{"as_of":"2026-08-09T02:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:eb4c372db7bb3c7cb217b22fa0f1194b5b9a1bf9bf15db4927bcbd383dc17b62","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T14:48:00.784384Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2512.19409/citation-record","integrity":"/paper/2512.19409/integrity","json":"/paper/2512.19409/citation-record.json","paper":"/paper/2512.19409"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T14:48:00.684080Z","title":"Methods of information geometry , volume 191","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.684080Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:0d2426c924027651dac92a3cbca954ce14c7c76d31e212ec1579333a7ec147dc","observation_id":"63e123aa-c270-4b9f-b148-12422cad7e62","resolution":{"observed_at":"2026-08-03T14:48:00.684080Z","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":"2026-08-03T14:48:00.689272Z","title":"Mathematical methods of classical mechanics , volume 60","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.689272Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:d44bff93dd33699f2d56cab4a4c2bd0b29132da5a9293c01f4eeca8c5e9de9e9","observation_id":"4f5b66e8-eb8a-47ae-a405-5a895ef343a1","resolution":{"observed_at":"2026-08-03T14:48:00.689272Z","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":"2026-08-03T14:48:00.692148Z","title":"On invariance and selectivity in representation learning","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.692148Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:20aaa2f6a98b33cb6ea8682a3bebc0b917e0f35b0f2dba5b6b3ccd8fdc6f0249","observation_id":"af854ae1-170f-40fd-8ede-b55c9678868d","resolution":{"observed_at":"2026-08-03T14:48:00.692148Z","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":"2026-08-03T14:48:00.695021Z","title":"Representation learning: A review and new perspectives","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.695021Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:a07f216d2ec8369ac7ba228e94540d05f6dde39d7da3408c75a058c3b4f9b95e","observation_id":"f6cedc63-a0f1-4909-83f3-663fd88270bf","resolution":{"observed_at":"2026-08-03T14:48:00.695021Z","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":"2026-08-03T14:48:00.698245Z","title":"On explaining the surprising success of reservoir computing forecaster of chaos? the universal machine learning dynamical system with contrast to var and dmd","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.698245Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:717fb7f2ba46a735dd256bc673b4fca900e3f569c818fdef72c86547c2ba0fd5","observation_id":"b2e9f0c3-2204-43f3-84aa-ed7dc71d1a1c","resolution":{"observed_at":"2026-08-03T14:48:00.698245Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0901.1308","last_updated":"2009-01-09T20:18:26Z","snapshot_observed_at":"2026-08-05T01:27:24.736101Z","submitted_at":"2009-01-09T20:18:26Z","title":"Projecting the Fokker-Planck Equation onto a finite dimensional exponential family","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0901.1308","snapshot_observed_at":"2026-08-03T14:48:00.700916Z","title":"Projecting the fokker-planck equation onto a finite dimensional exponential family","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.700916Z"},"links":{"cited_paper":"/paper/0901.1308","citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:afc4faf1bcbf834449edd8089be01ed58155377d55199c3e475dce17ba6dfd65","observation_id":"23fa1969-6ad6-41b4-bc4c-25e35228846d","resolution":{"observed_at":"2026-08-03T14:48:00.700916Z","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":"2026-08-03T14:48:00.704075Z","title":"Lectures on the Geometry of Quantization , volume 8","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.704075Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:77067b678afaa9718470dd9ff58e0ff8d807985d866f0d5afb13d330e45f11f8","observation_id":"4c7e277f-a03d-479e-a6bc-7bc714118844","resolution":{"observed_at":"2026-08-03T14:48:00.704075Z","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":"2026-08-03T14:48:00.706560Z","title":"Group equivariant convolutional networks","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.706560Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:78bb1a437d4369c8bf361e35cda7ed4ee11f2157e683d84ac995bf192033b994","observation_id":"d2f91c74-ec02-4b67-89fb-a9cab773d7c7","resolution":{"observed_at":"2026-08-03T14:48:00.706560Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1909.13334","last_updated":"2020-04-25T16:32:53Z","snapshot_observed_at":"2026-08-09T01:50:09.389140Z","submitted_at":"2019-09-29T18:04:07Z","title":"Symplectic Recurrent Neural