{"as_of":"2026-08-07T07:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4099e8ad7c11af3baf4280260e7a4335cbda1a7f9e52bb0ddde1356e4cd02df8","coverage":[{"denominator":30,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":30,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T00:54:50.434513Z","state":"measured"},{"denominator":30,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":30,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.14892/citation-record","integrity":"/paper/2607.14892/integrity","json":"/paper/2607.14892/citation-record.json","paper":"/paper/2607.14892"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.340822Z","title":"Derivation of the kinetic wave equation for quadratic dispersive problems in the inhomogeneous setting.American Journal of Mathematics, 147(4):1053–1158, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.340822Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:36faad05f782eb36a0cf06a9a1412d33603f3a52462feb64a49373c14918b8d0","observation_id":"e5374ceb-36c9-4ad9-a3f6-75f36ad2950d","resolution":{"observed_at":"2026-08-02T00:54:50.340822Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.345000Z","title":"On the ill-posedness of kinetic wave equations.Nonlinearity, 38:115004, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.345000Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:bc86f2258343aaf22d2535ad84aca23598dc53518c6a6adc5d79a23e677255f8","observation_id":"783c2add-1ad9-44a4-9aa9-d95b4b240264","resolution":{"observed_at":"2026-08-02T00:54:50.345000Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.348809Z","title":"On the optimal local well-posedness of the wave kinetic equation inL r","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.348809Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:3a92730f1ad2234440f38d892537eba59c904e4d365c020078a7276012bca541","observation_id":"1b4a1129-0067-4939-b382-2686f738d903","resolution":{"observed_at":"2026-08-02T00:54:50.348809Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.352607Z","title":"A collective description of electron interactions","venue":null,"work_id":null,"year":1951},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.352607Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:d2862829184ec57bdcc5baffbbe77d6e064b8cc98d997b21b5651f16197ca570","observation_id":"8a2bf717-ef05-4580-a5a1-b690c3dbffdd","resolution":{"observed_at":"2026-08-02T00:54:50.352607Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.355989Z","title":"Onset of the wave turbulence description of the longtime behavior of the nonlinear schr¨ odinger equation.Inventiones Mathematicae, 225(3):787–855, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.355989Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:7a5ccc17500436cda5faad2268ff7d454520a111f5e423334582db58c9aa9c68","observation_id":"66e12e51-f063-4eac-a8b7-64c023e65796","resolution":{"observed_at":"2026-08-02T00:54:50.355989Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.359237Z","title":"On the derivation of the homogeneous kinetic wave equation.Communications on Pure and Applied Mathematics, 78(4):856–909, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.359237Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:b1eb81cbc3414f6f3e574a8103b4688519586bf990ee10e28a5af90cc828a8e9","observation_id":"f4ff8139-aff8-4615-b841-0a323ea625f6","resolution":{"observed_at":"2026-08-02T00:54:50.359237Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.363198Z","title":"Derivation of the homogeneous kinetic wave equation: Longer time scales","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.363198Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:e786b75b126435a6cb53c6c79e09498be9085c466f37188ffee54980eda5b15b","observation_id":"9106da56-cbb1-4d3c-9eeb-0e920b90b3d0","resolution":{"observed_at":"2026-08-02T00:54:50.363198Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.366292Z","title":"On the derivation of the wave kinetic equation for NLS.Forum of Mathematics, Pi, 9:e6, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.366292Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:6786dc21977c7111137390b4441b905abc4130b48cda3cbc5cffcd50592c8e26","observation_id":"487936ee-40ce-45bd-9012-da4297a600c1","resolution":{"observed_at":"2026-08-02T00:54:50.366292Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.369687Z","title":"Derivation of the wave kinetic equation: full range of scaling laws, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.369687Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:73cd24665f4fd38a5563387a99518f754bbc2a1ff74cc6e1e32e15368e96acb3","observation_id":"b19d87f0-b2a4-49b5-b3d6-09b3bfb97dee","resolution":{"observed_at":"2026-08-02T00:54:50.369687Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.372854Z","title":"Full derivation of the wave kinetic equation.Inventiones Mathematicae, 233(2):543–724, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.372854Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:2c52955b2755bf7d9e9665cb2438933f86d2ad12af83a5fe24a5ea8f46e5a8aa","observation_id":"9531534e-ee3f-43f8-a685-41ebcbf41151","resolution":{"observed_at":"2026-08-02T00:54:50.372854Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.375678Z","title":"Long