{"as_of":"2026-08-11T18:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:81be66bb36d9fb27cabad727e94ed3e581f1fd48dca079283a90b0332df5579e","coverage":[{"denominator":138,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T04:24:42.344756Z","state":"measured"},{"denominator":100,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":100,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2608.06606/citation-record","integrity":"/paper/2608.06606/integrity","json":"/paper/2608.06606/citation-record.json","paper":"/paper/2608.06606"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:38.194745Z","title":null,"venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.194745Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:6022d06e1bb4483080c91a82d827a74af33dfd2cbcf68f6591634dfbebbc03e4","observation_id":"66211db3-79ca-40ad-8907-3a9bf715597f","resolution":{"observed_at":"2026-08-10T04:24:38.194745Z","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":"2026-08-10T04:24:38.234740Z","title":null,"venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.234740Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:6f04a53adf2498406131464af356381793409bb2464e02f3a0cf7701d937c330","observation_id":"38edd09f-abf9-4d5b-b485-06e7843b39a7","resolution":{"observed_at":"2026-08-10T04:24:38.234740Z","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":"2026-08-10T04:24:38.263250Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.263250Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:80e8d668b4f8ffb48e98b269cefc1575f456f7eb27278018c43cfe08f6fbc2e7","observation_id":"b02550d9-39bc-4f87-a6a3-42e7302af6ac","resolution":{"observed_at":"2026-08-10T04:24:38.263250Z","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":"2026-08-10T04:24:38.323116Z","title":"Smagorinsky, General circulation experiments with the primitive 56 equations: I","venue":null,"work_id":null,"year":1963},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.323116Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:6d4b998af28f57faf94bcafc4088823456c7af60aba00bdc57ed2c994accd71d","observation_id":"8afc7a22-077d-4b82-afe4-ae71cd298a19","resolution":{"observed_at":"2026-08-10T04:24:38.323116Z","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":"2026-08-10T04:24:38.364180Z","title":null,"venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.364180Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:f9656691ca697e5e4970f93ae98e6db07cbe261ee29b460521fb02fd1602f7b1","observation_id":"bfc20720-2c4c-4882-ad28-7b0a898bd075","resolution":{"observed_at":"2026-08-10T04:24:38.364180Z","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":"2026-08-10T04:24:38.444742Z","title":"Vreman, B","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.444742Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:b3051eb44608554de449b54d76dd69ee5c871af743113a46773eb6408239fbc0","observation_id":"2c40a85a-b892-4b89-8c3e-7dd62f4b5af0","resolution":{"observed_at":"2026-08-10T04:24:38.444742Z","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":"2026-08-10T04:24:38.484748Z","title":"Jakhar, Y","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.484748Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:765ae086b349d6dec61a9e49f084c88bd7c927f54589a9073e59595568aaf017","observation_id":"3970aff6-ad34-46bb-9d00-3c4016a09ea5","resolution":{"observed_at":"2026-08-10T04:24:38.484748Z","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":"2026-08-10T04:24:38.525307Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.525307Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:82756bb7250a0c40ae9c49749e9431a4f9493015e6aa2b7a6eabd63089bafa0c","observation_id":"735385b5-f312-45aa-8ce8-446e7b844804","resolution":{"observed_at":"2026-08-10T04:24:38.525307Z","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":"2026-08-10T04:24:38.560873Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.560873Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:9787a4c20ef812dcd935d790fc4717c96205b7e1aa8f66966f2ebc6553bf4d37","observation_id":"73221e03-73dd-45f0-9381-af1d5857f3f5","resolution":{"observed_at":"2026-08-10T04:24:38.560873Z","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":"2026-08-10T04:24:38.582191Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.582191Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:bb28c8e11030bfb7aec668f1e9161a7e4d433c40bbafbcb3e332dfb7d80566db","observation_id":"e5285d2f-21c4-4baa-9308-6d49e695fbc6","resolution":{"observed_at":"2026-08-10T04:24:38.582191Z","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":"2026-08-10T04:24:38.595192Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.595192Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:0c2cb1ef4848c553ef72314128ac56e609bf58937d1962942c72339ec482e16f","observation_id":"49028593-b409-4eee-a4ca-e4d3aaa64b63","resolution":{"observed_at":"2026-08-10T04:24:38.595192Z","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":"2026-08-10T04:24:38.644748Z","title":null,"venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.644748Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:4a7e26b50fec6960bfefe2d512d8e6de9dcb48f3019931f649f05e95ecf454c1","observation_id":"841abc92-c91c-4af0-92e0-4a42f2aeb91a","resolution":{"observed_at":"2026-08-10T04:24:38.644748Z","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