{"as_of":"2026-08-08T17:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c169782ed6a32e1e0816381cb5480cbaee9e8f36a3ecff602d46f4e665cbba4c","coverage":[{"denominator":55,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":55,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T22:41:43.026472Z","state":"measured"},{"denominator":55,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":55,"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/2509.07264/citation-record","integrity":"/paper/2509.07264/integrity","json":"/paper/2509.07264/citation-record.json","paper":"/paper/2509.07264"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.856441Z","title":null,"venue":null,"work_id":"32c3111e-346d-481e-9994-df29136a09ab","year":2008},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.808538Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:472ea5021a20a32942be8808b518e93cac40f0e8abd5337f5397e03b68289018","observation_id":"4e1385e8-7d26-4143-94dc-dbee41da238d","resolution":{"observed_at":"2026-08-04T22:41:43.860634Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.841924Z","title":"Dalton, and Roland R","venue":null,"work_id":"c8bfa11a-b021-4d06-861f-eb9498d00fd6","year":2022},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.813211Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:8ec5e4037ed682be18c6b3b2a35a3abee56423142ed1e7afbf7271cf0416665f","observation_id":"5bf5a98b-de26-4aa2-a31e-817238b34cde","resolution":{"observed_at":"2026-08-04T22:41:43.846140Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.826776Z","title":"Numerical integration of the extended variable generalized Langevin equation with a positive Prony representable memory kernel.The Journal of chemical physics, 139(4):044107, 2013","venue":null,"work_id":"880076e9-802c-41fd-ad78-557574af94c1","year":2013},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.817444Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:9beb22d2f70cf3ea6aa9a9e9fa3756a24ca600a29857b6491fcb04502175071d","observation_id":"7e75f0e3-70a6-487d-9a3f-22d4dabfa073","resolution":{"observed_at":"2026-08-04T22:41:43.831130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.812655Z","title":"Canonical sampling through velocity rescaling.The Journal of Chemical Physics, 126(1), 2007","venue":null,"work_id":"ccede3fc-d810-4cb1-be05-68f6705fc521","year":2007},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.821861Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:74d43413a2e9c252e74afd1f46642278e8ccd22968d298a42b07d94c8a6077c8","observation_id":"9ef95948-6ab6-4548-aed8-27988dece131","resolution":{"observed_at":"2026-08-04T22:41:43.817398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.796963Z","title":"Langevin equation with colored noise for constant-temperature molecular dynamics simulations.Physical review letters, 102(2):020601, 2009","venue":null,"work_id":"abf6db95-dc05-45a9-96d5-316c63804c64","year":2009},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.826121Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:3dea9088356fb5ef8c8cfafa210fcb9c45d426faf260081fa376b77345baa33f","observation_id":"8bfb2a5f-d07e-4570-9a39-6ee5fb5c0b16","resolution":{"observed_at":"2026-08-04T22:41:43.802159Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.782805Z","title":"Computation of the memory functions in the generalized Langevin models for collective dynamics of macromolecules.J","venue":null,"work_id":"cdf4a99d-ea6a-4eb3-b89f-cba2548e5de0","year":2014},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.830530Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:4d4835e3c34c62cf0a8acd8dcce80d9bec0ac717760998b80750df4536c95440","observation_id":"11940650-b2ce-4ece-9bef-c2d6e239c8ad","resolution":{"observed_at":"2026-08-04T22:41:43.787022Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.768564Z","title":"Calculating free energies using average force.The Journal of Chemical Physics, 115(20):9169–9183, 2001","venue":null,"work_id":"b181bbba-c4e5-4cd3-899c-938c1467aefc","year":2001},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.835292Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:6d40039740c8eda37f19351e28494653e7d10d8a86c6ce862d1a956e8128b083","observation_id":"b45c53e4-2403-4fa8-b26d-eea83359015e","resolution":{"observed_at":"2026-08-04T22:41:43.773391Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.752783Z","title":"Computing generalized Langevin equations and generalized fokker-planck