Networks","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1909.13334","snapshot_observed_at":"2026-08-03T14:48:00.709068Z","title":"Symplectic recurrent neural networks","venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.709068Z"},"links":{"cited_paper":"/paper/1909.13334","citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:4754283fdac10cf4c5d2f25a73ec79654d7e0c5a90a2e3d56e214b6e8755ecaf","observation_id":"7183fcbf-5abd-4f89-a2a1-c0e4e43ab2ac","resolution":{"observed_at":"2026-08-03T14:48:00.709068Z","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":"2026-08-03T14:48:00.711907Z","title":"Information processing capacity of dynamical systems","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.711907Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:c68f005d1972871140a54a1da64280a7445103b0762a16b2c945e3202bcc8e0e","observation_id":"259dcb13-d57f-47a8-bf0e-cc88fe9e441c","resolution":{"observed_at":"2026-08-03T14:48:00.711907Z","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":"2026-08-03T14:48:00.714502Z","title":"Universality of real minimal complexity reservoir","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.714502Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:fca0ea5aafb6834c49c2f7b03ec036b28544dcdbf97992b7b9b261e8fc4deb0a","observation_id":"1e0611c4-4643-4682-a8d1-956667cb559a","resolution":{"observed_at":"2026-08-03T14:48:00.714502Z","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":"2026-08-03T14:48:00.717057Z","title":"Linear simple cycle reservoirs at the edge of stability perform fourier decomposition of the input driving signals","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.717057Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:b1f48a1b619b7cf884f1de4284e11baf52b3d9ed955735abdacc74ff60f42ac9","observation_id":"4b6595a0-1491-4165-9def-0f49e0780463","resolution":{"observed_at":"2026-08-03T14:48:00.717057Z","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":"2026-08-03T14:48:00.719791Z","title":"Euler state networks: Non-dissipative reservoir computing","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.719791Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:d24be3621f035bcc0bde2e6a8b96b45ad36083af3a59fc3e316aa0ab0ba6bb72","observation_id":"33e8aa4c-ee5a-4984-963b-d0b97a0f47ac","resolution":{"observed_at":"2026-08-03T14:48:00.719791Z","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":"2026-08-03T14:48:00.722274Z","title":"Echo state networks are universal","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.722274Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:d6fce17c134723394e05c1bac820f1305649b3498cd71510537dc292aa936bc9","observation_id":"7d66a134-dc5e-4e98-af48-a00bb3260443","resolution":{"observed_at":"2026-08-03T14:48:00.722274Z","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":"2026-08-03T14:48:00.724824Z","title":"Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.724824Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:796182e29ae2b7035344befde9297078fe49d47debadbad8598925fa8dcfe72b","observation_id":"529f006c-4bd5-4186-b63c-d77a221489eb","resolution":{"observed_at":"2026-08-03T14:48:00.724824Z","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":"2026-08-03T14:48:00.727296Z","title":"Reservoir computing universality with stochastic inputs","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.727296Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:542a05deef8faacb69b907f1e05186ebc7375d40771c95804c4f912627f9958a","observation_id":"63b24ba1-33eb-446d-a0bf-33a972ed894d","resolution":{"observed_at":"2026-08-03T14:48:00.727296Z","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":"2026-08-03T14:48:00.730004Z","title":"Kalman filtering and smoothing solutions to temporal gaussian process regression models","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.730004Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:b214f7ee56ba58054a3a73d01572f0106ccfc9eadd3aa81e63cd91bb60577c2b","observation_id":"62a93db4-3a8b-4399-b363-0d9107c660f3","resolution":{"observed_at":"2026-08-03T14:48:00.730004Z","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":"2026-08-03T14:48:00.732515Z","title":"Reservoir computing beyond memory-nonlinearity trade-off","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.732515Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:4932da1cca6aa987e4e8572e0ba97c73b70fa1886b096c6957a8e6a5c0a5e69c","observation_id":"aeb77a5f-c226-4ad1-b0fb-94bfc030514e","resolution":{"observed_at":"2026-08-03T14:48:00.732515Z","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":"2026-08-03T14:48:00.734949Z","title":"Short term memory in echo state