B12) Then, the condition for 0 ≤ v2 c ≤ 1 is 0 ≤ (Γ⊥ ⊥ − ΓL z )ˆa2 3 − Γ⊥ ⊥ ≤ 2
Reference 19
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Observation 62ee67bb-f8c4-4abf-8a7b-6bf110a4a41d · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Therefore, the conditions are the following two inequalities: 0 ≤ −Γ⊥ ⊥, (B14) −ΓL z ≤ 2
Reference 20
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Therefore, the conditions are the following two inequalities: 0 ≤ −ΓL z , (B16) −Γ⊥ ⊥ ≤ 2
Reference 21
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Observation 542b5e0f-6d7a-4bd0-8621-b82d755bc0b2 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics The discriminant of f (v2 c ) is given by D = [Γ ⊥ ⊥(1 − ˆa2
Reference 22
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics (B20) Here, let t = ˆa2 3/1 − ˆa2
Reference 23
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics (B21) When ˆa2 3 takes any value in 0 ≤ ˆa2 3 ≤ 1, t takes any value in 0 ≤ t < +∞
Reference 24
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics (B28) These are the necessary and sufficient conditions for non- linear causality in V AH
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
Reference 26
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
Reference 29
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Observation fc4abad3-fe8f-4ad8-863c-7d060cc25f6d · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics (C19) Equations (C16), (C17), (C18), and (C19) are identical to Eqs
Reference 30
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Quark Gluon Plasma an Color Glass Condensate at RHIC? The perspective from the BRAHMS experiment
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Observation 6a2d7a90-acea-4f15-ab2b-619b52899083 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics The PHOBOS Perspective on Discoveries at RHIC
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Observation 8226c6b8-ecdf-4df3-8595-4538c29063d6 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions
Reference 33
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics The QGP Discovered at RHIC
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Results from the Relativistic Heavy Ion Collider
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics The Frontiers of Nuclear Science, A Long Range Plan
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Phases of QCD: Summary of the Rutgers Long Range Plan Town Meeting
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics The ALICE experiment: a journey through QCD
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Suppression of Hadrons with Large Transverse Momentum in Central Au+Au Collisions at $sqrt {s sub {sub {NN}}}_ = 130 GeV
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Evidence from d+Au measurements for final-state suppression of high $p_T$ hadrons in Au+Au collisions at RHIC
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Observation and studies of jet quenching in PbPb collisions at nucleon-nucleon center-of-mass energy = 2.76 TeV
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Observation of a Centrality-Dependent Dijet Asymmetry in Lead-Lead Collisions at sqrt(S(NN))= 2.76 TeV with the ATLAS Detector at the LHC
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Suppression of charged particle production at large transverse momentum in central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Unresolved cited work
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Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Phenomenological constraints on the transport properties of QCD matter with data-driven model averaging
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Observation 971555a1-4969-47f7-9893-1d305bd1a852 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Bulk Viscosity driven clusterization of quark-gluon plasma and early freeze-out in relativistic heavy-ion collisions
Reference 85
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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 73130c69-826f-49fb-9343-644767c30659 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Instability of Boost-invariant hydrodynamics with a QCD inspired bulk viscosity
Reference 86
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No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation ad6a383d-2564-4dec-8e37-f7b6e117b7fd · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Effects of Bulk Viscosity at Freezeout
Reference 87
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Observation fdefb57a-e601-4ca6-ad54-f00cad66dde5 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Bulk Viscosity and Cavitation in Boost-Invariant Hydrodynamic Expansion
Reference 88
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Observation 484370db-e32e-459a-a06f-5b9ec2042699 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Bulk Viscosity Effects in Event-by-Event Relativistic Hydrodynamics
Reference 89
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Observation e1cbea3c-7ca9-4e5e-911b-8a1ae70ea3bf · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Second-order (2+1)-dimensional anisotropic hydrodynamics
Reference 90
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Observation 76aebce9-34e3-4b4e-aece-4ea7dd8730d5 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Nonconformal viscous anisotropic hydrodynamics
Reference 91
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Observation 2922c45b-a964-4ca2-b8ba-c1654ccc1ad8 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Anisotropic matching principle for the hydrodynamics expansion
Reference 92
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Observation 981baf39-359e-4d06-b8e2-a93cfda06d34 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation
Reference 93
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Observation be2a6b84-29b6-49e8-8de2-55fca0ba7dc3 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Colliding shock waves and hydrodynamics in small systems
Reference 94
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Observation 2b8c75e4-e767-4484-a850-1dd3b5d4d69b · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
Reference 95
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Observation d321c554-2589-447c-909b-a17e215ebc14 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics (3+1)-dimensional anisotropic fluid dynamics with a lattice QCD equation of state
Reference 96
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Observation 28a3ca66-c6f9-4186-b949-a3217d0c34a6 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Matching the Nonequilibrium Initial Stage of Heavy Ion Collisions to Hydrodynamics with QCD Kinetic Theory
Reference 97
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Observation dcc638ac-f3e3-4e12-bb36-2f3a590f2882 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Anisotropic fluid dynamical simulations of heavy-ion collisions
Reference 98
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Observation a92420f4-4157-4966-af3b-e4b3b81d2657 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb collisions
Reference 99
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 179e72c2-74d6-462f-a095-a6d05e676912 · outbound
Necessary and sufficient conditions of nonlinear causality in viscous anisotropic hydrodynamics Bayesian calibration of viscous anisotropic hydrodynamic simulations of heavy-ion collisions
Reference 100
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No inbound Pith citation observations are available.