equations.Proc","venue":null,"work_id":"0bd3ae6e-0a80-4376-8890-83f060052e04","year":2009},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.839164Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:4101589a84a9f73d0e19e2d7546ed6680d417351183526d920ef762d98740c32","observation_id":"c190ca93-0ef0-49c9-b61d-297dc9467c17","resolution":{"observed_at":"2026-08-04T22:41:43.758083Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.737501Z","title":"The heterognous multiscale methods.Commun","venue":null,"work_id":"a4e971fe-159f-4df3-bd54-fea3b258cbee","year":2003},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.843191Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:39fd1d8a0f5505fede31159a304ca96e77356b7424768f0fa3d3ffe0f6b61a32","observation_id":"c3e291ac-8b2f-4662-a545-2bfd3c871528","resolution":{"observed_at":"2026-08-04T22:41:43.741905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.723567Z","title":"Het- erogeneous multiscale methods: A review.Communications in Computational Physics, 2(3):367–450, 2007","venue":null,"work_id":"03caeec9-4c62-4e53-8e46-83913a0324a7","year":2007},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.847015Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:89d3436cb1879313e4991b3a1b8b178a505ca2c71811b9ea175dfb5c6ac1bf49","observation_id":"353d7763-7bb4-4d7b-b90d-8a366efc20f4","resolution":{"observed_at":"2026-08-04T22:41:43.728130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.707590Z","title":"Transition-path theory and path-finding algorithms for the study of rare events.Annual Review of Physical Chemistry, 61(1):391–420, 2010","venue":null,"work_id":"410fba30-1683-4916-8d8c-50a6a9c67f0f","year":2010},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.851216Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:da18076bef779f1917db9dc0d83e214a877a04827806bfc086682b8a47088413","observation_id":"d0885680-6b45-437a-9292-236f30a79e7f","resolution":{"observed_at":"2026-08-04T22:41:43.712484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.692548Z","title":"Active learning based sampling for high-dimensional nonlinear partial differential equations.Journal of Computational Physics, 475:111848, 2023","venue":null,"work_id":"24361829-9888-429c-b123-5602e92903b9","year":2023},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.855761Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:991d3581151eaffb9ee3487da358caff4284a1436e133d88688a650a863c5607","observation_id":"d2abf69e-d069-4c47-9ef2-6c14506772f0","resolution":{"observed_at":"2026-08-04T22:41:43.697202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.678414Z","title":"Failure-informed adaptive sampling for pinns","venue":null,"work_id":"2ad3fc70-fdcf-408d-8e59-7ef761005cce","year":2023},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.859729Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:30f7b5a4548d6ee4ab0f4a7bc5c1a704a6cc82863f8f872b16721b746bec1a5e","observation_id":"4e5a3e12-569d-4dff-af81-620108c2e0f3","resolution":{"observed_at":"2026-08-04T22:41:43.682869Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:42.863559Z","title":"Data-driven learning of the generalized langevin equation with state-dependent memory.Physical Review Letters, 133(7):077301, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.863559Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:c0f5d664050424465f2b37c0b37775e85f4a59546e5f17aa77014ec852e4348b","observation_id":"b4c1dc8b-e358-44a5-a29d-a7b2d908f0a6","resolution":{"observed_at":"2026-08-04T22:41:42.863559Z","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":"2026-08-04T22:41:43.652100Z","title":null,"venue":null,"work_id":"ecae021d-560b-4d80-8367-e546dcc75827","year":2020},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.867628Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:11ca6d13dea531979efc669fc881bd179d9af18249855f9960b9d8ee81d64d67","observation_id":"13b3eaf2-4331-470a-a7db-8ddf147d2e9b","resolution":{"observed_at":"2026-08-04T22:41:43.656273Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.637481Z","title":"Lincs: A linear constraint solver for molecular simulations.Journal of Computational Chemistry, 18(12):1463–1472, 1997","venue":null,"work_id":"462c47f0-98c0-4e6c-8cb8-8c36bb4f2453","year":1997},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.871458Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:2bed009ace7853d84e5e60775e88a082f10e825839c9a44743a3dd8553f6343e","observation_id":"66ce9e0f-2e53-4cef-bf49-a8ba0a5208f5","resolution":{"observed_at":"2026-08-04T22:41:43.642073Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.624313Z","title":"Mori– Zwanzig