{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:X2FDWBG5FCL3AS6Q4S3VWPYHFL","short_pith_number":"pith:X2FDWBG5","canonical_record":{"source":{"id":"1910.09392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-10-21T14:13:51Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"edacd841612ae3653d293271bb5ece4f3821b64e67dd792a6991797d869c3786","abstract_canon_sha256":"9a7ab79d22ba00dee1efa83f513aabeb72002da1dcde4f39449936b2ea04bd72"},"schema_version":"1.0"},"canonical_sha256":"be8a3b04dd2897b04bd0e4b75b3f072ac03b4ce3dd2d67783e09e72cc2ed0ed6","source":{"kind":"arxiv","id":"1910.09392","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.09392","created_at":"2026-07-05T00:13:33Z"},{"alias_kind":"arxiv_version","alias_value":"1910.09392v1","created_at":"2026-07-05T00:13:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.09392","created_at":"2026-07-05T00:13:33Z"},{"alias_kind":"pith_short_12","alias_value":"X2FDWBG5FCL3","created_at":"2026-07-05T00:13:33Z"},{"alias_kind":"pith_short_16","alias_value":"X2FDWBG5FCL3AS6Q","created_at":"2026-07-05T00:13:33Z"},{"alias_kind":"pith_short_8","alias_value":"X2FDWBG5","created_at":"2026-07-05T00:13:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:X2FDWBG5FCL3AS6Q4S3VWPYHFL","target":"record","payload":{"canonical_record":{"source":{"id":"1910.09392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-10-21T14:13:51Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"edacd841612ae3653d293271bb5ece4f3821b64e67dd792a6991797d869c3786","abstract_canon_sha256":"9a7ab79d22ba00dee1efa83f513aabeb72002da1dcde4f39449936b2ea04bd72"},"schema_version":"1.0"},"canonical_sha256":"be8a3b04dd2897b04bd0e4b75b3f072ac03b4ce3dd2d67783e09e72cc2ed0ed6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:13:33.335865Z","signature_b64":"b4hr+5Te45SgnnuP4N3rmdQDYmJq32M7gTpgrYEBlcVu98zVny+7TN7Ecd3rwl1UczyN2d9u7Hbz8+UlZUSWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be8a3b04dd2897b04bd0e4b75b3f072ac03b4ce3dd2d67783e09e72cc2ed0ed6","last_reissued_at":"2026-07-05T00:13:33.335472Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:13:33.335472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.09392","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:13:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bqk3VdNVM2J49iQuL08PLP5f0JPsXf+VSQquixGFKjwpOhX0/sIhCgKodKh2nTbdkMmDbQECmdbCp8ColBwWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:43:25.044751Z"},"content_sha256":"b0ee2f520b4c470b4113ca6fef69b690486180a6390c527059c94195aae0d95b","schema_version":"1.0","event_id":"sha256:b0ee2f520b4c470b4113ca6fef69b690486180a6390c527059c94195aae0d95b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:X2FDWBG5FCL3AS6Q4S3VWPYHFL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hartree and Vlasov equations at positive density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Julien Sabin, Mathieu Lewin","submitted_at":"2019-10-21T14:13:51Z","abstract_excerpt":"We consider the nonlinear Hartree and Vlasov equations around a translation-invariant (homogeneous) stationary state in infinite volume, for a short range interaction potential. For both models, we consider time-dependent solutions which have a finite relative energy with respect to the reference translation-invariant state. We prove the convergence of the Hartree solutions to the Vlasov ones in a semi-classical limit and obtain as a by-product global well-posedness of the Vlasov equation in the (relative) energy space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.09392","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.09392/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:13:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WNMZ1BlGa6K9b8IlyXGfpxiXnBjRcXIy2v8KGxHdTC2IL/AgA+jh6Vlg0QzoOONsTiUxMx60EfjtG5KE5Ps9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:43:25.045267Z"},"content_sha256":"26444cea98321534f29916b7400dca4f17b8b384628bb6f865a98dbba63e48bc","schema_version":"1.0","event_id":"sha256:26444cea98321534f29916b7400dca4f17b8b384628bb6f865a98dbba63e48bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X2FDWBG5FCL3AS6Q4S3VWPYHFL/bundle.json","state_url":"https://pith.science