time justification of wave turbulence theory","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.375678Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:0147bc6840ffefee93ce07bc0cc4c1500f323e7921fc437e87197a2b9e1591a9","observation_id":"43083db7-d37e-43c2-a912-28ff3a2cbb6e","resolution":{"observed_at":"2026-08-02T00:54:50.375678Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.378768Z","title":"Long time derivation of the boltzmann equation from hard sphere dynamics","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.378768Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:1e554241b4a227237bf44ddaeb61511ad63bae44d98fe23a4240c0d970215307","observation_id":"a229305c-9b46-42ad-8965-b60acfce8c98","resolution":{"observed_at":"2026-08-02T00:54:50.378768Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.381703Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.381703Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:41476cbe78096154188e75047d9f4c10f8c9566f05b1bc3b4d5d6faf45c3f88b","observation_id":"353e2acf-4fb5-411e-9cea-a8d1b97e7c98","resolution":{"observed_at":"2026-08-02T00:54:50.381703Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.384456Z","title":"Linearized wave turbulence convergence results for three-wave systems.Communications in Mathe- matical Physics, 378:807–849, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.384456Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:e502f49b831312672a3d5974c0d0f9b01c981b0854a1c1c759870edd0a2d7617","observation_id":"7d8ae235-39b2-45df-a8a4-8ae63a91b387","resolution":{"observed_at":"2026-08-02T00:54:50.384456Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.388081Z","title":"Ionescu, and Minh-Binh Tran","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.388081Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:763fb2e3b5dabeb9788cfb87c9d7f0ad91e30424b26231f40b3bf6c255ff24aa","observation_id":"ddf89703-f0d5-4ea8-b4ff-41dbbe4f3cd0","resolution":{"observed_at":"2026-08-02T00:54:50.388081Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.01507","last_updated":"2024-09-03T00:15:44Z","snapshot_observed_at":"2026-07-06T19:09:27.758765Z","submitted_at":"2024-09-03T00:15:44Z","title":"Stability of Rayleigh-Jeans equilibria in the kinetic FPU equation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.01507","snapshot_observed_at":"2026-08-02T00:54:50.391006Z","title":"Stability of Rayleigh–Jeans equilibria in the kinetic FPU equation.arXiv preprint arXiv:2409.01507, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.391006Z"},"links":{"cited_paper":"/paper/2409.01507","citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:849c6618b7ad797bbbd25a71b240ef1c9216d2ba131a6526718c9c8625f19b2c","observation_id":"2f6f1a58-c50a-45ac-9f7d-a8b752bc8f77","resolution":{"observed_at":"2026-08-02T00:54:50.391006Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.01358","last_updated":"2026-05-31T17:29:42Z","snapshot_observed_at":"2026-08-03T00:19:09.866858Z","submitted_at":"2026-05-31T17:29:42Z","title":"A review on the kinetic theory of oscillator chains","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.01358","snapshot_observed_at":"2026-08-02T00:54:50.394562Z","title":"A review on the kinetic theory of oscillator chains.arXiv preprint arXiv:2606.01358, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.394562Z"},"links":{"cited_paper":"/paper/2606.01358","citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:3daa0103c344d41fe0e3aec34457f16b9c8e1c1514daafe933962a02bd1be89b","observation_id":"d7ed2114-2be3-47fc-b56d-06012d5e7850","resolution":{"observed_at":"2026-08-02T00:54:50.394562Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.397771Z","title":"Local well-posedness for the kinetic MMT model","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.397771Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:f351915f69fd3d5451680b670b485c14e1cd9511895d660b62d290ed89e9cd19","observation_id":"482b7070-c1e0-4a4e-b05f-907411ca44de","resolution":{"observed_at":"2026-08-02T00:54:50.397771Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.400601Z","title":"Inhomogeneous turbulence for the wick nonlinear schr¨ odinger equation","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.400601Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:d1b98b1f9cea484e9090d62de17943a34b78dd359f95935af61705762e149855","observation_id":"9a8af66f-43c0-4b8e-9f02-5dc764fb7223","resolution":{"observed_at":"2026-08-02T00:54:50.400601Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.403739Z","title":"On the wave turbulence theory for a stochastic KdV type equation – generalization for the inhomogeneous kinetic limit","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.403739Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:50380058eae0289f618fcd5ac89bea2c17ef76bc433520b5234a486e8e496464","observation_id":"aa7daacb-46b2-4df4-b565-4c5deda7e090","resolution":{"observed_at":"2026-08-02T00:54:50.403739Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.406721Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.406721Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:75aed4cbbd8556bcbe01de7182e044c1a29c564bbc8f12643a3f09f85b5e5aec","observation_id":"f53017fc-63ed-4318-9e50-654d806d4424","resolution":{"observed_at":"2026-08-02T00:54:50.406721Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.409630Z","title":"Almost