{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:Z52QBRJWPM7HSZOPRWHZTO23RS","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":"1f9e2a47aae21421be4847415af38324789e8792a7c470a0f9c8832f6a9d099f","cross_cats_sorted":["cond-mat.dis-nn","math.CA","math.MP","math.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-23T00:15:26Z","title_canon_sha256":"c38104abd6df8dbf383d6d1db28f5077ac5d1bddcb989f9a5212bd0779cbe603"},"schema_version":"1.0","source":{"id":"1010.4832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4832","created_at":"2026-05-18T04:38:50Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4832v1","created_at":"2026-05-18T04:38:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4832","created_at":"2026-05-18T04:38:50Z"},{"alias_kind":"pith_short_12","alias_value":"Z52QBRJWPM7H","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Z52QBRJWPM7HSZOP","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Z52QBRJW","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:9e22cf5fcbbd923e2b43a14ec5313d12670e48f6d0cebaaa80292cec43b4ec59","target":"graph","created_at":"2026-05-18T04:38:50Z","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 study the closure problem for continuum balance equations that model mesoscale dynamics of large ODE systems. The underlying microscale model consists of classical Newton equations of particle dynamics. As a mesoscale model we use the balance equations for spatial averages obtained earlier by a number of authors: Murdoch and Bedeaux, Hardy, Noll and others. The momentum balance equation contains a flux (stress), which is given by an exact function of particle positions and velocities. We propose a method for approximating this function by a sequence of operators applied to average density a","authors_text":"Alexander Panchenko, Lyudmyla L. Barannyk, Robert P. Gilbert","cross_cats":["cond-mat.dis-nn","math.CA","math.MP","math.NA","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-23T00:15:26Z","title":"Closure method for spatially averaged dynamics of particle chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4832","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":"sha256:370d03046217056f4c11dfacb87742eade70760107d9d7475b3b839515920168","target":"record","created_at":"2026-05-18T04:38:50Z","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":"1f9e2a47aae21421be4847415af38324789e8792a7c470a0f9c8832f6a9d099f","cross_cats_sorted":["cond-mat.dis-nn","math.CA","math.MP","math.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-23T00:15:26Z","title_canon_sha256":"c38104abd6df8dbf383d6d1db28f5077ac5d1bddcb989f9a5212bd0779cbe603"},"schema_version":"1.0","source":{"id":"1010.4832","kind":"arxiv","version":1}},"canonical_sha256":"cf7500c5367b3e7965cf8d8f99bb5b8ca1048a68ef42dcefcd4802ebbf542490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf7500c5367b3e7965cf8d8f99bb5b8ca1048a68ef42dcefcd4802ebbf542490","first_computed_at":"2026-05-18T04:38:50.091222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:50.091222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zkXesNkiIZ3tFL6uBA2bnlDLWeX5Hs03hUwO3Rbl7irshZ8w3uy1U2KNeJqVNU36P33u6Vwd7vx59SzYobmNDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:50.091723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:370d03046217056f4c11dfacb87742eade70760107d9d7475b3b839515920168","sha256:9e22cf5fcbbd923e2b43a14ec5313d12670e48f6d0cebaaa80292cec43b4ec59"],"state_sha256":"4de9c3cca334865e78ef3791e1058e95d6c09900be4b2f52523ff9d8f9a7e2ab"}