{"as_of":"2026-08-10T19:09:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:43a96ed718ce0eb3057aed92380467edaade0e52d75a9dd43cc1b4a5bfd835c3","coverage":[{"denominator":36,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":36,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T20:45:48.960650Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.16529/citation-record","integrity":"/paper/2607.16529/integrity","json":"/paper/2607.16529/citation-record.json","paper":"/paper/2607.16529"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T20:45:46.025191Z","title":"Proceedings of the National Academy of Sciences113(15), 3932–3937 (2016) https://doi.org/10.1073/pnas.1517384113 https://www.pnas.org/doi/pdf/10.1073/pnas.1517384113","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.025191Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:eb80a23d7f6cbaeb77be509ec18d76051b0cf70ce616e0017c58090206bce44d","observation_id":"dbb14497-32c1-43c9-9649-99af58c5f41d","resolution":{"observed_at":"2026-08-01T20:45:46.025191Z","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":"2026-08-01T20:45:46.112409Z","title":"Proceedings of the National Academy of Sciences116(45), 22445–22451 (2019) https://doi.org/10.1073/pnas.1906995116 https://www.pnas.org/doi/pdf/10.1073/pnas.1906995116","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.112409Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:530124ace46c169fdfbb3d5b5d5b20f5d18b30886794b2c7aaab296c60d44b97","observation_id":"93812789-400a-4276-9918-9dd6dcd425b6","resolution":{"observed_at":"2026-08-01T20:45:46.112409Z","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":"2026-08-01T20:45:46.207648Z","title":"Nature Communications9(1), 4950 (2018) https://doi.org/10.1038/s41467-018-07210-0","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.207648Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:c50cc211fe994bec4d578e1403877054b31dc134cfb4359a757582ac1d4c21bf","observation_id":"3c742608-8227-4bbd-8cd3-634a4bb7cc52","resolution":{"observed_at":"2026-08-01T20:45:46.207648Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1806.07366","last_updated":"2019-12-14T02:01:18Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2018-06-19T17:50:12Z","title":"Neural Ordinary Differential Equations","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1806.07366","snapshot_observed_at":"2026-08-01T20:45:46.300465Z","title":"In: Advances in Neural Information Processing Systems (NeurIPS), vol","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.300465Z"},"links":{"cited_paper":"/paper/1806.07366","citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:2945abc9d4598b8133787c713157f5b3a0343ab2b3eb0656558f376c3fa70518","observation_id":"a8f9d8e2-370a-4584-b081-d3bd5300c33e","resolution":{"observed_at":"2026-08-01T20:45:46.300465Z","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":"2026-08-01T20:45:46.361829Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.361829Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:f9895b41356e4c62a0a6f5c6730e80ff111bc276c37778074c25f6a907d5c552","observation_id":"a10e1a16-11fc-434f-826e-6a92e64b3d0b","resolution":{"observed_at":"2026-08-01T20:45:46.361829Z","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":"2026-08-01T20:45:46.445900Z","title":"Prentice Hall PTR, Upper Saddle River, NJ (1999)","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.445900Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:f028263df4f65496f5401b8733f21a6be9f9a1761e70fdb84fb607cee6577489","observation_id":"6a402d32-8757-49b1-a093-b451da7aaae0","resolution":{"observed_at":"2026-08-01T20:45:46.445900Z","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":"2026-08-01T20:45:46.507753Z","title":"Nature Machine Intelligence1(5), 206–215 (2019) https://doi.org/10","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.507753Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:5ff5db75351981f4423e289722232e62b866d1f2731f7b40a3d9e52dd4bc73e3","observation_id":"9e3f5417-c192-49a7-87c6-77d5b9006c7c","resolution":{"observed_at":"2026-08-01T20:45:46.507753Z","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":"2026-08-01T20:45:46.599664Z","title":"Theoretical and Computational Fluid Dynamics31, 349–368 (2017) https://doi.org/10.1007/s00162-017-0432-2","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.599664Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:26e255309f916fa1a6bdd14fbdb6e753cb25d5c452b91491793239b38678d826","observation_id":"b6ea79a5-4f1e-4990-8927-2d2f1bf20931","resolution":{"observed_at":"2026-08-01T20:45:46.599664Z","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":"2026-08-01T20:45:46.691724Z","title":"Flow, Turbulence and Combustion (2024) https://doi.org/10.1007/s10494-024-00595-7","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.691724Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:c712942aa8bd0ef956b67e4b0f54b44c22e1b16bb58087ea1f185ea9ee022c33","observation_id":"9abbc413-2421-49fa-9d7b-02ed2cb0cddf","resolution":{"observed_at":"2026-08-01T20:45:46.691724Z","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":"2026-08-01T20:45:46.783000Z","title":"Journal of Nonlinear Science33(1), 14 (2023) https: //doi.org/10.1007/s00332-022-09862-1","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.783000Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:445fefc3d48387d5fa881a7358c94b996a27375a1f29c7aa18382f019d11f397","observation_id":"0a1d5556-6046-4102-b487-0d1042b2888d","resolution":{"observed_at":"2026-08-01T20:45:46.783000Z","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":"2026-08-01T20:45:46.875247Z","title":"SIAM Review64(2), 229–340 (2022) https://doi.org/10.1137/21M1401243","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.875247Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:fa127c7f77c56c5d76aec4a0388bb9806b0a86a35ca03f77457a134af30f3fc1","observation_id":"269c98c8-fe77-482d-87d6-5ce2a159a852","resolution":{"observed_at":"2026-08-01T20:45:46.875247Z","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":"2026-08-01T20:45:46.929420Z","title":"Journal of Fluid Mechanics641, 115–127 (2009) https://doi.org/10.1017/S0022112009992059","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.929420Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:c5ce18121610d9f7522e3dbb791643165b37c36e6aa489c6c0e2fc4c1bfd6a77","observation_id":"778f3fe5-c9ec-4935-a733-2b099663e0b5","resolution":{"observed_at":"2026-08-01T20:45:46.929420Z","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":"2026-08-01T20:45:46.989010Z","title":"Annual Review of Fluid Mechanics45, 357–378 (2013) https://doi.org/10.1146/annurev-fluid-011212-140652","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:46.989010Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:1f34129b908336c5cadb26840b7497522609e39f814b911f6fdf10e3ef50d0b0","observation_id":"4f9c468b-4539-4def-a1b0-6476d68b3f6c","resolution":{"observed_at":"2026-08-01T20:45:46.989010Z","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":"10.1137/24m1662370","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"SIAM Journal on Applied Dynamical Systems24(2), 1150–1190 (2025) https://doi.org/10.1137/24M1662370","venue":"SIAM Journal on Applied Dynamical Systems","work_id":"a21d5df0-35d5-431f-80c5-00bbe5aeed5f","year":2025},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.051621Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:b5054ae8382c1654f4c20e2b7b983811a1d1fc314c411f6a821f899bd4918d33","observation_id":"5555cc5e-c26b-437d-b598-c8574798566c","resolution":{"observed_at":"2026-08-01T20:48:24.733017Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-01T20:45:47.102593Z","title":"In: Koyejo, S., Mohamed, S., Agarwal, A., Belgrave, D., Cho, K., Oh, A","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.102593Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:e6d9af3223e84ed9a146b45d481e8397137fe11ce9caa59a0a29ad76d01a609e","observation_id":"c1b9ca86-018b-41bf-bb49-ead066658d86","resolution":{"observed_at":"2026-08-01T20:45:47.102593Z","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":"10.1016/j.arcontrol.2021.09","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T20:48:24.505981Z","title":"Annual Reviews in Control52, 197–212 (2021) https://doi.org/10.1016/j.arcontrol.2021.09","venue":null,"work_id":"20a33ee3-10e7-4a67-b94c-d192ce61e7c8","year":2021},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.191296Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:b3042a98597e0bd6482e517d66fc6da4866e7eeeae83fbbb97a7c3dfeedf3d42","observation_id":"5b36c62b-da0d-41b0-8f50-f6c6d5cd4a20","resolution":{"observed_at":"2026-08-01T20:48:24.589854Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-01T20:45:47.276686Z","title":"Journal of Computational Dynamics1(2), 391–421 (2014) https://doi.org/10.3934/jcd.2014.1.391","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.276686Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:fd65cda7b77d692ad573b1393bc00de5de628600445d64c243b1f36343e0a3b0","observation_id":"2ecb8df3-a154-4930-b752-f6f815c07621","resolution":{"observed_at":"2026-08-01T20:45:47.276686Z","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":"2026-08-01T20:45:47.360286Z","title":"Journal of Nonlinear Science25(6), 1307–1346 (2015) https://doi.org/10.1007/s00332-015-9258-5","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.360286Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:a5afb886bed33c350d77f195715a366a8449ac0bc1579804b9b9d076b1a557b2","observation_id":"24e1f737-87e5-4333-882b-82041631231b","resolution":{"observed_at":"2026-08-01T20:45:47.360286Z","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":"2026-08-01T20:45:47.420625Z","title":"SIAM Journal on Applied