formalism as a practical computational tool.Faraday discuss., 144:301–322, 2010","venue":null,"work_id":"7f148c14-9a45-472f-b9c7-cd452f855ec9","year":2010},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.875070Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:4dfa5ba12ecfe282ad9820fb91480aee082337e2ad184fb58e3d0a58b7db1e5c","observation_id":"2b2552e7-86cb-4a4c-8582-98efa34e38e9","resolution":{"observed_at":"2026-08-04T22:41:43.628486Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.610515Z","title":"Comparison of multiple amber force fields and development of improved pro- tein backbone parameters.Proteins: Structure, Function, and Bioinformatics, 65(3):712– 725, 2006","venue":null,"work_id":"3c9b9c84-1c26-4330-8cd8-02be0d66a4f6","year":2006},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.878961Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:1ed6bfdd68a7c04069f2c3fcbed2f91e3f77884ca4151fdb605207624c25feb4","observation_id":"3b95b6fc-1d7c-4b19-a8bb-6c9d13e3e4c7","resolution":{"observed_at":"2026-08-04T22:41:43.614862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.597106Z","title":null,"venue":null,"work_id":"73e42f33-d93b-46e7-a695-d56304547c3e","year":2020},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.882833Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:b07c500e4fc98600029300940d91a18f9d840f0362d3559c71e9fe22f5fa6a9b","observation_id":"8778625d-10c7-4c88-bf37-cbca7f0bf76a","resolution":{"observed_at":"2026-08-04T22:41:43.601116Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.582482Z","title":"Iterative reconstruction of memory kernels.Journal of Chemical Theory and Computation, 13(6):2481–2488, 2017","venue":null,"work_id":"66edfe3e-5fb2-4f71-96f5-21010edda36d","year":2017},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.886850Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:4246c3d7ae231f11be4f88de46a245b5449bc7cd445bbcd74cd0c2ba48f6791d","observation_id":"b84cfa3d-3d84-4917-a9d0-bca7a4a6f270","resolution":{"observed_at":"2026-08-04T22:41:43.587370Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.568600Z","title":"Kevrekidis, C","venue":null,"work_id":"4985a1f0-7b7c-4e1c-82cf-1f95a66dbe62","year":2003},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.890702Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:fc00043edc6738d5f44c3b764a7755433b769b28d2eb09488772ed0913c73c2d","observation_id":"7d698885-31ff-4aed-9e73-c7e708ebe0e8","resolution":{"observed_at":"2026-08-04T22:41:43.573083Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.555053Z","title":"Kevrekidis and Giovanni Samaey","venue":null,"work_id":"6c1e1f84-fd73-4b77-b873-db4abe504424","year":2009},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.894632Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:30448f774df1de38f8764f735970a882023ff8dddc0d33ad9c3e3923416ce579","observation_id":"a01506df-03a6-4c9e-9ae5-9e1df4c82f6c","resolution":{"observed_at":"2026-08-04T22:41:43.559137Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.541132Z","title":"Adam: A method for stochastic optimization.Interna- tional Conference on Learning Representations (ICLR), 12 2015","venue":null,"work_id":"74ba2d13-eb8d-48c6-ab66-c8f1979ca771","year":2015},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.898474Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:511f49afa584244b3be6da701a82c08d3f787dd98596a788d2f2faae72a0fe15","observation_id":"701d97b3-f3fc-4277-b9f1-21293f84cfed","resolution":{"observed_at":"2026-08-04T22:41:43.545544Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.527298Z","title":null,"venue":null,"work_id":"e8e7e974-1f59-4c11-ab51-4ed9bcffedb0","year":2021},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.902431Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:dcd76e548b7edcb53df4c3e132ac5b3f689622158058bb4e2e6a5777b9440877","observation_id":"6c189abf-e8ed-4a50-bf49-e2c62dd0f3c6","resolution":{"observed_at":"2026-08-04T22:41:43.531281Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.513199Z","title":"Rosenberg, Djamal Bouzida, Robert H","venue":null,"work_id":"a8473fe0-b897-46c3-8906-2a4a8fa5e78b","year":1992},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.906434Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:76fd5342d9f508682b74b82ab7b0ad540eedf28b8221a492c5306e0a79bcf195","observation_id":"9f330aff-ecb2-4ad8-8667-3f66e936a030","resolution":{"observed_at":"2026-08-04T22:41:43.517659Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.498789Z","title":"Escaping