":"2026-08-10T04:24:38.668338Z","title":null,"venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.668338Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:8113e6fa2271bd3df666ae1caa9ad65b9113cc38626e6f306454ce84ba15c6cc","observation_id":"bdf038a9-b03f-4798-b8c2-8f2072062da4","resolution":{"observed_at":"2026-08-10T04:24:38.668338Z","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":"2026-08-10T04:24:38.684751Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.684751Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:c84f4b5e8e8e9b87de13f4b657bd3096b24019550f2eb773ce53f1df7722a2ac","observation_id":"e99960a8-0d8b-4d76-a92b-9418b11ed098","resolution":{"observed_at":"2026-08-10T04:24:38.684751Z","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":"2026-08-10T04:24:38.711708Z","title":null,"venue":null,"work_id":null,"year":1953},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.711708Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:b705e98eb8221deac2096e781cd820cf31444268de848678f2ee393fdc2028d0","observation_id":"0e621652-be6a-4dd2-8316-721f3f56941c","resolution":{"observed_at":"2026-08-10T04:24:38.711708Z","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":"2026-08-10T04:24:38.724742Z","title":null,"venue":null,"work_id":null,"year":1955},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.724742Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:03e703bf19b36342dacee7395a8c5a2026d165d3431e71d0bcbb2755942078f6","observation_id":"2c46271f-637f-489b-bfb7-f378ea57ed87","resolution":{"observed_at":"2026-08-10T04:24:38.724742Z","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":"2026-08-10T04:24:38.737987Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.737987Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:881334dad9e15eee66a5bc5b84c712e81cb73689dcddaab5d1d9842e9673113c","observation_id":"5dd69d77-ded2-415b-8bc5-d6faa5bc64ba","resolution":{"observed_at":"2026-08-10T04:24:38.737987Z","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":"2026-08-10T04:24:38.740980Z","title":null,"venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.740980Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:b29157e7666261a802adad775836711c5fc1ccfaf134c157e43b473948f69eca","observation_id":"be78dc60-f914-46be-929b-c6e94de99354","resolution":{"observed_at":"2026-08-10T04:24:38.740980Z","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":"2026-08-10T04:24:38.742885Z","title":"(Oxford University Press, 2002)","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.742885Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:665ad34998da7005e557b83860aad411371ce1b5bdac6d2463014846029e0698","observation_id":"40b5094a-416d-4671-aa79-44a45e0ac0f6","resolution":{"observed_at":"2026-08-10T04:24:38.742885Z","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":"2026-08-10T04:24:38.762984Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.762984Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:57d1ba12da68432bea9aeaf5336fa2e1636aa1a6d0186890389767fcf00c1140","observation_id":"2ff8bca6-bd78-4c7c-9711-0afb14ace7e0","resolution":{"observed_at":"2026-08-10T04:24:38.762984Z","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":"2026-08-10T04:24:38.814749Z","title":"16 (1966) pp","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.814749Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:20f93699a42c7634fc6458be573a9a5e29d97c6392cc58837e550f951c1ddc67","observation_id":"e37af85b-7992-4cb1-b3a6-7a7c630c41c1","resolution":{"observed_at":"2026-08-10T04:24:38.814749Z","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":"2026-08-10T04:24:38.861519Z","title":null,"venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.861519Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:4977a8f24322af46c412158691479d59f98f5b11ee831e6144437fd421053057","observation_id":"34d703c4-037a-470c-84ee-d22c6a1798cd","resolution":{"observed_at":"2026-08-10T04:24:38.861519Z","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":"2026-08-10T04:24:38.897735Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.897735Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:f8d1de1b6615d68132c8ae9e17b60963cdf6bdc7c4a32ecabbf1d23de78a43d8","observation_id":"5d8d0c77-56aa-48ff-b46d-425315c5d23c","resolution":{"observed_at":"2026-08-10T04:24:38.897735Z","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":"2026-08-10T04:24:38.924754Z","title":null,"venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.924754Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:d61b127301db197c3acadf7e3acb13e91449c1a68c38eba81590eb0f940a3d65","observation_id":"1915fd76-f3a0-4c0e-be5c-36292a1e4777","resolution":{"observed_at":"2026-08-10T04:24:38.924754Z","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":"2026-08-10T04:24:38.954743Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.954743Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:776f6b5a1dca4691d81d18f87b71f1d09f954002f9f764d55e974715b3b9972a","observation_id":"ceed805e-4887-4561-b40d-e5c77256ae82","resolution":{"observed_at":"2026-08-10T04:24:38.954743Z","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":"2026-08-10T04:24:38.968010Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:38.968010Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:d9639ceefc37fe753e0e3f8b86bfdce757fc00d825e024