Dynamical Systems16(4), 2096– 2126 (2017) https://doi.org/10.1137/17M1125236","venue":null,"work_id":null,"year":2096},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.420625Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:98db0c697e5b5b11cdea13bd122171eb487d027058077dc9fea2ec04ba3550cb","observation_id":"bcd7ff7c-ea14-4bcd-bae6-d1433331c7f4","resolution":{"observed_at":"2026-08-01T20:45:47.420625Z","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":"2026-08-01T20:45:47.500309Z","title":"Journal of Computational Dynamics2(2), 247–265 (2015) https://doi.org/10","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.500309Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:e2cf7a948046ef84cc3fadf7ce2354dc0307b9b919c89ebef2455d51e55c4911","observation_id":"9070ef63-7570-46a1-84ad-13996db1d544","resolution":{"observed_at":"2026-08-01T20:45:47.500309Z","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":"2026-08-01T20:45:47.558802Z","title":"IEEE Control Systems Letters7(7) (2023) https://doi.org/10.1109/lcsys","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.558802Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:eeba190e3bc6a2314918be4423daa3633e99301fb9efb9b289bc04c8f5ee00ed","observation_id":"2a929df8-9866-437e-ac75-06f914471843","resolution":{"observed_at":"2026-08-01T20:45:47.558802Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.17976","last_updated":"2025-01-31T20:46:56Z","snapshot_observed_at":"2026-08-10T04:25:11.233532Z","submitted_at":"2025-01-29T20:21:23Z","title":"KoopAGRU: A Koopman-based Anomaly Detection in Time-Series using Gated Recurrent Units","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.17976","snapshot_observed_at":"2026-08-01T20:45:47.646666Z","title":"arXiv preprint arXiv:2501.17976 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.646666Z"},"links":{"cited_paper":"/paper/2501.17976","citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:e624181efaa2ad85c21403e1739cb21dee7ac02d96303dca28a0b3fe5d816508","observation_id":"488a2ca4-38b1-4797-9aee-bfd55b40c24c","resolution":{"observed_at":"2026-08-01T20:45:47.646666Z","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":"2026-08-01T20:45:47.704220Z","title":"Chaos: An Interdisciplinary Journal of Nonlinear Science22(4), 047510 (2012) https://doi.org/10.1063/1.4772195 26 Positive-Allocation Companion Predictions Flores and Pascoe","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.704220Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:01670b88b76b4e53485ed5249ee9526191d199048df37293ff1b6af3542c772f","observation_id":"74b6a23f-e14e-4757-ad2f-6aaa9ef9ea36","resolution":{"observed_at":"2026-08-01T20:45:47.704220Z","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":"2026-08-01T20:45:47.790635Z","title":"IEEE Transactions on Automatic Control65(12), 5114–5129 (2020) https://doi.org/10.1109/TAC","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.790635Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:433d962c7c66a72426eee65a33ef310bb209d4fce0de3884e3c2115111bc04ae","observation_id":"3e435a51-33df-49a3-ad4d-bae8aae60a10","resolution":{"observed_at":"2026-08-01T20:45:47.790635Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-01T20:45:47.852024Z","title":"Physica D: Nonlinear Phenomena406, 132416 (2020) https://doi.org/10.1016/j.physd.2020.132416","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.852024Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:f0b0916b56ea8011048c186ddae9871f056e1afc40f4685aa81edb12e88b9ebe","observation_id":"1231d4bd-af32-4057-91f6-fb80adee8355","resolution":{"observed_at":"2026-08-01T20:45:47.852024Z","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":"2026-08-01T20:45:47.934604Z","title":"(eds.): The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.934604Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:eeae93ac904c78b08180757b7de5413c2a45dc051d269f6cf0b2be5911d7b9f9","observation_id":"7b5f2f34-2465-410c-8679-e5b911c814d7","resolution":{"observed_at":"2026-08-01T20:45:47.934604Z","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":"2026-08-01T20:45:47.995913Z","title":"IEEE Transactions on Robotics (2021) https://doi.org/10.1109/ TRO.2021.3076581","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:47.995913Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:a624e855e63d94281d5a46899b5bddfd5b821db09410f35fcd914fd58b3a80c7","observation_id":"9cf0a044-d658-40bf-a46d-76b44f3a1f91","resolution":{"observed_at":"2026-08-01T20:45:47.995913Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-01T20:45:48.085981Z","title":"Communications on Pure and Applied Mathematics77(1), 221–283 (2024) https://doi.org/10.1002/cpa.22125","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:48.085981Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:39ce6644df9ddb2c7a05748951cf0be050a557e10869be197122d6c10f90d426","observation_id":"bdf185a8-0b79-4fcf-84a8-13a31cc01f4c","resolution":{"observed_at":"2026-08-01T20:45:48.085981Z","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":"2026-08-01T20:45:48.197105Z","title":"Journal