Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T11:22:23.081049Z
Paper Citation Record · LEDGER
As of 8 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 5 inbound Pith citation observations for arXiv:2506.02948.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T11:22:23.081049Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-02T00:54:50.434513Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-02T20:17:22.330990Z
59 of 59 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation bf65f8eb-66ad-468d-8ca8-218e4be0a0fb · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Studies of the nonlinear problems I
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2e67d76e-e520-423d-b81f-c3d29e220786 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Exact discrete res- onances in the Fermi-Pasta-Ulam–Tsingou system
Reference 2
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Unavailable: canonical work link unavailable.
Observation 2ced9728-e0e0-46f7-9164-fb490cd2d1da · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Dimostrazione che in generale un sistema meccanico normale È QUASI—ergodico
Reference 3
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Unavailable: canonical work link unavailable.
Observation 585fb311-4fe4-433e-8796-04b7c63f001b · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Collected Papers:(Note E Memorie)
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 322e4a6c-1d5d-43cf-90f1-f6f5bbf3d8e6 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Counter-propagating waves on fluid surfaces and the contin- uum limit of the Fermi-Pasta-Ulam model
Reference 5
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Unavailable: canonical work link unavailable.
Observation ae08048e-8a13-4e84-8f10-4a88869ecc88 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Interaction of
Reference 6
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Unavailable: canonical work link unavailable.
Observation 3f112ebe-fc0f-4759-855a-d58f9d8c79ad · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Statistical Properties of a Nonlinear String
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 9f79660b-bea7-4748-913f-fc321ad4839c · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Stochastic instability of non-linear oscillations
Reference 8
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Unavailable: canonical work link unavailable.
Observation a798781c-a7c5-4713-b8a2-803a9c2adc83 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System The Fermi-Pasta-Ulam problem: a status report
Reference 9
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Unavailable: canonical work link unavailable.
Observation 009f1dbc-7f6b-4e2c-817f-7f590f645479 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System ProofofNishida’sconjectureonanharmoniclattices
Reference 10
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Unavailable: canonical work link unavailable.
Observation 70e65d7e-5ecb-4ed5-82cd-b254bc2c5d33 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Results on normal forms for FPU chains
Reference 11
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Unavailable: canonical work link unavailable.
Observation 0c539df9-4cfd-4254-8cf1-268ef9731a53 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Route to thermalization in the α-Fermi–Pasta–Ulam system
Reference 12
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Unavailable: canonical work link unavailable.
Observation e271760b-4647-46ad-8a6e-a22f7c948c20 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System The two-stage dynamics in the Fermi-Pasta- Ulam problem: From regular to diffusive behavior
Reference 13
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Unavailable: canonical work link unavailable.
Observation 60058322-f00c-4b32-a458-cc0cdc4d6892 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System The Fermi-Pasta-Ulam problem in the thermodynamic limit: Scaling laws of the energy cascade
Reference 14
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Unavailable: canonical work link unavailable.
Observation 6f2002b3-3044-4c6f-b075-991ca63f7f91 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Anharmonic Chain with Lennard-Jones Interac- tion
Reference 15
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Unavailable: canonical work link unavailable.
Observation 6ee9281b-c38e-458b-aa65-423287d9d540 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the specific heat of Fermi–Pasta–Ulam systems and their glassy behavior
Reference 16
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Unavailable: canonical work link unavailable.
Observation 52ad7994-18f8-4aba-8554-f872b5ba997e · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the definition of temperature in FPU systems
Reference 17
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Unavailable: canonical work link unavailable.
Observation f5c90254-5304-415d-9f99-d0aa71c6a45a · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Localization of energy in FPU chains
Reference 18
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Unavailable: canonical work link unavailable.
Observation dee12423-b9c1-4c0f-aab8-e3d6d937e42a · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On metastability in FPU
Reference 19
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Unavailable: canonical work link unavailable.
Observation 6890c7d6-52e2-4dde-bba6-16bbd34012e8 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System An averaging theorem for Hamiltonian dynamical systems in the thermodynamic limit
Reference 20
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Unavailable: canonical work link unavailable.