b7707d21c0ccd33b9e","observation_id":"6838fa93-e1f3-4ba3-9a83-3768ce56f0bc","resolution":{"observed_at":"2026-08-10T04:24:38.968010Z","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":"2026-08-10T04:24:39.014781Z","title":"Resseguier, E","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.014781Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:2bf7a1d5ddb2c2de6ca51dcde25ffc33c1d6766457ec772e16db20ab46b9c2e9","observation_id":"abd5e7e7-a91e-4822-9a7f-31dc8be9c0d6","resolution":{"observed_at":"2026-08-10T04:24:39.014781Z","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":"2026-08-10T04:24:39.064861Z","title":"Resseguier, E","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.064861Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:1ab3a3ac8c982bd96fe166d606aa319c6b853a96c9e217714975e3075790229a","observation_id":"ba6347a7-c283-487e-885d-6d5c287b78b2","resolution":{"observed_at":"2026-08-10T04:24:39.064861Z","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":"2026-08-10T04:24:39.114742Z","title":null,"venue":null,"work_id":null,"year":1948},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.114742Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:e0ad4d44d3ebd970f4ee37286c7cab79e9bad2729899a8504682135a0058dba5","observation_id":"94e240f2-0a59-4f9f-823e-7265a537d606","resolution":{"observed_at":"2026-08-10T04:24:39.114742Z","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":"2026-08-10T04:24:39.142613Z","title":null,"venue":null,"work_id":null,"year":1949},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.142613Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:5e0e93de514b698191e6ef8d5ee3a6592d8c83e96ae8bab12e3493ddce3e7e27","observation_id":"898676f7-98db-4ea1-80a7-fdee368d0334","resolution":{"observed_at":"2026-08-10T04:24:39.142613Z","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":"2026-08-10T04:24:39.194751Z","title":"Forster, D","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.194751Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:533ae28136466eaec210aa3e6538f5abd3e300c50e04e05b70340ac3f0a48d8b","observation_id":"9fde8fe4-78d8-4787-881a-4d68b19c941d","resolution":{"observed_at":"2026-08-10T04:24:39.194751Z","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":"2026-08-10T04:24:39.234761Z","title":"Yakhot and S","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.234761Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:39f3362b4db7be2da377daf000b294d4b5a69f6fd278feae9b19d4bdc1459441","observation_id":"925ba388-97c8-44b5-9685-26a22defaea7","resolution":{"observed_at":"2026-08-10T04:24:39.234761Z","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":"2026-08-10T04:24:39.284751Z","title":null,"venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.284751Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:80f4349ec108b6739c045aa5b4e92351715f1753cf37c68f7dcb96d2f95953d6","observation_id":"60653ba7-a3df-483c-9000-12352068073a","resolution":{"observed_at":"2026-08-10T04:24:39.284751Z","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":"2026-08-10T04:24:39.336205Z","title":null,"venue":null,"work_id":null,"year":1973},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.336205Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:69849a65a85a084f61b291b80c0ee1c75c2067a9fe7ceb03fd883015a71de2a8","observation_id":"1537fe64-4601-4c81-911c-f82a6a28fa9a","resolution":{"observed_at":"2026-08-10T04:24:39.336205Z","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":"2026-08-10T04:24:39.384748Z","title":null,"venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.384748Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:225c2d6d2bfb0f20ebd3a62e2aa9c6eede985146af2310a42d3c5083df6351d9","observation_id":"c4570ca7-ce5a-4b1a-8629-74b1fb6a04ba","resolution":{"observed_at":"2026-08-10T04:24:39.384748Z","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":"2026-08-10T04:24:39.415603Z","title":null,"venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.415603Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:4237f693a32561acfc3e6a51bc1810eecb6f95c00b9b01151bdf117fcdfcff81","observation_id":"aaf73362-5382-4814-813f-11bb96862bc8","resolution":{"observed_at":"2026-08-10T04:24:39.415603Z","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":"2026-08-10T04:24:39.464753Z","title":null,"venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.464753Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:b27f7bb1e47c5d67c2b97da60650474b670717247bfa0f708d5d703c53c2d504","observation_id":"722ce9a6-b383-4254-8a9d-dcf4f06fdcb0","resolution":{"observed_at":"2026-08-10T04:24:39.464753Z","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":"2026-08-10T04:24:39.561355Z","title":"Berera, M","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.561355Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:b275407010b93bfc096ece41773ef4d4d2570106a761fdf3638a8db368fcab24","observation_id":"97ad4974-3b74-4adf-84a4-c96c82104748","resolution":{"observed_at":"2026-08-10T04:24:39.561355Z","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":"2026-08-10T04:24:39.604743Z","title":null,"venue":null,"work_id":null,"year":1965},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.604743Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:2efa808749a50406c60b1f7ca35cdc3ab2b94320034fe08f1ebb9c7c666d767e","observation_id":"71b74476-f511-4f0c-9392-189565c86296","resolution":{"observed_at":"2026-08-10T04:24:39.604743Z","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":"2026-08-10T04:24:39.644745Z","title":"Zwanzig, Memory