of Fluid Mechanics955, 21 (2023) https://doi.org/10.1017/jfm.2022.1032","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:48.197105Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:b2834031b6edec0bf393fa536e50b6bb407d1babe24484cb82d8aee2a5ad90c4","observation_id":"d0f09374-080d-4ea2-9b2f-3b740daa521e","resolution":{"observed_at":"2026-08-01T20:45:48.197105Z","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":"2026-08-01T20:45:48.363136Z","title":"Nonlinear Dynamics41(1), 309–325 (2005) https://doi.org/10.1007/s11071-005-2824-x","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:48.363136Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:0d58420724afab1248336969c14a1b784176b44ce0c36c525b96999b2bdb2207","observation_id":"ef3f1ecb-6d22-43d3-840e-ae61cb52ef70","resolution":{"observed_at":"2026-08-01T20:45:48.363136Z","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":"2026-08-01T20:45:48.531117Z","title":"Journal of Financial and Quantitative Analysis27(4), 513–537 (1992)","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:48.531117Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:1f6c6d918d9ebdab76f699e4b830aa8bcf8f2f59f56bf0b5c9b8a814476c1543","observation_id":"203e8e7f-cf77-4d43-8850-7006b53a4dc7","resolution":{"observed_at":"2026-08-01T20:45:48.531117Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.18201","last_updated":"2024-12-24T06:12:31Z","snapshot_observed_at":"2026-08-10T11:08:45.587009Z","submitted_at":"2024-12-24T06:12:31Z","title":"Indices of quadratic programs over reproducing kernel Hilbert spaces for fun and profit","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.18201","snapshot_observed_at":"2026-08-01T20:45:48.685558Z","title":"arXiv preprint arXiv:2412.18201 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:48.685558Z"},"links":{"cited_paper":"/paper/2412.18201","citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:9f8e29b6a10d392bcb83a46d5d6a3e4cbc9e38101647977b9b7f1de38a06a93f","observation_id":"8f35922c-c2c2-4d64-ad7c-cb5e9905573c","resolution":{"observed_at":"2026-08-01T20:45:48.685558Z","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":"2026-08-01T20:45:48.760444Z","title":"Soci- ety for Industrial and Applied Mathematics, Philadelphia, PA (2016)","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:48.760444Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:c173a41a9e4c10f3d1d09dbadfec85b03548927a81c5cd71a511aff12f6fc1de","observation_id":"d6bf80d2-0b8d-4d19-8e8e-a0a970ae87d8","resolution":{"observed_at":"2026-08-01T20:45:48.760444Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-01T20:45:48.803188Z","title":"Biophys- ical Journal1(6), 445–466 (1961) https://doi.org/10.1016/S0006-3495(61)86902-6","venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:48.803188Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:e1d742e626375ba7a7e721341dbc955fa4de00a80d0d658517654f4f13014eee","observation_id":"f3cc10c9-b4d1-4851-a8b4-5ede698c4a2d","resolution":{"observed_at":"2026-08-01T20:45:48.803188Z","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":"2026-08-01T20:45:48.856335Z","title":"Proceedings of the IRE50(10), 2061–2070 (1962) https://doi.org/10.1109/JRPROC.1962.288235","venue":null,"work_id":null,"year":2061},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:48.856335Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:89f57f8f0b7223c2025772c919de457ed05e6e088123a1a13048af7522e054bb","observation_id":"55544901-5fdd-4411-aece-19c30c371e40","resolution":{"observed_at":"2026-08-01T20:45:48.856335Z","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":"2026-08-01T20:45:48.960650Z","title":"Pro- ceedings of the Royal Society of London","venue":null,"work_id":null,"year":1927},"citing_paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-01T20:45:48.960650Z"},"links":{"citing_paper":"/paper/2607.16529"},"observation_digest":"sha256:1ad5f317e83bd5176c8186adb8423b874fcb0eb3993e7dffe3869aa14da37e79","observation_id":"80e8631b-edcf-4371-bc1f-ee0c15e55f3e","resolution":{"observed_at":"2026-08-01T20:45:48.960650Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.16529","last_updated":"2026-07-17T22:09:51Z","latest_version":1,"primary_category":"math.DS","snapshot_observed_at":"2026-08-09T10:24:05.215467Z","submitted_at":"2026-07-17T22:09:51Z","title":"Positive-Allocation Companion Predictors for Nonlinear Dynamics and Their Finite-Difference Diagnostics"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":4,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":30,"verified_exact":2,"verified_fuzzy":0},"total_outbound_references":36},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2607.16529."}