free-energy minima.Proceedings of the National Academy of Sciences, 99(20):12562–12566, 2002","venue":null,"work_id":"ab8574e5-8686-477c-84db-d053a2b6cf32","year":2002},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.910375Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:f46635c1d433d9cc4afd681d9ea94846ee6cd6b23bb5d52b2bcbb6e848778653","observation_id":"1ec86d3c-ed95-4ada-8ff2-6220111a72af","resolution":{"observed_at":"2026-08-04T22:41:43.503083Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.484801Z","title":"Collective Langevin dynamics of conformational motions in proteins.J","venue":null,"work_id":"859bf0e6-025c-4844-904b-d298a8975cc8","year":2006},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.914224Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:bc21f58d2d86808f2fbe397c842c9a41d00e9310518e93c51fecdab8f45481a2","observation_id":"aa367300-1088-4323-9f55-0ae9816974cf","resolution":{"observed_at":"2026-08-04T22:41:43.489090Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.471522Z","title":null,"venue":null,"work_id":"06c96041-7b2d-4f75-88a6-f2dde743b708","year":2019},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.918350Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:291fe53c65d94f066454204274bb602a7df738570c56ca6dcefa4bea68e3b21b","observation_id":"c211b918-9f3d-42f9-af0e-ebb27c741d60","resolution":{"observed_at":"2026-08-04T22:41:43.475730Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.457654Z","title":null,"venue":null,"work_id":"60699c3d-4117-4700-9b84-18d6635075c0","year":2010},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.922359Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:b7365d402f6a2bf2785651a0210cd4f690aa0fd28210d602f8f92b0bf2be306d","observation_id":"df1bd7be-9741-43f2-8deb-80c02539ca35","resolution":{"observed_at":"2026-08-04T22:41:43.462024Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.444906Z","title":null,"venue":null,"work_id":"3ed83e59-e1a8-479c-be42-fb1a24ffbdac","year":2016},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.926068Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:c2dc66b0e1e6a03697af3a8f449ac397d99ed8ca526dbe8035cfe8e4927f7e34","observation_id":"4d902d2e-2449-4c86-942f-4cc0b45fc624","resolution":{"observed_at":"2026-08-04T22:41:43.448868Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.431094Z","title":"Incorporation of memory ef- fects in coarse-grained modeling via the Mori-Zwanzig formalism.The Journal of chemical physics, 143(24):243128, 2015","venue":null,"work_id":"989c6fab-6ff2-4935-9f03-956bc761b875","year":2015},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.929896Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:b5c5d1e39935570f0422949f8ce01cfd0214fe5cf8e12ab25ab564cb309fb7a4","observation_id":"3e079638-2681-4059-8d3a-63694db392c0","resolution":{"observed_at":"2026-08-04T22:41:43.435436Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.417182Z","title":"Gromacs 2019.2 source code, April 2019","venue":null,"work_id":"7060f908-944d-44e9-bbcf-b88aeaa33abd","year":2019},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.934059Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:a5b42b7019df768eb6658b73ebf718e28f90c3e0cec26645a74ba981151a2f85","observation_id":"b5164fc8-4a7d-4eaf-b697-e13bd29ef935","resolution":{"observed_at":"2026-08-04T22:41:43.421447Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.05009","last_updated":"2026-06-05T19:02:55Z","snapshot_observed_at":"2026-07-06T16:44:55.494764Z","submitted_at":"2023-11-08T20:32:27Z","title":"Consensus-based adaptive sampling and approximation for high-dimensional energy landscapes","version":5},"cited_work":{"arxiv_id":"2311.05009","doi":null,"metadata_source":"pith","pith_arxiv_id":"2311.05009","snapshot_observed_at":"2026-08-04T22:41:43.107527Z","title":"Consensus-based adaptive sampling and approximation for high-dimensional energy landscapes","venue":"physics.comp-ph","work_id":"fe578df9-d198-4774-bc4f-74ef352d80c8","year":2023},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.938011Z"},"links":{"cited_paper":"/paper/2311.05009","citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:7bc40e922fba662af53b1b4951d3c0a7cd5c959e40d3a20afa61d2b0ff429214","observation_id":"d153a95e-8f59-40a6-b62d-07ac3a8f2fab","resolution":{"observed_at":"2026-08-04T22:41:43.112577Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.403176Z","title":"Construction of coarse-grained molecular dynamics with many- body non-markovian