networks","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.734949Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:ddde58721bebee4981ef0191b50c8691e7b913867f710ebf01ff0eb64d4e2c92","observation_id":"95c489a7-1333-410d-aadb-e268f364cf90","resolution":{"observed_at":"2026-08-03T14:48:00.734949Z","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":"2026-08-03T14:48:00.737508Z","title":"echo state","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.737508Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:7472cc1106172de061674889ec0ac3f887562b4bc21942da7b3c5f5394f23bc4","observation_id":"4c942d37-ff81-45ac-b5d0-1dd0a2c2ba66","resolution":{"observed_at":"2026-08-03T14:48:00.737508Z","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":"2026-08-03T14:48:00.740257Z","title":"Tutorial on training recurrent neural networks, covering bppt, rtrl, ekf and the echo state network approach","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.740257Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:87342097c1fe78767886d4538f5064e99bfbf98c02730aadfb48612a770ee492","observation_id":"60f16439-2a35-4c6a-8b8b-045930677ca2","resolution":{"observed_at":"2026-08-03T14:48:00.740257Z","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":"2026-08-03T14:48:00.742787Z","title":"Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.742787Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:ed7944a391b26a4c9e5db2e3c5347f8be2a6cf7d42481aa9577ce059adffa243","observation_id":"911cc78a-96e4-41d5-a325-19b974ee9106","resolution":{"observed_at":"2026-08-03T14:48:00.742787Z","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":"2026-08-03T14:48:00.745219Z","title":"An introduction to probabilistic graphical models, 2003","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.745219Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:41caf25c181f1ced57c8a2f2fa3eb98d76fdcddd4ad1efbda8576bc510efeea6","observation_id":"045ea248-3a07-4fae-8b95-4d7c62053493","resolution":{"observed_at":"2026-08-03T14:48:00.745219Z","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":"2026-08-03T14:48:00.747652Z","title":"Markov-modulated affine processes","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.747652Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:fac70d49d0a55a6ecbbde01c004937874204d268f5b02cea5d8bbe97c4f73d1b","observation_id":"daa5b118-8768-4ae4-b11c-94dff37bc1cf","resolution":{"observed_at":"2026-08-03T14:48:00.747652Z","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":"2026-08-03T14:48:00.750167Z","title":"On translation invariance in cnns: Convolutional layers can exploit absolute spatial location","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.750167Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:51ae27070637bebea29075c156c0b1641bb819b9c6aa41cd1be1d8bb1af3c78a","observation_id":"0f99b053-0bef-4caf-9f4f-249c9a2519c5","resolution":{"observed_at":"2026-08-03T14:48:00.750167Z","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":"2026-08-03T14:48:00.752751Z","title":"Metric learning: A survey","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.752751Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:6ac51857e75b24ab48f6820a623c2b8e7d9ee6605f7485e453f53cbd423fd85d","observation_id":"a400ea4e-bc67-49b1-a208-689b94082411","resolution":{"observed_at":"2026-08-03T14:48:00.752751Z","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":"2026-08-03T14:48:00.755317Z","title":"Introduction to smooth manifolds","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.755317Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:cd683793d0f540fcf7393f683945a4d1ca5257d9ea9b1b92d917016d4caea5f0","observation_id":"e7fb5cd0-8a8d-47ee-9034-68059427a4e6","resolution":{"observed_at":"2026-08-03T14:48:00.755317Z","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":"2026-08-03T14:48:00.757868Z","title":"Simple Cycle Reservoirs are Universal","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.757868Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:14b2fb8d847d8a20fda22ef37acd9ca6f61717b80b30331b98148e186ca49e91","observation_id":"7b0158d2-8f93-4a72-ab66-9ca64af1fdfd","resolution":{"observed_at":"2026-08-03T14:48:00.757868Z","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":"2026-08-03T14:48:00.760500Z","title":"Reservoir computing approaches to recurrent neural network training","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.760500Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:e6fd27da69e12a3e06441a6fff23985000f843d3862776e4c2cc92b5b481c810","observation_id":"3d57361f-1247-46fe-a84d-f7884c534b0c","resolution":{"observed_at":"2026-08-03T14:48:00.760500Z","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":"2026-08-03T14:48:00.763035Z","title":"Real-time computing without stable states: A new framework