effects in irreversible thermodynamics, Physical Review124, 983 (1961)","venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.644745Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:1f905f85bfe789ee4ef599f9117d697ba53a93b72de301e967c88a893397d2d2","observation_id":"8b790d1a-e194-44cb-8ea2-8a3cf5c2ef41","resolution":{"observed_at":"2026-08-10T04:24:39.644745Z","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":"2026-08-10T04:24:39.684745Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.684745Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:980fd872d97963151091c8d8d116716bf7be1c2a73823646a555014ca937b0c5","observation_id":"d18a0c61-754e-4eab-860f-38a2845820e3","resolution":{"observed_at":"2026-08-10T04:24:39.684745Z","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":"2026-08-10T04:24:39.724891Z","title":"Chorin and O","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.724891Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:0008f44e5ed60ea2ea12bd0bd9f7f56d5b7fb729c423d2ad9eb53b08949e8099","observation_id":"b30d0f98-c5e9-48ef-b38f-df372d917c2d","resolution":{"observed_at":"2026-08-10T04:24:39.724891Z","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":"2026-08-10T04:24:39.774754Z","title":"Lucarini and M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.774754Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:cdb5680b297f833b093a3ca2246737b57c7bccb532795d8e3e4a8359127c14d7","observation_id":"59dee6e3-1e06-48d6-ae18-d485751b21c6","resolution":{"observed_at":"2026-08-10T04:24:39.774754Z","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":"2026-08-10T04:24:39.824753Z","title":"Isserlis, On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables, Biometrika12, 134 (1918)","venue":null,"work_id":null,"year":1918},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.824753Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:93bd81186ee68aadb82842c4ace03f13c93c07c2ffac25698785664bd84a26c9","observation_id":"914dfcc9-2189-4f6f-9b61-246edf83bab8","resolution":{"observed_at":"2026-08-10T04:24:39.824753Z","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":"2026-08-10T04:24:39.874741Z","title":"129 (Cambridge University Press, Cambridge, 1997)","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.874741Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:9c7c80647a1cd863dcd2d65ec8272feced9e732350427e9f3bbea63c7e601943","observation_id":"d136f6a8-5fc5-464a-bb2c-710db1f4ff16","resolution":{"observed_at":"2026-08-10T04:24:39.874741Z","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":"2026-08-10T04:24:39.904907Z","title":"Peccati and M","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.904907Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:12c9edb9c7a32d6d36d913e63185a748618c4375ae9fb9fd94f0e93d618a9921","observation_id":"d3e2ede5-50e1-41f8-823b-862f2c3b5b21","resolution":{"observed_at":"2026-08-10T04:24:39.904907Z","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":"2026-08-10T04:24:39.944750Z","title":"Nakano, A theory of homogeneous, isotropic turbulence of incom- pressible fluids, Annals of Physics73, 326 (1972)","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.944750Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:dec19710418b0d361b28e8c1bd04eeda1c404c4f7d5204b5ba4efacd547be839","observation_id":"3932da4c-9482-493a-bb4c-48d534be9ce6","resolution":{"observed_at":"2026-08-10T04:24:39.944750Z","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":"2026-08-10T04:24:39.994750Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:39.994750Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:8fe99a6b2d74e33bc82a9121cfb181e8ed8d8f8e26ec0d9686cd2633bdc41cc6","observation_id":"965a786c-a3c5-434f-be73-ac44618c0c13","resolution":{"observed_at":"2026-08-10T04:24:39.994750Z","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":"2026-08-10T04:24:40.035417Z","title":"Da Prato and J","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.035417Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:f6c31165950c62307893397dd768ff8cd640d624ac26dfc0bf83f99285e5d821","observation_id":"756e65a4-fbfe-4bdb-8ee9-f58161383da1","resolution":{"observed_at":"2026-08-10T04:24:40.035417Z","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":"2026-08-10T04:24:40.069867Z","title":null,"venue":null,"work_id":null,"year":1964},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.069867Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:59e4ded38273639bae4bb04226a72682bbb1003b8bda2c8003aef5ccf0b349bc","observation_id":"29029dca-313e-4e23-83de-b6d78f19bf23","resolution":{"observed_at":"2026-08-10T04:24:40.069867Z","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":"2026-08-10T04:24:40.114752Z","title":"Chen and R","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.114752Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:a404cadb8c9317f2eb38319e7f90010484b086d83fafeec9f646f21bbe7b3318","observation_id":"37f37266-f297-4c2c-b40a-96109459473d","resolution":{"observed_at":"2026-08-10T04:24:40.114752Z","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":"2026-08-10T04:24:40.142868Z","title":"Eyink