/pith/X2FDWBG5FCL3AS6Q4S3VWPYHFL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X2FDWBG5FCL3AS6Q4S3VWPYHFL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T07:43:25Z","links":{"resolver":"https://pith.science/pith/X2FDWBG5FCL3AS6Q4S3VWPYHFL","bundle":"https://pith.science/pith/X2FDWBG5FCL3AS6Q4S3VWPYHFL/bundle.json","state":"https://pith.science/pith/X2FDWBG5FCL3AS6Q4S3VWPYHFL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X2FDWBG5FCL3AS6Q4S3VWPYHFL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:X2FDWBG5FCL3AS6Q4S3VWPYHFL","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":"9a7ab79d22ba00dee1efa83f513aabeb72002da1dcde4f39449936b2ea04bd72","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-10-21T14:13:51Z","title_canon_sha256":"edacd841612ae3653d293271bb5ece4f3821b64e67dd792a6991797d869c3786"},"schema_version":"1.0","source":{"id":"1910.09392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.09392","created_at":"2026-07-05T00:13:33Z"},{"alias_kind":"arxiv_version","alias_value":"1910.09392v1","created_at":"2026-07-05T00:13:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.09392","created_at":"2026-07-05T00:13:33Z"},{"alias_kind":"pith_short_12","alias_value":"X2FDWBG5FCL3","created_at":"2026-07-05T00:13:33Z"},{"alias_kind":"pith_short_16","alias_value":"X2FDWBG5FCL3AS6Q","created_at":"2026-07-05T00:13:33Z"},{"alias_kind":"pith_short_8","alias_value":"X2FDWBG5","created_at":"2026-07-05T00:13:33Z"}],"graph_snapshots":[{"event_id":"sha256:26444cea98321534f29916b7400dca4f17b8b384628bb6f865a98dbba63e48bc","target":"graph","created_at":"2026-07-05T00:13:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1910.09392/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the nonlinear Hartree and Vlasov equations around a translation-invariant (homogeneous) stationary state in infinite volume, for a short range interaction potential. For both models, we consider time-dependent solutions which have a finite relative energy with respect to the reference translation-invariant state. We prove the convergence of the Hartree solutions to the Vlasov ones in a semi-classical limit and obtain as a by-product global well-posedness of the Vlasov equation in the (relative) energy space.","authors_text":"Julien Sabin, Mathieu Lewin","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-10-21T14:13:51Z","title":"The Hartree and Vlasov equations at positive density"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.09392","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:b0ee2f520b4c470b4113ca6fef69b690486180a6390c527059c94195aae0d95b","target":"record","created_at":"2026-07-05T00:13:33Z","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":"9a7ab79d22ba00dee1efa83f513aabeb72002da1dcde4f39449936b2ea04bd72","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-10-21T14:13:51Z","title_canon_sha256":"edacd841612ae3653d293271bb5ece4f3821b64e67dd792a6991797d869c3786"},"schema_version":"1.0","source":{"id":"1910.09392","kind":"arxiv","version":1}},"canonical_sha256":"be8a3b04dd2897b04bd0e4b75b3f072ac03b4ce3dd2d67783e09e72cc2ed0ed6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be8a3b04dd2897b04bd0e4b75b3f072ac03b4ce3dd2d67783e09e72cc2ed0ed6","first_computed_at":"2026-07-05T00:13:33.335472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:13:33.335472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b4hr+5Te45SgnnuP4N3rmdQDYmJq32M7gTpgrYEBlcVu98zVny+7TN7Ecd3rwl1UczyN2d9u7Hbz8+UlZUSWAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:13:33.335865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.09392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0ee2f520b4c470b4113ca6fef69b690486180a6390c527059c94195aae0d95b","sha256:26444cea98321534f29916b7400dca4f17b8b384628bb6f865a98dbba63e48bc"],"state_sha256":"0124a74c2882d10b31b6e3676ce7146984cca630fa78d9bb40c736a86c4301c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ri9i6IvwIBcWN+4kRZ9El3CpeQ58wJHfFHk2+9zzcJQA+Y7j+acv2icW5XEX+Ahsf8LnS52dM9drL+xn79kWAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T07:43:25.050734Z","bundle_sha256":"13c6d214a505174a00d44c1184389d473993b93fbcaa596c486d65bce51cdd42"}}