{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RCBXSPH5CKTS2SAROFXDVNYWEB","short_pith_number":"pith:RCBXSPH5","canonical_record":{"source":{"id":"1310.0974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T13:28:00Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"0e0879422aefd559cb74b01eac178bf6223e6b5f571892a47c04b4d459f6b9a3","abstract_canon_sha256":"c08e43eed1a6deea9f32c566ae0a37b20e00339e3f2e4a10aedf07d4ca122ae9"},"schema_version":"1.0"},"canonical_sha256":"8883793cfd12a72d4811716e3ab716204594942aeec54c40a147e15d91586544","source":{"kind":"arxiv","id":"1310.0974","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0974","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0974v1","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0974","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"RCBXSPH5CKTS","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RCBXSPH5CKTS2SAR","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RCBXSPH5","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RCBXSPH5CKTS2SAROFXDVNYWEB","target":"record","payload":{"canonical_record":{"source":{"id":"1310.0974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T13:28:00Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"0e0879422aefd559cb74b01eac178bf6223e6b5f571892a47c04b4d459f6b9a3","abstract_canon_sha256":"c08e43eed1a6deea9f32c566ae0a37b20e00339e3f2e4a10aedf07d4ca122ae9"},"schema_version":"1.0"},"canonical_sha256":"8883793cfd12a72d4811716e3ab716204594942aeec54c40a147e15d91586544","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:24.883376Z","signature_b64":"LTf5Y6QndsZg33JHNdsOwfsC48xu73J6XyvjPoJU+Iks37j+8WqzzxLZY315rdUCopEeTTerlfzJMhJSUoHlAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8883793cfd12a72d4811716e3ab716204594942aeec54c40a147e15d91586544","last_reissued_at":"2026-05-18T03:11:24.882646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:24.882646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.0974","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":"2026-05-18T03:11:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ICJE0bGc/at2w4XhZjQ70XjsXAt43nST62dcPc4JD15oYSibNhUbPo13OfnrpsSj8EsQHjVWI9Do8EG+qtcjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T03:01:58.502239Z"},"content_sha256":"553a5c9718862dbacaab157a4fedecabb7b86cc749007aefa4d4a8a47e8d45c1","schema_version":"1.0","event_id":"sha256:553a5c9718862dbacaab157a4fedecabb7b86cc749007aefa4d4a8a47e8d45c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RCBXSPH5CKTS2SAROFXDVNYWEB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Two-dimensional Hamiltonian Transport Equations with $L^p_{loc}$ coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Maxime Hauray","submitted_at":"2013-10-03T13:28:00Z","abstract_excerpt":"We consider two-dimensional autonomous divergence free vector-fields in $\\Lde_{loc}$. Under a condition on direction of the flow and on the set of critical points, we prove the existence and uniqueness of a stable a.e. flow and of renormalized solutions of the associated transport equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0974","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e4iKZ09cHzhW4idrnkAz/6QZRqndT2NTfjGm1sx1YrLFUnLFM4xrDoNsOS1+3xYP8NxojP/6A9WZGzCqVm7VAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T03:01:58.502589Z"},"content_sha256":"168a0d888d2e6fc04f185d2e382fc35edec304cb7789f91b4d6bc66d0afd1d57","schema_version":"1.0","event_id":"sha256:168a0d888d2e6fc04f185d2e382fc35edec304cb7789f91b4d6bc66d0afd1d57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RCBXSPH5CKTS2SAROFXDVNYWEB/bundle.json","state_url":"https://pith.science/pith/RCBXSPH5CKTS2SAROFXDVNYWEB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RCBXSPH5CKTS2SAROFXDVNYWEB/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":"2026-07-05T03:01:58Z","links":{"resolver":"https://pith.science/pith/RCBXSPH5CKTS2SAROFXDVNYWEB","bundle":"https://pith.science/pith/RCBXSPH5CKTS2SAROFXDVNYWEB/bundle.json","state":"https://pith.science/pith/RCBXSPH5CKTS2SAROFXDVNYWEB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RCBXSPH5CKTS2SAROFXDVNYWEB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RCBXSPH5CKTS2SAROFXDVNYWEB","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":"c08e43eed1a6deea9f32c566ae0a37b20e00339e3f2e4a10aedf07d4ca122ae9","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T13:28:00Z","title_canon_sha256":"0e0879422aefd559cb74b01eac178bf6223e6b5f571892a47c04b4d459f6b9a3"},"schema_version":"1.0","source":{"id":"1310.0974","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0974","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0974v1","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0974","created_at":"2026-05-18T03:11:24Z"},{"alias_kind":"pith_short_12","alias_value":"RCBXSPH5CKTS","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RCBXSPH5CKTS2SAR","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RCBXSPH5","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:168a0d888d2e6fc04f185d2e382fc35edec304cb7789f91b4d6bc66d0afd1d57","target":"graph","created_at":"2026-05-18T03:11:24Z","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 consider two-dimensional autonomous divergence free vector-fields in $\\Lde_{loc}$. Under a condition on direction of the flow and on the set of critical points, we prove the existence and uniqueness of a stable a.e. flow and of renormalized solutions of the associated transport equation.","authors_text":"Maxime Hauray","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T13:28:00Z","title":"On Two-dimensional Hamiltonian Transport Equations with $L^p_{loc}$ coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0974","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":"sha256:553a5c9718862dbacaab157a4fedecabb7b86cc749007aefa4d4a8a47e8d45c1","target":"record","created_at":"2026-05-18T03:11:24Z","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":"c08e43eed1a6deea9f32c566ae0a37b20e00339e3f2e4a10aedf07d4ca122ae9","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T13:28:00Z","title_canon_sha256":"0e0879422aefd559cb74b01eac178bf6223e6b5f571892a47c04b4d459f6b9a3"},"schema_version":"1.0","source":{"id":"1310.0974","kind":"arxiv","version":1}},"canonical_sha256":"8883793cfd12a72d4811716e3ab716204594942aeec54c40a147e15d91586544","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8883793cfd12a72d4811716e3ab716204594942aeec54c40a147e15d91586544","first_computed_at":"2026-05-18T03:11:24.882646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:24.882646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LTf5Y6QndsZg33JHNdsOwfsC48xu73J6XyvjPoJU+Iks37j+8WqzzxLZY315rdUCopEeTTerlfzJMhJSUoHlAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:24.883376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0974","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:553a5c9718862dbacaab157a4fedecabb7b86cc749007aefa4d4a8a47e8d45c1","sha256:168a0d888d2e6fc04f185d2e382fc35edec304cb7789f91b4d6bc66d0afd1d57"],"state_sha256":"71cff1e87bdbfbafe40e7477f2d941da9881d82dfe318b68bd44ea078515add5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YrMIsBWnxUNNuVeWVp0wK9Z4vC5XOLzouJdpEiP3JWum49am5WkV+Lww0S/iuCwu1bdpes/UG5km8LPtu7vrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T03:01:58.504449Z","bundle_sha256":"7b5dedc4087a5478fc8dbb131bf6162799f2813d422dde69cb6a27ab262db1b8"}}