{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VVRJHYE4QI26SYOTDW7CTAWTGT","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":"da8d2b6372c820d718383357c3ec11c93409b388a1836177ae93a31df2ba6431","cross_cats_sorted":["cond-mat.stat-mech","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.plasm-ph","submitted_at":"2009-09-09T06:15:27Z","title_canon_sha256":"9eadfe141d2eb5d0ce2d06c4d7273ea04653f3cf3d947ffe12474cc2bac3a282"},"schema_version":"1.0","source":{"id":"0909.1631","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1631","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1631v1","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1631","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"VVRJHYE4QI26","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VVRJHYE4QI26SYOT","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VVRJHYE4","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:528421f2037100df50b2d3775b5193c7cd1e0bbc321d117ffdcc74d7a010e2f4","target":"graph","created_at":"2026-05-18T04:39:59Z","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":"The evolution equations for the generalized microscopic phase densities are introduced. The evolution equations of average values of microscopic phase densities are derived and a solution of the initial-value problem of the obtained hydrodynamic type hierarchy is constructed.","authors_text":"A.G. Zagorodny, V.I. Gerasimenko, V.O. Shtyk","cross_cats":["cond-mat.stat-mech","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.plasm-ph","submitted_at":"2009-09-09T06:15:27Z","title":"Hydrodynamic Equations for Microscopic Phase Densities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1631","kind":"arxiv","version":1},"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":"sha256:23ea40419dae4083f082c0646b318cd5837382be61cc7f1108c48480449d2e01","target":"record","created_at":"2026-05-18T04:39:59Z","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":"da8d2b6372c820d718383357c3ec11c93409b388a1836177ae93a31df2ba6431","cross_cats_sorted":["cond-mat.stat-mech","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.plasm-ph","submitted_at":"2009-09-09T06:15:27Z","title_canon_sha256":"9eadfe141d2eb5d0ce2d06c4d7273ea04653f3cf3d947ffe12474cc2bac3a282"},"schema_version":"1.0","source":{"id":"0909.1631","kind":"arxiv","version":1}},"canonical_sha256":"ad6293e09c8235e961d31dbe2982d334c710b8fd4a08960376fa28fa396eb166","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad6293e09c8235e961d31dbe2982d334c710b8fd4a08960376fa28fa396eb166","first_computed_at":"2026-05-18T04:39:59.494779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:59.494779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MlLmpJvrAGBVXQiIznuFLRCIbllZu0ljFyrIKSSonNImOUGuuILTji45p39kCCt7G7hl9fuOW6JUwhKToy6XDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:59.495226Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.1631","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23ea40419dae4083f082c0646b318cd5837382be61cc7f1108c48480449d2e01","sha256:528421f2037100df50b2d3775b5193c7cd1e0bbc321d117ffdcc74d7a010e2f4"],"state_sha256":"c170c9088b3c6a23b8f31605ae51f942e3e61715765d468cc3e4b891d4e0f1ea"}