{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XANHOLAHMRPIVVQZIH62ABZDOX","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":"222d62581dac891f6aa2860bc53d6da9617905e7fef15e3caf83332293bffd12","cross_cats_sorted":["q-bio.MN","q-bio.NC"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DS","submitted_at":"2012-08-07T20:22:31Z","title_canon_sha256":"e5f49f83f03cd4b5f46217ee741e8f9570b2f040de70a4261ea53f5af5a3f8fd"},"schema_version":"1.0","source":{"id":"1208.1513","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1513","created_at":"2026-05-18T02:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1513v4","created_at":"2026-05-18T02:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1513","created_at":"2026-05-18T02:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"XANHOLAHMRPI","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XANHOLAHMRPIVVQZ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XANHOLAH","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:cacb46d0af0d7143461aaf91b02ff355158d7fc5a833db9c9cf112da084e0a44","target":"graph","created_at":"2026-05-18T02:24:36Z","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":"We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently surjective graph fibrations give rise to invariant subsystems and injective graph fibrations give rise to projections of dynamical systems.","authors_text":"Eugene Lerman, Lee DeVille","cross_cats":["q-bio.MN","q-bio.NC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DS","submitted_at":"2012-08-07T20:22:31Z","title":"Dynamics on Networks of Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1513","kind":"arxiv","version":4},"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":"sha256:07219b0f27c3e6b81e67ea1d0b562ea96369ce763ca9427120b96aa71e7da8de","target":"record","created_at":"2026-05-18T02:24:36Z","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":"222d62581dac891f6aa2860bc53d6da9617905e7fef15e3caf83332293bffd12","cross_cats_sorted":["q-bio.MN","q-bio.NC"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DS","submitted_at":"2012-08-07T20:22:31Z","title_canon_sha256":"e5f49f83f03cd4b5f46217ee741e8f9570b2f040de70a4261ea53f5af5a3f8fd"},"schema_version":"1.0","source":{"id":"1208.1513","kind":"arxiv","version":4}},"canonical_sha256":"b81a772c07645e8ad61941fda0072375eb0cb93fd63f2023bca9f5d6ca24cdfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b81a772c07645e8ad61941fda0072375eb0cb93fd63f2023bca9f5d6ca24cdfc","first_computed_at":"2026-05-18T02:24:36.108949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:36.108949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5ld/5Pb0H5zMGUIu5Qs8wrANpxzQ1nVEzNWxnQfqFPAsHpR0co4ALz6RoLYekRWPM+ooShCWuEQOrN6grsScDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:36.109643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1513","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07219b0f27c3e6b81e67ea1d0b562ea96369ce763ca9427120b96aa71e7da8de","sha256:cacb46d0af0d7143461aaf91b02ff355158d7fc5a833db9c9cf112da084e0a44"],"state_sha256":"0a250553736dce662442dc03923f49df09f510f7c5ac67e5cdb96c25e465db02"}