{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:BAEMHWAAF7T54K3RQ6JC5F4JOI","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":"bc73d08aeed91896228ab8c23946a008b9e567c375f1bfaa3227b202fecf994e","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2003-10-03T12:00:59Z","title_canon_sha256":"23ca4c149f6ea120deba80652531ae26d2913b304f616a6406839db3bbb1f527"},"schema_version":"1.0","source":{"id":"math/0310039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0310039","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0310039v1","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0310039","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"BAEMHWAAF7T5","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"BAEMHWAAF7T54K3R","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"BAEMHWAA","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:c5eb40f89e42a557df3a322a600906e2a9991e5900923fc6b2fea3d08345c003","target":"graph","created_at":"2026-05-18T01:05:28Z","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":"On demontre la convergence pour tout temps d'une approximation de l'equation de Vlasov par un systeme de particules sans regularisation du champ, ceci pour des potentiels singuliers, avec une force du type $1/|x|^{\\alpha}$, pour \\alpha plus petit que 1.","authors_text":"Jabin Pierre-Emmanuel, Maxime Hauray","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2003-10-03T12:00:59Z","title":"N particles approximation of the Vlasov equations with singular potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0310039","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:cd3b99ca6f5ad8386d029e46f074df008d36ce7dd3c5900f1d873c294984e566","target":"record","created_at":"2026-05-18T01:05:28Z","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":"bc73d08aeed91896228ab8c23946a008b9e567c375f1bfaa3227b202fecf994e","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2003-10-03T12:00:59Z","title_canon_sha256":"23ca4c149f6ea120deba80652531ae26d2913b304f616a6406839db3bbb1f527"},"schema_version":"1.0","source":{"id":"math/0310039","kind":"arxiv","version":1}},"canonical_sha256":"0808c3d8002fe7de2b7187922e9789720938547c39bdb64ced9219ff6dd516c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0808c3d8002fe7de2b7187922e9789720938547c39bdb64ced9219ff6dd516c9","first_computed_at":"2026-05-18T01:05:28.599366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:28.599366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MHD3KBYZXN6XOdPWXnEOkKKeBpbHPDJt9pcarve8U4rAGn1AbH2UxzYAhi9N5K2mRWxV/v53wpwt5J4Sn7E7DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:28.599842Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0310039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd3b99ca6f5ad8386d029e46f074df008d36ce7dd3c5900f1d873c294984e566","sha256:c5eb40f89e42a557df3a322a600906e2a9991e5900923fc6b2fea3d08345c003"],"state_sha256":"fb9a9702fd01cc15bd546f4350bc4510620015c72ecbd3752f3b93e58707d696"}