{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KDFWZNJIV3GZF24RG4ZHW6OAN3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"87fb82062b75dcd6da23d29ae4bb3207edd9565f2a14d2f355e2d1ba582bf7c2","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2018-10-03T17:09:47Z","title_canon_sha256":"8ea553e8f59ee385ba900e0615a1fb907b42a93e9f1b581b19f8a13efc85992c"},"schema_version":"1.0","source":{"id":"1810.01841","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01841","created_at":"2026-05-17T23:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01841v2","created_at":"2026-05-17T23:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01841","created_at":"2026-05-17T23:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"KDFWZNJIV3GZ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KDFWZNJIV3GZF24R","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KDFWZNJI","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:6c4cfb580f7b9905a2c10365c4e6f05eba7c363d407d8ba662b083a9b264145d","target":"graph","created_at":"2026-05-17T23:39:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Understanding chemical mechanisms requires estimating dynamical statistics such as expected hitting times, reaction rates, and committors. Here, we present a general framework for calculating these dynamical quantities by approximating boundary value problems using dynamical operators with a Galerkin expansion. A specific choice of basis set in the expansion corresponds to estimation of dynamical quantities using a Markov state model. More generally, the boundary conditions impose restrictions on the choice of basis sets. We demonstrate how an alternative basis can be constructed using ideas f","authors_text":"Aaron R. Dinner, Dimitrios Giannakis, Erik H. Thiede, Jonathan Weare","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2018-10-03T17:09:47Z","title":"Galerkin Approximation of Dynamical Quantities using Trajectory Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01841","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e5ea579ad4a1e7618f432b66939e2e894197dadaf6a13731a88ad8d55cbaaf8b","target":"record","created_at":"2026-05-17T23:39:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"87fb82062b75dcd6da23d29ae4bb3207edd9565f2a14d2f355e2d1ba582bf7c2","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2018-10-03T17:09:47Z","title_canon_sha256":"8ea553e8f59ee385ba900e0615a1fb907b42a93e9f1b581b19f8a13efc85992c"},"schema_version":"1.0","source":{"id":"1810.01841","kind":"arxiv","version":2}},"canonical_sha256":"50cb6cb528aecd92eb9137327b79c06efd08b8bda32b6be0773b292a0ee15e23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50cb6cb528aecd92eb9137327b79c06efd08b8bda32b6be0773b292a0ee15e23","first_computed_at":"2026-05-17T23:39:48.369870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:48.369870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"62FK6TKGi54UZLb9L80shwctBQ2aJXgJjIKkZM4t15Uc6FVVCxWmxociWiVzm916EJ+1BbtJBKWBkFphYj26DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:48.370493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.01841","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5ea579ad4a1e7618f432b66939e2e894197dadaf6a13731a88ad8d55cbaaf8b","sha256:6c4cfb580f7b9905a2c10365c4e6f05eba7c363d407d8ba662b083a9b264145d"],"state_sha256":"9bbd890029a3e1bde98ba72175d3b7fc974adb24b3861b5ea034792cc59d9034"}