Observation f720812f-0445-49bf-bf61-0827073614b4 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Some analytic results on the FPU paradox
Reference 21
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Unavailable: canonical work link unavailable.
Observation e5047c16-b934-40e6-9ff6-9dd3143f83bf · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Zur kinetischen Theorie der Wärmeleitung in Kristallen
Reference 22
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Unavailable: canonical work link unavailable.
Observation 6a93647c-91f2-46c3-8cdc-6e8baa2f6b74 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Theory of a weakly turbulent plasma
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 1e7176a3-906d-4dd6-b758-f172d5a26e0d · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the non-linear energy transfer in a gravity-wave spectrum. I. General theory
Reference 24
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Unavailable: canonical work link unavailable.
Observation 61f05334-78fc-4659-bf23-ebed99a3114d · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the non-linear energy transfer in a gravity wave spectrum. II. Conservation the- orems; wave-particle analogy; irreversibility
Reference 25
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Unavailable: canonical work link unavailable.
Observation ea0e5b17-ffb8-4a33-b06d-c8ff638c13ad · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Zakharov, Victor S
Reference 26
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Unavailable: canonical work link unavailable.
Observation d8ba893e-94f2-46e5-86cf-c7beab5cd95e · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Weak turbulence in media with a decay spectrum
Reference 27
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Unavailable: canonical work link unavailable.
Observation 8bdf6eb4-2521-4b0a-b944-dfd694128773 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Nazarenko
Reference 28
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Unavailable: canonical work link unavailable.
Observation 4f78b9ff-4547-4556-a613-ffbbb06c8a86 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System The weakly nonlinear large-box limit of the 2D cu- bic nonlinear Schrödinger equation
Reference 29
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Unavailable: canonical work link unavailable.
Observation ea931301-c41a-4632-9983-951297e7e6d4 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Analysis of (CR) in higher dimension
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 26fa3725-3fe4-4688-b1b1-456973443f32 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Effective dynamics of the nonlinear Schrödinger equation on large domains
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation eeca6a04-edd8-4fd1-aa07-a47764397768 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation
Reference 32
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Unavailable: canonical work link unavailable.
Observation 9b195979-f396-4799-b346-24157995bfec · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the Boltzmann equation for weakly nonlinear wave equations
Reference 33
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Unavailable: canonical work link unavailable.
Observation a8c03e1e-eca2-400e-a58d-4396bae640e9 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation fa4c5948-c1a3-49de-bc65-5c5e3fa9f6c8 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Quantum diffusion of the random Schrödinger evolution in the scaling limit
Reference 35
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Unavailable: canonical work link unavailable.
Observation a594c582-0bcb-4a75-b41e-116e47182ccc · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the derivation of the wave kinetic equation for NLS
Reference 36
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Unavailable: canonical work link unavailable.
Observation 0e0bc2e1-1435-492f-90d3-b12fae1b3624 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the derivation of the homogeneous kinetic wave equation
Reference 37
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Unavailable: canonical work link unavailable.
Observation 1f546b0d-d157-43d3-91be-6231c6cae5ae · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Derivation of the homogeneous kinetic wave equation: longer time scales
Reference 38
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Unavailable: canonical work link unavailable.
Observation 2db5ec68-3f1e-42db-94f9-1fa30d3f3a27 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Full derivation of the wave kinetic equation
Reference 39
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Unavailable: canonical work link unavailable.
Observation 7d323c57-2135-4d33-83a8-5b13fa0bc3ea · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Derivation of the wave kinetic equation: full range of scaling laws
Reference 40
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Unavailable: canonical work link unavailable.
Observation 99429a13-d76f-459e-a9d0-669d0a979828 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Long time justification of wave turbulence theory
Reference 41
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Unavailable: canonical work link unavailable.
Observation 1adc147a-e9cf-4b72-b448-f19ccaa54918 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Long time derivation of the Boltzmann equation from hard sphere dynamics
Reference 42
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Unavailable: canonical work link unavailable.
