{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YP2BH46CB5JX7CIYRPZBM76CHL","short_pith_number":"pith:YP2BH46C","canonical_record":{"source":{"id":"1107.4782","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-24T18:16:24Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"0118b0d785183e3cb0dcc9f60d762f1eb58e7fbaf0ca57b7afc9eb2f6f4d243b","abstract_canon_sha256":"6240775b432766807a079dcff123c7469e20c6a31c01b212c1be355bb37e4134"},"schema_version":"1.0"},"canonical_sha256":"c3f413f3c20f537f89188bf2167fc23ae8265eedfd018a236e6ddccf73da83d7","source":{"kind":"arxiv","id":"1107.4782","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4782","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4782v2","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4782","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"YP2BH46CB5JX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YP2BH46CB5JX7CIY","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YP2BH46C","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YP2BH46CB5JX7CIYRPZBM76CHL","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4782","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-24T18:16:24Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"0118b0d785183e3cb0dcc9f60d762f1eb58e7fbaf0ca57b7afc9eb2f6f4d243b","abstract_canon_sha256":"6240775b432766807a079dcff123c7469e20c6a31c01b212c1be355bb37e4134"},"schema_version":"1.0"},"canonical_sha256":"c3f413f3c20f537f89188bf2167fc23ae8265eedfd018a236e6ddccf73da83d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:31.732809Z","signature_b64":"ODMY73HyhSxsR9ZajtTsUKNEFeyhL7vKW4aWmMDtvuo0mmlO1Br0BiJWyW0vs72l/o6qdckguq0d7fRgCVW8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3f413f3c20f537f89188bf2167fc23ae8265eedfd018a236e6ddccf73da83d7","last_reissued_at":"2026-05-18T03:46:31.731520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:31.731520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4782","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEvzP+7R1G9hUR4PNJNsvK7u7ld4xUG2aiXccLzymx1w8BmQS/xaG235086Wo8D2WvH14vw44US4RX3QfQ6PAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T07:02:41.714031Z"},"content_sha256":"12dd0fbcb42c7dd8fc5c31ce9e95a16a53e7a9c7de7030898cba20d640081a25","schema_version":"1.0","event_id":"sha256:12dd0fbcb42c7dd8fc5c31ce9e95a16a53e7a9c7de7030898cba20d640081a25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YP2BH46CB5JX7CIYRPZBM76CHL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Martial Agueh, Reinel Sospedra-Alfonso","submitted_at":"2011-07-24T18:16:24Z","abstract_excerpt":"We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in J. Math. Pures Appl. 86, 68-79 (2006) to obtain uniqueness results for the Vlasov-Poisson system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4782","kind":"arxiv","version":2},"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":"2026-05-18T03:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vuvV/qCzcuOgBbb8U4dBf23ocZIRq7+yKaxs36Va8x6rC9LVWJ0iADKsytRN62dCaJTN+bJS53nz9X2fWb6AAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T07:02:41.714391Z"},"content_sha256":"0b9d4019c83eb0d0fbb0bbc777b5dbf9eafbf07d83bbcfe7bfe31e99763a289c","schema_version":"1.0","event_id":"sha256:0b9d4019c83eb0d0fbb0bbc777b5dbf9eafbf07d83bbcfe7bfe31e99763a289c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YP2BH46CB5JX7CIYRPZBM76CHL/bundle.json","state_url":"https://pith.science/pith/YP2BH46CB5JX7CIYRPZBM76CHL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YP2BH46CB5JX7CIYRPZBM76CHL/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":"2026-07-02T07:02:41Z","links":{"resolver":"https://pith.science/pith/YP2BH46CB5JX7CIYRPZBM76CHL","bundle":"https://pith.science/pith/YP2BH46CB5JX7CIYRPZBM76CHL/bundle.json","state":"https://pith.science/pith/YP2BH46CB5JX7CIYRPZBM76CHL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YP2BH46CB5JX7CIYRPZBM76CHL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YP2BH46CB5JX7CIYRPZBM76CHL","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":"6240775b432766807a079dcff123c7469e20c6a31c01b212c1be355bb37e4134","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-24T18:16:24Z","title_canon_sha256":"0118b0d785183e3cb0dcc9f60d762f1eb58e7fbaf0ca57b7afc9eb2f6f4d243b"},"schema_version":"1.0","source":{"id":"1107.4782","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4782","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4782v2","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4782","created_at":"2026-05-18T03:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"YP2BH46CB5JX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YP2BH46CB5JX7CIY","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YP2BH46C","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:0b9d4019c83eb0d0fbb0bbc777b5dbf9eafbf07d83bbcfe7bfe31e99763a289c","target":"graph","created_at":"2026-05-18T03:46:31Z","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 use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in J. Math. Pures Appl. 86, 68-79 (2006) to obtain uniqueness results for the Vlasov-Poisson system.","authors_text":"Martial Agueh, Reinel Sospedra-Alfonso","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-24T18:16:24Z","title":"Uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4782","kind":"arxiv","version":2},"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":"sha256:12dd0fbcb42c7dd8fc5c31ce9e95a16a53e7a9c7de7030898cba20d640081a25","target":"record","created_at":"2026-05-18T03:46:31Z","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":"6240775b432766807a079dcff123c7469e20c6a31c01b212c1be355bb37e4134","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-07-24T18:16:24Z","title_canon_sha256":"0118b0d785183e3cb0dcc9f60d762f1eb58e7fbaf0ca57b7afc9eb2f6f4d243b"},"schema_version":"1.0","source":{"id":"1107.4782","kind":"arxiv","version":2}},"canonical_sha256":"c3f413f3c20f537f89188bf2167fc23ae8265eedfd018a236e6ddccf73da83d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3f413f3c20f537f89188bf2167fc23ae8265eedfd018a236e6ddccf73da83d7","first_computed_at":"2026-05-18T03:46:31.731520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:31.731520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ODMY73HyhSxsR9ZajtTsUKNEFeyhL7vKW4aWmMDtvuo0mmlO1Br0BiJWyW0vs72l/o6qdckguq0d7fRgCVW8Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:31.732809Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4782","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12dd0fbcb42c7dd8fc5c31ce9e95a16a53e7a9c7de7030898cba20d640081a25","sha256:0b9d4019c83eb0d0fbb0bbc777b5dbf9eafbf07d83bbcfe7bfe31e99763a289c"],"state_sha256":"2ca30cfdc04befd8a0420c3f8ea094889d609ed1c1cecf9004c97c48de4141cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bOUllkfph8AT5HL1xZNE3Uyp8wxLxrMUXStuqGeOxQW/oa3oYdbdiXhXT7gI9mW+NyS1zvPxdAqSqWwywr8/Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T07:02:41.716413Z","bundle_sha256":"f07695e49d8c98ed44558194f55b98371684dd1d7a91eb9a4b67a42f67d5123f"}}