and U","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.142868Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:39ec6abaf7856ea0cc12952f10627b9d66e9943cba66acdbc2493ac8a4f7e835","observation_id":"5dc5f507-4a22-4cdc-9d9c-1b1262b15ad8","resolution":{"observed_at":"2026-08-10T04:24:40.142868Z","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":"2026-08-10T04:24:40.150340Z","title":"Fjørtoft, On the Changes in the Spectral Distribution of Kinetic EnergyforTwo-Dimensional,NondivergentFlow,Tellus5,225(1953)","venue":null,"work_id":null,"year":1953},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.150340Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:7a86896a46b7e250ec22f2cf8e9f0252a1386f3eb4751213867d8641798daa1c","observation_id":"3a837ed4-44a3-47a5-9998-1e1c07ba3be3","resolution":{"observed_at":"2026-08-10T04:24:40.150340Z","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":"2026-08-10T04:24:40.170470Z","title":"Greydanus, M","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.170470Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:acf6b6e1e36d4c1d3e8e5990bdb6da381ad1a258b6f91725c207b5d7c38e2e00","observation_id":"c61bf4c7-23d9-4249-ace2-1feebb354220","resolution":{"observed_at":"2026-08-10T04:24:40.170470Z","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":"2026-08-10T04:24:40.178344Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.178344Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:d472ed3186c449675b52b21d8e63cfc2c728e1bd89d7c53ac1d11e1683da0879","observation_id":"f9427fee-7b33-4401-a79a-e6eaf0bcee06","resolution":{"observed_at":"2026-08-10T04:24:40.178344Z","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":"2026-08-10T04:24:40.204763Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.204763Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:46582061a25a9003fe6d0f42427f609746e667720029569a16307a1fcdb951e8","observation_id":"1fa2ac68-a4a7-40da-8a65-39861f23c0ed","resolution":{"observed_at":"2026-08-10T04:24:40.204763Z","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":"2026-08-10T04:24:40.234751Z","title":"68 (Springer- Verlag, New York, 1997)","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.234751Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:69811cb46b361d3609f0d9560250ce9ba2078bfcacb04fd073753fce2fb10f20","observation_id":"99eed95d-73c6-4336-ab7c-a53f09b2af5a","resolution":{"observed_at":"2026-08-10T04:24:40.234751Z","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":"2026-08-10T04:24:40.276434Z","title":"Foias, O","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.276434Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:641447bd9c1d7eec17e4657c09640c03241d9a8a940a6e21a003f3588e322506","observation_id":"777bb0b1-ff70-4bca-9c26-7724057fb847","resolution":{"observed_at":"2026-08-10T04:24:40.276434Z","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":"2026-08-10T04:24:40.314751Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.314751Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:d4af7367fc7f44852a326d1ecaa1fb2afdfdaa957132011b1a976277620ba399","observation_id":"9639b4d0-6b24-4bad-8313-101b9c8161b9","resolution":{"observed_at":"2026-08-10T04:24:40.314751Z","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":"2026-08-10T04:24:40.354743Z","title":"Kondrashov, M","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.354743Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:a474e79a766253c7586a944e08ab9e7ece8e6aaad0145463105ad3f9f9e42fb5","observation_id":"3600c85d-0df9-4a3c-ac67-e7e030f32a7b","resolution":{"observed_at":"2026-08-10T04:24:40.354743Z","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":"2026-08-10T04:24:40.391354Z","title":"Wouters and V","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.391354Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:42aa0f144163ddeaa906fb11370c5ebc59e645be81722864c54f6b617b7f3679","observation_id":"35220308-d5fd-438b-af23-b920da0c6799","resolution":{"observed_at":"2026-08-10T04:24:40.391354Z","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":"2026-08-10T04:24:40.416895Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.416895Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:b2f466d0ba0c73911f7485e9c0b14f53c10e970f9cf53ab3cc0d633a6afde756","observation_id":"fb18bcfe-ae0d-405e-a119-70723bd36012","resolution":{"observed_at":"2026-08-10T04:24:40.416895Z","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":"2026-08-10T04:24:40.444746Z","title":"Santos Gutiérrez, V","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.444746Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:584f86fa5dde55c57cb3e0fd81c0d740a117066ec06018966c0e9658c4df5a44","observation_id":"e3f158ce-6acf-4dc5-b0e9-19365544e69c","resolution":{"observed_at":"2026-08-10T04:24:40.444746Z","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":"2026-08-10T04:24:40.484751Z","title":"Canet, Functional renormalisation group for turbulence, Journal of Fluid Mechanics950, P1 (2022)","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.484751Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:221eae2e924095d3d9af5b3e191354d15438aab0ed2aafdf415e4a0590ca1657","observation_id":"8c0fa826-552b-439d-81cc-82f4a4297748","resolution":{"observed_at":"2026-08-10T04:24:40.484751Z","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":"2026-08-10T04:24:40.534746Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.534746Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:6a9e899c0c56bb289fbd8660b4bd0f134023cedc4a40c4fe9400a543aa2114fc","observation_id":"a5c13262-510d-4f41-bdb8-c87c1fdea6e6","resolution":{"observed_at":"2026-08-10T04:24:40.534746Z","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":"2026-08-10T04:24:40.584906Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.584906Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:92dc12b05989fbe19d71e927f18b66fb54f7e81d3569a2e04b5eb07a3dc76842","observation_id":"194fcd80-8a9e-4531-bff8-6637f73113da","resolution":{"observed_at":"2026-08-10T04:24:40.584906Z","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":"2026-08-10T04:24:40.634742Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.634742Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:228c129840d47847ae9802d42c16d3b34393b84cb06529135506c8c2def06698","observation_id":"b8263433-0db0-4d09-bc7e-88def66a5456","resolution":{"observed_at":"2026-08-10T04:24:40.634742Z","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":"2026-08-10T04:24:40.684760Z","title":"Chueshov,Monotone Random Systems — Theory and Applications, Lecture Notes in Mathematics, Vol","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.684760Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:2ee84edf8bac1e43c1b49dfffdcb1963004e8a9758d13ea83b9ed1001f2b1e04","observation_id":"a9d914be-240c-4941-a9d9-af68342e88df","resolution":{"observed_at":"2026-08-10T04:24:40.684760Z","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":"2026-08-10T04:24:40.744808Z","title":"Crauel and F","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.744808Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:fb08145d2a8e6b67d3ca56f4f0778c8a35baa3cc803bde4dd9216c79bc8233e7","observation_id":"e4d3fbb7-aa42-4c0c-be05-4dc5c90e4a13","resolution":{"observed_at":"2026-08-10T04:24:40.744808Z","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":"2026-08-10T04:24:40.784751Z","title":"Crauel, A","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.784751Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:97509e561edb3b311d97b6dc1a90e9ff6c5f8bd938d342a6e272ac843a7bccbf","observation_id":"c8b8d3db-820e-4a2e-b861-106a1c00cc9d","resolution":{"observed_at":"2026-08-10T04:24:40.784751Z","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":"2026-08-10T04:24:40.834756Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.834756Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:708e63810d6206260a1298cb7796f7f53cd1749f98c84d170fdce963a2e792d1","observation_id":"27e69c28-7149-439e-846b-940855249f79","resolution":{"observed_at":"2026-08-10T04:24:40.834756Z","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":"2026-08-10T04:24:40.882734Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.882734Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:4ec16069161f03a717571a509e33e3a5dd239f2a7bede6328ae266e6bf8b126f","observation_id":"c95898e6-19d9-4108-adaf-70f09a4536e7","resolution":{"observed_at":"2026-08-10T04:24:40.882734Z","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":"2026-08-10T04:24:40.924748Z","title":"Cotter, D","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.924748Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:fd9480eace9eac7ced2dff6da86d34358e8d6f1f80fb050c0218f4d60a716e41","observation_id":"4491810a-daf1-4cd7-a7c6-0f9a9515b4ac","resolution":{"observed_at":"2026-08-10T04:24:40.924748Z","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":"2026-08-10T04:24:40.974752Z","title":"Abraham, J","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:40.974752Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:9ffc61f1ad85c49fc9413cec53be5bdbe79b021f77b991a7d9192f101616d76b","observation_id":"5ae5f0f2-f6fa-4ba0-a2b4-3e8209f494b9","resolution":{"observed_at":"2026-08-10T04:24:40.974752Z","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":"2026-08-10T04:24:41.024747Z","title":null,"venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.024747Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:0799563cbd2171dd1ac57e36190357414bd5d40f09961c3c475a8367ff4a10c5","observation_id":"bd50cfb4-f61c-4e09-98c7-7ac276b3a277","resolution":{"observed_at":"2026-08-10T04:24:41.024747Z","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":"2026-08-10T04:24:41.074739Z","title":"Bühler,Waves and Mean Flows, 2nd ed., Cambridge Monographs on Mechanics (Cambridge University Press, 2014)","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.074739Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:81cc5c76cc162570e86c6ab3471989caccaeea69349422d482febefce8274cab","observation_id":"9acf9ba0-6b3c-4b2b-8eab-bb25ee342515","resolution":{"observed_at":"2026-08-10T04:24:41.074739Z","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":"2026-08-10T04:24:41.114743Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.114743Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:da063df0d8d2c095978177f503f79023d67df6a7141832b3198f13231679f9f7","observation_id":"422e976e-c47f-47c7-bad7-3276ef925fec","resolution":{"observed_at":"2026-08-10T04:24:41.114743Z","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":"2026-08-10T04:24:41.164754Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.164754Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:31fb1ca655941a4f898988ed8784522bef076c735862d120a48ab78fd8a05ccb","observation_id":"31939e4f-dfd7-4239-a205-7bcf06d3a878","resolution":{"observed_at":"2026-08-10T04:24:41.164754Z","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":"2026-08-10T04:24:41.204744Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.204744Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:3aa260c2d27006ec42aa1ea8a9dd504f72dff4b12cf2d674f4bbebce145f5560","observation_id":"dc978076-406b-4a88-a38c-7611f630936f","resolution":{"observed_at":"2026-08-10T04:24:41.204744Z","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":"2026-08-10T04:24:41.254756Z","title":null,"venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.254756Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:9f46a98d8a38dbab284cbef63413cb871a5dd963bd35a77be7d30d64dac0362f","observation_id":"c6272da5-3766-4dc1-945d-07c723befce8","resolution":{"observed_at":"2026-08-10T04:24:41.254756Z","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":"2026-08-10T04:24:41.304758Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.304758Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:b0ac2151bfe0c92100d69cb6e00d42f402b646271480c136047a1e8936ab5030","observation_id":"e4eb02cc-443c-4da7-b7fa-71f0cf251e7c","resolution":{"observed_at":"2026-08-10T04:24:41.304758Z","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":"2026-08-10T04:24:41.344738Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.344738Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:74bdb33ba449149449897e30a430ab2cf731aa5602bb0b040642be4eaad77d77","observation_id":"bc5b2836-3658-4c3a-b802-597f23358bd8","resolution":{"observed_at":"2026-08-10T04:24:41.344738Z","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":"2026-08-10T04:24:41.387436Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.387436Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:46f9f184e7b444cf5d7b90d967569e6454f3d4b93917bd855e1b32a710cafaf3","observation_id":"5d36d19d-ef13-47da-98ef-927b1cfa120d","resolution":{"observed_at":"2026-08-10T04:24:41.387436Z","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":"2026-08-10T04:24:41.434751Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.434751Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:70e816517f414f9f798e46d82cd368dd5ef9e553ec0bc11b4ccbed77764e6b26","observation_id":"7bac1670-2648-40f0-81fa-0db4ab0f267d","resolution":{"observed_at":"2026-08-10T04:24:41.434751Z","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":"2026-08-10T04:24:41.468465Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.468465Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:59abf9e09dd21ec0ead5ef1f49271f0e7ee2d83ab14142f605e1e6874faa0d27","observation_id":"ce9fbc1a-82b7-4a7d-aec6-f51c4554a3e1","resolution":{"observed_at":"2026-08-10T04:24:41.468465Z","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":"2026-08-10T04:24:41.544630Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.544630Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:94dddf5d271307166d2727e13d207e177acf0a31052b8afd65adebf92378b9a5","observation_id":"6485e3ee-cfed-4760-babf-374574cadc3a","resolution":{"observed_at":"2026-08-10T04:24:41.544630Z","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":"2026-08-10T04:24:41.634750Z","title":null,"venue":null,"work_id":null,"year":1963},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.634750Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:96e42c8f0e791b16c09dcc0bd317db859b2915c1d049d5716312ddf5610bc779","observation_id":"efae1b40-99c6-4c9a-8165-7d077894f579","resolution":{"observed_at":"2026-08-10T04:24:41.634750Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:48.590856Z","title":"Huilgol, A second order fluid of the differential type, International Journal of Non-Linear Mechanics3, 471 (1968)","venue":null,"work_id":"7f4a9ee2-27e3-4707-aa0f-a7e3b281a4d2","year":1968},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.724767Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:5b5bfcfa4ea2041e8e37c9ed2dbb07890102f70439ce02ea134d01505822ca34","observation_id":"9704c27a-1d5a-45c1-845b-1ed6a9b1bc37","resolution":{"observed_at":"2026-08-10T04:24:48.624750Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:48.434741Z","title":null,"venue":null,"work_id":"0ee216bd-23a4-44e3-aa86-ccc242c8badb","year":1974},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.844740Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:8229f22cb7a2ebe8f191956bbc5684cff54dc51a95a662b8e9c6525e5dc04fd5","observation_id":"731f83cb-4dd2-4a75-b583-5bb0ef1673bb","resolution":{"observed_at":"2026-08-10T04:24:48.484743Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:48.264754Z","title":null,"venue":null,"work_id":"89f12b78-f401-4821-9ef8-c377a7ba72a4","year":1985},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.914751Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:942130176b72d26638de44f9216c27e86622062d3fcaf57205be106198b56b0d","observation_id":"38b2d5df-837d-49e0-ab22-70b279aea6c0","resolution":{"observed_at":"2026-08-10T04:24:48.305345Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:48.132722Z","title":null,"venue":null,"work_id":"af89c906-d14b-45d7-a8a7-651dc2d297be","year":1978},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.944765Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:964d6a646d60069c1f40c2460fe3c97f2927c48406dc47e4130a2c6f7d02949b","observation_id":"b8ec0b1e-2f96-4fb1-9b6d-d771b35d35e1","resolution":{"observed_at":"2026-08-10T04:24:48.165270Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:48.110802Z","title":null,"venue":null,"work_id":"283b02e5-89ca-4010-8e6e-d1981dd713b6","year":1970},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:41.984410Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:ddb1f6ca6f89e357262d8d2f331f3b37ff12d4b899cc49c06a83aa6a3070c487","observation_id":"691e2554-7325-46e6-9175-4fa0ca772bbc","resolution":{"observed_at":"2026-08-10T04:24:48.117426Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:47.994744Z","title":"Leith, Atmospheric