memory.Physical Review Letters, 131(17):177301, 2023","venue":null,"work_id":"5f878419-b7a7-4f65-b591-c5cf0d570078","year":2023},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.942237Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:a570414476bedeb10695322d88d3c57c87d1a1249398d2189a9942ab07be2a27","observation_id":"8f0dddf9-25be-4789-8866-1b154a1af601","resolution":{"observed_at":"2026-08-04T22:41:43.407645Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.389008Z","title":"On the generalization ability of coarse-grained molecular dynam- ics models for nonequilibrium processes.Multiscale Modeling&Simulation, 23(2):816– 837, 2025","venue":null,"work_id":"60b36a25-aeef-4ae5-b868-687e30fd4ab7","year":2025},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.946111Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:1e12b4603dbe561f1142fe4461bc5f715bc480fd7c41f67a88e43a06d1a55fd8","observation_id":"ea8ad39d-708d-49dd-b6cc-d60b00eeecaf","resolution":{"observed_at":"2026-08-04T22:41:43.393552Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.375023Z","title":"The derivation and approximation of coarse-grained dynamics from Langevin dynamics.The Journal of Chemical Physics, 145(20):204117, 2016","venue":null,"work_id":"04d6fff4-087c-437b-af7d-97f3a789fd51","year":2016},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.950282Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:d011e4f77630aaf4b6aa246657ce997da0ef9135254c3a945c99869f15dba372","observation_id":"6b16cbc0-bf3a-41e3-ab7c-184e70eb4f84","resolution":{"observed_at":"2026-08-04T22:41:43.379334Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.359748Z","title":"Coarse-graining langevin dynamics using reduced- order techniques.Journal of Computational Physics, 380:170–190, 2019","venue":null,"work_id":"041910f5-b120-4560-93f6-390a34f5bde7","year":2019},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.954218Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:be8e9dbea1da379e82ee1a876560f465e747ad374fd200e35ccff7160ff09f02","observation_id":"fd234fb3-b892-4007-ae83-df56da986fc0","resolution":{"observed_at":"2026-08-04T22:41:43.364801Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.344529Z","title":"A temperature accelerated method for sam- pling free energy and determining reaction pathways in rare events simulations.Chemical Physics Letters, 426(1):168 – 175, 2006","venue":null,"work_id":"a593f169-6fb5-4792-a080-bef3f6116482","year":2006},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.958196Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:e442f875faea4bd6208a2fe2193480d8e455b353ca26fbcc7d8146f0bce6e356","observation_id":"63343e4e-2d3f-42d2-96a6-ec5f3c8d6e7c","resolution":{"observed_at":"2026-08-04T22:41:43.349447Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.329694Z","title":"Settle: An analytical version of the shake and rattle algorithm for rigid water models.Journal of Computational Chemistry, 13(8):952– 962, 1992","venue":null,"work_id":"ae537575-cfa2-40c1-85f8-5cde5ab8ea02","year":1992},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.962026Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:5f7cefb7e1369ea768f6ac7b23347ca565b3eb89c38efda1e963b72b647b8ffe","observation_id":"4018055b-0474-4da3-94af-8e40b202860a","resolution":{"observed_at":"2026-08-04T22:41:43.334143Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.314837Z","title":"Transport, collective motion, and Brownian motion.Progress of Theoretical Physics, 33(3):423–455, 1965","venue":null,"work_id":"7a4a01f6-1e66-41d4-a181-8ccf00bbdf4d","year":1965},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.966012Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:586e11022f61e4833cbbc28aaa0f69a117f95c7e46bcc616c2ef5b9fe1e0a57f","observation_id":"ae547a7d-44f5-433b-924d-d064adc5d866","resolution":{"observed_at":"2026-08-04T22:41:43.319147Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.299965Z","title":"Polymorphic transitions in single crystals: A new molecular dynamics method.Journal of Applied Physics, 52(12):7182–7190, 1981","venue":null,"work_id":"abb18ec8-97d8-4683-b02e-94ae3feae59a","year":1981},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.970175Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:57a94b2d062877a179c310a5221029cecf7dd4dfc21c9efbfe160aa35df9e3bd","observation_id":"6750d46c-56a4-42ce-b4b8-446c7ac81ed3","resolution":{"observed_at":"2026-08-04T22:41:43.305026Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1903.09562","last_updated":"2022-11-21T13:43:02Z","snapshot_observed_at":"2026-07-06T07:41:01.122805Z","submitted_at":"2019-03-22T15:38:20Z","title":"Machine