{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:P4LE5FQVUFHGM2J4V3M3CZI2LO","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":"d6ac0b3b96d96227b02429e2cd8be9be4955be95f4e56fa0c7ad1077fbef0939","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-05-15T13:25:34Z","title_canon_sha256":"36049e26511b2b2a92c37fa8308e0f21ba24a4d9c42d2a2e7be0d1af839422a3"},"schema_version":"1.0","source":{"id":"2405.09324","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.09324","created_at":"2026-07-05T10:45:08Z"},{"alias_kind":"arxiv_version","alias_value":"2405.09324v2","created_at":"2026-07-05T10:45:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.09324","created_at":"2026-07-05T10:45:08Z"},{"alias_kind":"pith_short_12","alias_value":"P4LE5FQVUFHG","created_at":"2026-07-05T10:45:08Z"},{"alias_kind":"pith_short_16","alias_value":"P4LE5FQVUFHGM2J4","created_at":"2026-07-05T10:45:08Z"},{"alias_kind":"pith_short_8","alias_value":"P4LE5FQV","created_at":"2026-07-05T10:45:08Z"}],"graph_snapshots":[{"event_id":"sha256:a555f1f2890a8dbe714cb10e48608e5eb337aba41aea06464c44ad766c74ad5e","target":"graph","created_at":"2026-07-05T10:45:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.09324/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a Graph Neural Network (GNN) non-Markovian modeling framework to identify coarse-grained dynamical systems on graphs. Our main idea is to systematically determine the GNN architecture by inspecting how the leading term of the Mori-Zwanzig memory term depends on the coarse-grained interaction coefficients that encode the graph topology. Based on this analysis, we found that the appropriate GNN architecture that will account for $K$-hop dynamical interactions has to employ a Message Passing (MP) mechanism with at least $2K$ steps. We also deduce that the memory length required for an","authors_text":"Daning Huang, John Harlim, Yan Li, Yin Yu","cross_cats":["cond-mat.dis-nn","cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-05-15T13:25:34Z","title":"Learning Coarse-Grained Dynamics on Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.09324","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":"sha256:07e33b10c7dff5fdbea7c30dc5560dcddb61ddee27c6d7ae4ccd86dd5dae4534","target":"record","created_at":"2026-07-05T10:45:08Z","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":"d6ac0b3b96d96227b02429e2cd8be9be4955be95f4e56fa0c7ad1077fbef0939","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-05-15T13:25:34Z","title_canon_sha256":"36049e26511b2b2a92c37fa8308e0f21ba24a4d9c42d2a2e7be0d1af839422a3"},"schema_version":"1.0","source":{"id":"2405.09324","kind":"arxiv","version":2}},"canonical_sha256":"7f164e9615a14e66693caed9b1651a5b992275109375bd82d564d6262f1e97be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f164e9615a14e66693caed9b1651a5b992275109375bd82d564d6262f1e97be","first_computed_at":"2026-07-05T10:45:08.012572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:45:08.012572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tk8uDsVUYqwLrkyoH5NCs/C7MnSK15JlDwb8ungBzhe3f0w4PM6Kz+Yz+OOW4FRRIL0R8yCnXKc8miOuqx99BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:45:08.013054Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.09324","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07e33b10c7dff5fdbea7c30dc5560dcddb61ddee27c6d7ae4ccd86dd5dae4534","sha256:a555f1f2890a8dbe714cb10e48608e5eb337aba41aea06464c44ad766c74ad5e"],"state_sha256":"f00f218a5e0058095f83857ac02b05aa7881b9053aad011770e15d4266d7d4eb"}