{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2O344AYDXCU6B2SYHVBWXAZU6J","short_pith_number":"pith:2O344AYD","schema_version":"1.0","canonical_sha256":"d3b7ce0303b8a9e0ea583d436b8334f25e24bbb829419288292cb53669a6cf61","source":{"kind":"arxiv","id":"1504.03215","version":1},"attestation_state":"computed","paper":{"title":"On the evolution of the empirical measure for the Hard-Sphere dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Mario Pulvirenti, Sergio Simonella","submitted_at":"2015-04-13T15:21:07Z","abstract_excerpt":"We prove that the evolution of marginals associated to the empirical measure of a finite system of hard spheres is driven by the BBGKY hierarchical expansion. The usual hierarchy of equations for $L^1$ measures is obtained as a corollary. We discuss the ambiguities arising in the corresponding notion of microscopic series solution to the Boltzmann-Enskog equation."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.03215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-04-13T15:21:07Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"5b837c6ead12e04444da372be5cd694d5068f105702ed0a88bbefe95b61ecb86","abstract_canon_sha256":"b59610ac72b8cd388a12aa6681dd8509ec3dc5396ec067e04795853eb00b7b67"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:46.845652Z","signature_b64":"PHl/OSBOjDE1/gZm9aiQm71/5MpLNIf6qP5f+Jy5/EFTnsQaZjbCw0Ouc3VUG2LdMKt5GGTjVIX9LJiwKx69CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3b7ce0303b8a9e0ea583d436b8334f25e24bbb829419288292cb53669a6cf61","last_reissued_at":"2026-05-18T00:56:46.845173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:46.845173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the evolution of the empirical measure for the Hard-Sphere dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Mario Pulvirenti, Sergio Simonella","submitted_at":"2015-04-13T15:21:07Z","abstract_excerpt":"We prove that the evolution of marginals associated to the empirical measure of a finite system of hard spheres is driven by the BBGKY hierarchical expansion. The usual hierarchy of equations for $L^1$ measures is obtained as a corollary. We discuss the ambiguities arising in the corresponding notion of microscopic series solution to the Boltzmann-Enskog equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03215","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1504.03215","created_at":"2026-05-18T00:56:46.845242+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.03215v1","created_at":"2026-05-18T00:56:46.845242+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03215","created_at":"2026-05-18T00:56:46.845242+00:00"},{"alias_kind":"pith_short_12","alias_value":"2O344AYDXCU6","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"2O344AYDXCU6B2SY","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"2O344AYD","created_at":"2026-05-18T12:29:02.477457+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2O344AYDXCU6B2SYHVBWXAZU6J","json":"https://pith.science/pith/2O344AYDXCU6B2SYHVBWXAZU6J.json","graph_json":"https://pith.science/api/pith-number/2O344AYDXCU6B2SYHVBWXAZU6J/graph.json","events_json":"https://pith.science/api/pith-number/2O344AYDXCU6B2SYHVBWXAZU6J/events.json","paper":"https://pith.science/paper/2O344AYD"},"agent_actions":{"view_html":"https://pith.science/pith/2O344AYDXCU6B2SYHVBWXAZU6J","download_json":"https://pith.science/pith/2O344AYDXCU6B2SYHVBWXAZU6J.json","view_paper":"https://pith.science/paper/2O344AYD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.03215&json=true","fetch_graph":"https://pith.science/api/pith-number/2O344AYDXCU6B2SYHVBWXAZU6J/graph.json","fetch_events":"https://pith.science/api/pith-number/2O344AYDXCU6B2SYHVBWXAZU6J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2O344AYDXCU6B2SYHVBWXAZU6J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2O344AYDXCU6B2SYHVBWXAZU6J/action/storage_attestation","attest_author":"https://pith.science/pith/2O344AYDXCU6B2SYHVBWXAZU6J/action/author_attestation","sign_citation":"https://pith.science/pith/2O344AYDXCU6B2SYHVBWXAZU6J/action/citation_signature","submit_replication":"https://pith.science/pith/2O344AYDXCU6B2SYHVBWXAZU6J/action/replication_record"}},"created_at":"2026-05-18T00:56:46.845242+00:00","updated_at":"2026-05-18T00:56:46.845242+00:00"}