learning memory kernels as closure for non-Markovian stochastic processes","version":4},"cited_work":{"arxiv_id":"1903.09562","doi":null,"metadata_source":"pith","pith_arxiv_id":"1903.09562","snapshot_observed_at":"2026-08-04T22:41:43.086683Z","title":"Machine learning memory kernels as closure for non-Markovian stochastic processes","venue":"cond-mat.stat-mech","work_id":"9547b9ce-7904-4b3a-a906-e2dda506d8f3","year":2019},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.974448Z"},"links":{"cited_paper":"/paper/1903.09562","citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:cac9c266898fd48d2160c64309ddd65e7aaa0e15bd2526c89be8e09be7c2db0d","observation_id":"3405ffbf-4867-466a-a549-809108d4208c","resolution":{"observed_at":"2026-08-04T22:41:43.091558Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.284884Z","title":"Data-driven construction of stochastic reduced dy- namics encoded with non-markovian features.The Journal of Chemical Physics, 158(3), 2023","venue":null,"work_id":"318ca608-e09e-4c82-977a-473abdaffaaa","year":2023},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.978690Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:a922c827c49c95af9778b432a3d271afafefcb25cef3c1da32a98ec948e48a0b","observation_id":"952d6734-b975-4785-8eae-f7c2414193d9","resolution":{"observed_at":"2026-08-04T22:41:43.289853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.270609Z","title":"Adaptive deep density approximation for fokker-planck equations.Journal of Computational Physics, 457:111080, 2022","venue":null,"work_id":"ebda1827-6a47-42a4-a2e5-ae88b3dbf2d9","year":2022},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.982807Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:cb11cd72802d5b70a48e436ef988ded18ecf58b4e6c875c945544c75a20e1434","observation_id":"6d58775e-c89f-4733-a8e6-00574da05265","resolution":{"observed_at":"2026-08-04T22:41:43.275116Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2305.18702","last_updated":"2024-03-15T03:48:23Z","snapshot_observed_at":"2026-07-06T15:35:11.938380Z","submitted_at":"2023-05-30T02:59:18Z","title":"Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs","version":2},"cited_work":{"arxiv_id":"2305.18702","doi":null,"metadata_source":"pith","pith_arxiv_id":"2305.18702","snapshot_observed_at":"2026-08-04T22:41:43.063018Z","title":"Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs","venue":"stat.ML","work_id":"5316c71d-41f2-458d-9f16-1c0654363f19","year":2023},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.986709Z"},"links":{"cited_paper":"/paper/2305.18702","citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:8dfcadfa2303ab035d7bb0bcf6e973701aeef8054ddd35cc8ab335413429f7ed","observation_id":"5f859293-d46c-44f6-a4a5-e163854748e1","resolution":{"observed_at":"2026-08-04T22:41:43.070105Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.255843Z","title":"Torrie and J.P","venue":null,"work_id":"64268015-58f4-4746-98dd-3eb96bc6f2ff","year":1977},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.991052Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:64e9bb229d8332a8038ea396fa1e5c954c94f0adee29e7e3ab354ff4731d25c3","observation_id":"4da2db93-c663-4767-9aa0-8399a928b66a","resolution":{"observed_at":"2026-08-04T22:41:43.260261Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.241240Z","title":"Plumed 2: New feathers for an old bird.Computer physics communications, 185(2):604–613, 2014","venue":null,"work_id":"b5f55d82-0b61-4c2b-a2bd-786ef5f20311","year":2014},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.995183Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:c2d18536f19116536e34b4b4ab49a3cab7ba854bd65af89cdd6a89a9a93b16d3","observation_id":"9bba6bda-9277-4382-bd3b-7facacacf570","resolution":{"observed_at":"2026-08-04T22:41:43.245468Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.227369Z","title":"Likelihood-based non-markovian models from molecular dynamics.Pro- ceedings of the National Academy of Sciences, 119(13):e2117586119, 2022","venue":null,"work_id":"5de8ad24-8b62-430e-899e-8d726a56e5b4","year":2022},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:42.998964Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:77c7d3b7626fc6703e95874de466f87aef11f16f93fcf018ee398d6fc56916ec","observation_id":"62e6019a-819f-4ebe-8f72-02f40d3dab4b","resolution":{"observed_at":"2026-08-04T22:41:43.231955Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.213260Z","title":"Position-dependent