sharp wave kinetic theory of multidimensional KdV type equations withdě3","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.409630Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:99b60f45879664371d05c012548f4b731163b1b98916c35672803f3064ecdaa7","observation_id":"d6ed8db9-258c-47fd-a0c2-7c75cff83283","resolution":{"observed_at":"2026-08-02T00:54:50.409630Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.412811Z","title":"Springer-Verlag, Berlin, 1966","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.412811Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:59a02f439a9de333ada4a0a5957b74e6b6ae61432d6be804ac2c7be4e6e99ff6","observation_id":"b301a4b3-5adb-41ce-93aa-7b2106596360","resolution":{"observed_at":"2026-08-02T00:54:50.412811Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.415896Z","title":"Springer, Heidelberg, 2011","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.415896Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:3dd4d4d1fe2380a933e264504825df6727dc7e7aaee06059965b94ddd1165c23","observation_id":"684c582d-e950-42b2-9ad2-dece166490df","resolution":{"observed_at":"2026-08-02T00:54:50.415896Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.418881Z","title":"Local-in-time existence ofL 1 solutions to the gravity water wave kinetic equation","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.418881Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:79a4ec002d15955765bc43ecacbf1528b697095cebd12f77fdcb0750e2ad19f0","observation_id":"d9f1cac7-9e20-4710-b90b-b05dbdc522fb","resolution":{"observed_at":"2026-08-02T00:54:50.418881Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.422304Z","title":"On the wave turbulence theory for a stochastic KdV type equation","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.422304Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:c7e3c96737f11334cc75231a4932ff39b639e1284488f5812e7edfb82f87e87b","observation_id":"f306db20-d968-4c6f-8484-80d486e8aa49","resolution":{"observed_at":"2026-08-02T00:54:50.422304Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.425166Z","title":"American Mathematical Society, Providence, RI, 4th edition, 1975","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.425166Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:c186bbb0fcfd963f8d1d1a1cb3e12d62b3ef651bfeba7e18ea7a8c4c3beeecbc","observation_id":"50c64a20-06c1-4907-81b2-4abfa703d6db","resolution":{"observed_at":"2026-08-02T00:54:50.425166Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.19308","last_updated":"2026-05-19T03:40:44Z","snapshot_observed_at":"2026-07-06T23:30:02.207108Z","submitted_at":"2026-05-19T03:40:44Z","title":"Rigorous Derivation of the Wave Kinetic Equation for full $\\beta$-FPUT System","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.19308","snapshot_observed_at":"2026-08-02T00:54:50.428481Z","title":"Rigorous derivation of the wave kinetic equation for fullβ-FPUT system.arXiv preprint arXiv:2605.19308, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.428481Z"},"links":{"cited_paper":"/paper/2605.19308","citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:651e59025700faef0166eeb56314ac2855ed873454639a84a15c4afac761b1e0","observation_id":"ba9fe5b8-fa49-438e-b7a9-b4b85ada0cc9","resolution":{"observed_at":"2026-08-02T00:54:50.428481Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:54:50.431729Z","title":"Vassilev","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.431729Z"},"links":{"citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:5ec86d4c80af7f71698bf8d47e5e3d11a44d17352343000a6487a20d5b4a7ab3","observation_id":"907d741f-8369-45c9-8229-d2a0a6c5135a","resolution":{"observed_at":"2026-08-02T00:54:50.431729Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.02948","last_updated":"2025-06-12T16:12:56Z","snapshot_observed_at":"2026-07-06T21:35:51.635385Z","submitted_at":"2025-06-03T14:44:43Z","title":"Rigorous Derivation of the Wave Kinetic Equation for $\\beta$-FPUT System","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.02948","snapshot_observed_at":"2026-08-02T00:54:50.434513Z","title":"Rigorous derivation of the wave kinetic equation forβ-FPUT system.arXiv preprint arXiv:2506.02948, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-02T00:54:50.434513Z"},"links":{"cited_paper":"/paper/2506.02948","citing_paper":"/paper/2607.14892"},"observation_digest":"sha256:58ea1dee12b90891f154261662d4b9bf8ec603d71ab5a7096878dc98f461d793","observation_id":"4c4acca1-d77d-45a2-83ec-5453b9835009","resolution":{"observed_at":"2026-08-02T00:54:50.434513Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.14892","last_updated":"2026-07-16T12:09:08Z","latest_version":1,"primary_category":"math.AP","snapshot_observed_at":"2026-08-02T00:54:47.227093Z","submitted_at":"2026-07-16T12:09:08Z","title":"Sharp decay thresholds in weighted $L^\\infty$ for wave kinetic equations with power-law dispersion"},"reference_resolution":{"displayed":30,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":30,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":30},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2607.14892."}