Observation 84eeb605-61c6-4867-9999-ddba60a1b9fd · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System One-dimensional wave kinetic theory
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation a5b34684-fd28-4b1b-8e73-c378e86d5e86 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Stages of Energy Transfer in the FPU Model
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation a930888d-0616-4678-8539-a1d8fb56cb69 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Application of weak turbulence theory to FPU model
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 1d191f37-d020-4069-a815-12c357f94c2c · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Universal route to thermalization in weakly-nonlinear one-dimensional chains
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d93094ff-8899-4be0-b7a8-b685ddc5802b · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Double scaling in the relaxation time in theβ-Fermi-Pasta-Ulam- Tsingou model
Reference 47
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Unavailable: canonical work link unavailable.
Observation 800a4f6b-3677-484a-8c57-ff3065f3460a · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Coexistence of Ballistic and Fourier Regimes in theβ Fermi-Pasta-Ulam-Tsingou Lattice
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e2a4c028-763a-43d6-8585-98a6e810f014 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Anomalous conduction in one-dimensional particle lattices: Wave-turbulence approach
Reference 49
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Unavailable: canonical work link unavailable.
Observation 0883392f-f9e5-4da4-adff-d7e840f4b528 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Anomalous energy transport in the FPU-β chain
Reference 50
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Unavailable: canonical work link unavailable.
Observation 4ef57354-c20e-4c6b-ad51-059ccdbc6909 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Multi-wave resonances in the diatomic α-FPUT system
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7fcf360c-16f2-4e10-bb13-42728e42b746 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Quasiperiodicity in the α-Fermi–Pasta–Ulam–Tsingou problem revisited: An ap- proach using ideas from wave turbulence
Reference 52
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 71ae2a53-33f4-4416-a557-662db14f86e8 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Six-wave systems in one-dimensional wave turbulence
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 1343b459-0aa3-4247-b1ac-e5754bc53f8c · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System 4-wave dynamics in kinetic wave tur- bulence
Reference 54
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Unavailable: canonical work link unavailable.
Observation c968a359-9e77-4a76-acfd-d6f2e9d333ef · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System On the wave turbulence theory of 2D gravity waves, II: propagation of randomness
Reference 55
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Unavailable: canonical work link unavailable.
Observation b4f0193e-ae6a-4820-accf-28efbba9392d · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System A pedestrian approach to the invariant Gibbs measures for the 2-d defocusing nonlinear Schrödinger equations
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 1f5b4aa5-1ede-48f1-88b4-0fb4835f5019 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Unresolved cited work
Reference 276
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Unavailable: canonical work link unavailable.
Observation a9963eb2-5bf7-42e2-83ee-435dfc051f07 · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Unresolved cited work
Reference 312
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Unavailable: canonical work link unavailable.
Observation 7c778b1e-161f-4903-9c47-ac9dd6eb396b · outbound
Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System Stages of Energy Transfer in the FPU Model
Reference 2002
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Unavailable: canonical work link unavailable.
Observation a6fd4837-06ca-4618-86a6-1a50690fbf69 · inbound
Rigorous Derivation of the Wave Kinetic Equation for full $\beta$-FPUT System Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System
Reference 76
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4a2e226a-b5d9-4fdd-8478-3d819e26ef7c · inbound
Resonant interactions in the $\alpha$-FPUT lattice with site-dependent coefficients Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 3c54c731-096f-47ad-bb55-7d3af9455daf · inbound
A review on the kinetic theory of oscillator chains Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 43b9389a-94f9-479f-828e-840618cd3541 · inbound
A survey on rigorous results for the dynamics of periodic FPU chains Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4c4acca1-d77d-45a2-83ec-5453b9835009 · inbound
Sharp decay thresholds in weighted $L^\infty$ for wave kinetic equations with power-law dispersion Rigorous Derivation of the Wave Kinetic Equation for $\beta$-FPUT System
Reference 30
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Unavailable: canonical work link unavailable.