memory kernel in gener- alized Langevin equations: Theory and numerical estimation.The Journal of Chemical Physics, 156(24):244105, 06 2022","venue":null,"work_id":"d6ad7929-586d-44e5-a643-80078670f406","year":2022},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:43.003112Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:1be2553e0c90bf6e7b9beed2c2ed8b59ada3f504cbc2c201483ba43a06479a1b","observation_id":"b8014574-6b21-42fd-96ce-b425bba75ee4","resolution":{"observed_at":"2026-08-04T22:41:43.217848Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.197943Z","title":"Ab initio generalized langevin equation.Pro- ceedings of the National Academy of Sciences, 121(14):e2308668121, 2024","venue":null,"work_id":"6edd1758-054d-4fc2-9853-23a24ab9b551","year":2024},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:43.006987Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:3d9a043f1aa755a07a967d1d690ff2f61804aa92b32cce375beaf92a5561fc41","observation_id":"c8aac304-e33e-4cb2-afe9-4ad52607e4cd","resolution":{"observed_at":"2026-08-04T22:41:43.202465Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.181597Z","title":"Coarse-graining conformational dynamics with multidimen- sional generalized langevin equation: How, when, and why.Journal of Chemical Theory and Computation, 20, 2024","venue":null,"work_id":"15acc380-33dd-4ab6-8f49-daf6b1500d14","year":2024},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:43.011090Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:bf17b5db97c491910b79feef9a2487b30ae1781cdd9a8cfe75cde4e661fc15c9","observation_id":"543fb42c-4033-4cad-9fcc-1ec1a52e76d2","resolution":{"observed_at":"2026-08-04T22:41:43.186514Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.167450Z","title":"Learning stochastic dynamics with statistics-informed neural network.Journal of Computational Physics, 474:111819, 2023","venue":null,"work_id":"e5ac57ff-fdfb-459d-9458-8b4db5623e90","year":2023},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:43.015102Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:7b603a0b48b1048b4f5a3db8e29f328d2ae1b7437e0782ba691f53f8ed84f334","observation_id":"529daae0-edcb-4ec9-be81-f5449ec36c34","resolution":{"observed_at":"2026-08-04T22:41:43.172087Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.152618Z","title":"Faber approximation of the Mori-Zwanzig equation","venue":null,"work_id":"fc9c0522-11c1-4c86-8d64-1b72f4aad7a0","year":2018},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:43.018757Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:2aff6518367049ab435a7e9d8ebfc71f0ff89db53bf2fb75dfb048dee11e2bf8","observation_id":"74700c60-6b1a-43d3-a20a-b0f0e8cdf57d","resolution":{"observed_at":"2026-08-04T22:41:43.157407Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.137202Z","title":"Generalized langevin equations for systems with local interactions.Journal of Statistical Physics, 178:1217, 2020","venue":null,"work_id":"29bdd540-eee0-4d57-8c4d-8d89a63cb85b","year":2020},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:43.022632Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:5cf3766e4a6fcca3e96dec20cc5b1bc919d224a6ba2de0bb3bceee2c9d0e5f50","observation_id":"29e6fe9c-07ae-4d59-baab-11407422d05f","resolution":{"observed_at":"2026-08-04T22:41:43.141887Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T22:41:43.122591Z","title":null,"venue":null,"work_id":"2ad66a3e-5dcf-4f21-bb3a-4a149ad66ce6","year":1961},"citing_paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-04T22:41:43.026472Z"},"links":{"citing_paper":"/paper/2509.07264"},"observation_digest":"sha256:0e297d33c791fb950fb16635c08fb9f5477b41135909ffd595fe7b082020870d","observation_id":"aecfb2c8-fc24-4a42-8e81-a95823ee23c0","resolution":{"observed_at":"2026-08-04T22:41:43.126868Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.07264","last_updated":"2025-09-08T22:50:00Z","latest_version":1,"primary_category":"physics.comp-ph","snapshot_observed_at":"2026-08-04T22:41:38.845067Z","submitted_at":"2025-09-08T22:50:00Z","title":"A unified framework for data-driven construction of stochastic reduced models with state-dependent memory"},"reference_resolution":{"displayed":55,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":3,"verified_fuzzy":43},"total_outbound_references":55},"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 8 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 0 inbound Pith citation observations for arXiv:2509.07264."}