for neural computation based on perturbations","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.763035Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:ed7fb47167c687cc39db85b4cb78de17261408fb5abaf6c6f3f65fe0e0b54ae2","observation_id":"26e18586-2611-4d0e-9cce-170ac60d13a6","resolution":{"observed_at":"2026-08-03T14:48:00.763035Z","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":"2026-08-03T14:48:00.765496Z","title":"Stochastic processes and applications","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.765496Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:72075b262b2e2589d195f853ab3c11036e2bad4315c6c62dc29941db68e7f853","observation_id":"01d6a0ac-ba56-4b1f-a4ce-d24fe683cd8c","resolution":{"observed_at":"2026-08-03T14:48:00.765496Z","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":"2026-08-03T14:48:00.767962Z","title":"Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.767962Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:4a19e9fdc1ca3ad0bfe74de29a0f7449c69ed07062b2db998f6c02232f6eac7b","observation_id":"f611d4e0-74cb-44ad-90cf-f5a01ddc52af","resolution":{"observed_at":"2026-08-03T14:48:00.767962Z","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":"2026-08-03T14:48:00.770511Z","title":"Minimum complexity echo state network","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.770511Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:4145ca61cdb6b10e8cf93c343f0e1235a4000eb5a58937c0b947dcaf4f23cd11","observation_id":"1a56b45c-7d6a-417c-8e88-06f69c041397","resolution":{"observed_at":"2026-08-03T14:48:00.770511Z","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":"2026-08-03T14:48:00.773047Z","title":"Bayesian filtering and smoothing , volume 17","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.773047Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:6a1921c0d69912d0a216205797e5e20ec12303ad2b80ea692b5ea022dc9fdeb8","observation_id":"b99ceb4a-9ccc-4aef-b291-bc307e3384bf","resolution":{"observed_at":"2026-08-03T14:48:00.773047Z","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":"2026-08-03T14:48:00.775752Z","title":"Predicting the future of discrete sequences from fractal representations of the past","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.775752Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:9ab6ea99a23630c8e583b316d0c9e10ba4d0154132687fcd1770d5fd6ee791e5","observation_id":"abfe06c8-4893-4b28-8abe-7eb0f1fd1ebc","resolution":{"observed_at":"2026-08-03T14:48:00.775752Z","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":"2026-08-03T14:48:00.778611Z","title":"Dynamical systems as temporal feature spaces","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.778611Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:9be3cde6ff8d350217693fb458625de0a9dcb97396d7b06f0cde5075fe1b6188","observation_id":"1f95d7ea-46eb-43c5-a4a8-ee313e66b603","resolution":{"observed_at":"2026-08-03T14:48:00.778611Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.03717","last_updated":"2026-05-16T18:59:42Z","snapshot_observed_at":"2026-08-02T21:39:50.574099Z","submitted_at":"2024-01-08T08:00:04Z","title":"Universal Time-Series Representation Learning: A Survey","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.03717","snapshot_observed_at":"2026-08-03T14:48:00.781479Z","title":"Universal time-series representation learning: A survey","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.781479Z"},"links":{"cited_paper":"/paper/2401.03717","citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:d3ab2882b15b4990f749000d36ba70f99d41aed30ad3b5f26ee5fd603a99c65d","observation_id":"638aa0f6-ee47-4290-8e6c-59281f48d650","resolution":{"observed_at":"2026-08-03T14:48:00.781479Z","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":"2026-08-03T14:48:00.784384Z","title":"Recent advances in physical reservoir computing: A review","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics","version":2},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-03T14:48:00.784384Z"},"links":{"citing_paper":"/paper/2512.19409"},"observation_digest":"sha256:febdde6d7247dc4a9bd856f93a623c801a9dee684112a1441227b182d23bd021","observation_id":"a7ab4038-d19a-42db-ab1f-be022f69dc8c","resolution":{"observed_at":"2026-08-03T14:48:00.784384Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2512.19409","last_updated":"2026-07-31T10:57:31Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-09T02:13:41.834261Z","submitted_at":"2025-12-22T14:04:13Z","title":"Symplectic Representation of Legendre Dynamics"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":38,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":38},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2512.19409."}