predictability and two-dimensional turbulence, Journal of Atmospheric Sciences28, 145 (1971)","venue":null,"work_id":"0f0edb9c-b13c-4109-ae9d-22a6e2d55fa2","year":1971},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:42.024753Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:cc693f1ba837967e7937bef27c71066918ca9789cfa9026b16124687101de73c","observation_id":"34e7e178-a611-4c57-97b2-c66cef77ff4d","resolution":{"observed_at":"2026-08-10T04:24:48.044752Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:47.814754Z","title":null,"venue":null,"work_id":"81c0f3d5-c3e3-43d4-b640-37708df6eb32","year":1973},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:42.054753Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:b3684035816c84f95c2b7af33a133c99d1ecec842b671409cf5d4c28319a908d","observation_id":"d558452e-23b3-4f72-952a-49795b8a1dbc","resolution":{"observed_at":"2026-08-10T04:24:47.854751Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:47.654744Z","title":"Wick, The evaluation of the collision matrix, Physical Review 80, 268 (1950)","venue":null,"work_id":"b1769ab1-77c3-43ee-93ec-55e9ac825d17","year":1950},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:42.097064Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:9c1dd32b8a2afc57d7347c6f1e4a7ad9945d02c480e6cc1186fef5509ea70768","observation_id":"93883c15-354e-4ed9-949b-4cb55a4a4a6f","resolution":{"observed_at":"2026-08-10T04:24:47.694790Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:47.514159Z","title":null,"venue":null,"work_id":"bffe2cf1-7f5e-4313-97c1-d9889108b7a1","year":1971},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:42.143773Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:4e78349a26641f78bdf717bff004b14ff21bca319220f76f178c327d59420ed2","observation_id":"0c0e6760-d11d-4347-acc4-7a89ab5c0350","resolution":{"observed_at":"2026-08-10T04:24:47.544755Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:47.344756Z","title":null,"venue":null,"work_id":"c016d4c2-a4a1-4c43-8c8e-1db0ac2b9b89","year":1994},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:42.184739Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:ddf7e7391077fce59c1af2dde15213c5ec2b4655ea5df512bf63655445943333","observation_id":"42921605-dd14-4069-952d-04aafaff76b8","resolution":{"observed_at":"2026-08-10T04:24:47.394752Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:47.214756Z","title":null,"venue":null,"work_id":"f1dc3e11-3558-419f-919d-e55836c08792","year":1984},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:42.233901Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:56a1bd120c0f0619313d7893dd1b75f36c2af6b5a4ae79cbe304c6fd35a01c03","observation_id":"8bac65c7-ff87-43d2-ae13-fff0fb51bd1f","resolution":{"observed_at":"2026-08-10T04:24:47.264756Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:42.294748Z","title":"Tennekes, Eulerian and lagrangian time microscales in isotropic turbulence, Journal of Fluid Mechanics67, 561 (1975)","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":101,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:42.294748Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:5e892702209d3356e98d89090136b4cb5d4fec9ee4a0ad36fa1fb3f68a688c8d","observation_id":"b2bbeb88-142c-4a7d-b359-6827d8cf4c81","resolution":{"observed_at":"2026-08-10T04:24:42.294748Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T04:24:47.001513Z","title":"Boffetta and R","venue":null,"work_id":"67046069-2221-45a9-b595-5c7a33fc0014","year":2012},"citing_paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades","version":1},"reference_index":102,"source":"pdf_text","source_observed_at":"2026-08-10T04:24:42.344756Z"},"links":{"citing_paper":"/paper/2608.06606"},"observation_digest":"sha256:fb6b888cc9b6a457c76bf929bab6ab2ba9908c2caa99c29695b1a42d5690d4ae","observation_id":"0eac00ff-afa2-4039-9412-1121275e9409","resolution":{"observed_at":"2026-08-10T04:24:47.024318Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.06606","last_updated":"2026-08-06T21:33:56Z","latest_version":1,"primary_category":"physics.flu-dyn","snapshot_observed_at":"2026-08-11T17:10:20.753102Z","submitted_at":"2026-08-06T21:33:56Z","title":"A Symplectic Theory of Turbulence Closure: Hidden Reservoir Dynamics, Endogenous Stochastic Transport, and Kraichnan Dual Cascades"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":96,"verified_exact":0,"verified_fuzzy":4},"total_outbound_references":138},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 100 of 138 outbound references and 0 inbound Pith citation observations for arXiv:2608.06606."}