{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UQDZW4XOOAOD4L4FVL5XSUEGFI","short_pith_number":"pith:UQDZW4XO","canonical_record":{"source":{"id":"1710.07427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-20T06:39:42Z","cross_cats_sorted":[],"title_canon_sha256":"4f9a72d3b4b4a3c32187dacf55763d3e9d998558e00035affcca75a9acad84c6","abstract_canon_sha256":"013e2a49a3c0281015b1c6a93c30b18fae59dbadd75b028f763299f60c1353a5"},"schema_version":"1.0"},"canonical_sha256":"a4079b72ee701c3e2f85aafb7950862a04747d33a49dabe40ec2c19f2579f8ba","source":{"kind":"arxiv","id":"1710.07427","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.07427","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"arxiv_version","alias_value":"1710.07427v1","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07427","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"pith_short_12","alias_value":"UQDZW4XOOAOD","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UQDZW4XOOAOD4L4F","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UQDZW4XO","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UQDZW4XOOAOD4L4FVL5XSUEGFI","target":"record","payload":{"canonical_record":{"source":{"id":"1710.07427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-20T06:39:42Z","cross_cats_sorted":[],"title_canon_sha256":"4f9a72d3b4b4a3c32187dacf55763d3e9d998558e00035affcca75a9acad84c6","abstract_canon_sha256":"013e2a49a3c0281015b1c6a93c30b18fae59dbadd75b028f763299f60c1353a5"},"schema_version":"1.0"},"canonical_sha256":"a4079b72ee701c3e2f85aafb7950862a04747d33a49dabe40ec2c19f2579f8ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:24.841844Z","signature_b64":"wcqAmFN0Ik+bG32T26IBc+Fcko1QwG3+j8pYv0XXSwGyC5vKMc38Cq37172rQkpw0OCD0g4n0RndMSJwxCb9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4079b72ee701c3e2f85aafb7950862a04747d33a49dabe40ec2c19f2579f8ba","last_reissued_at":"2026-05-18T00:32:24.841176Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:24.841176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.07427","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":"2026-05-18T00:32:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dEvnAbRSsKjqYbYPL2cuujcCuWBGBNALBGt6t3dzZm7i3PQEqMDpm5NsSI0qTCBD6QgYXac8DWnC0Fkw2tLMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:17:24.392034Z"},"content_sha256":"0be5e07c14e4d53742a815c0ea1826f2686373c27b7ce364e41f475a158a166b","schema_version":"1.0","event_id":"sha256:0be5e07c14e4d53742a815c0ea1826f2686373c27b7ce364e41f475a158a166b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UQDZW4XOOAOD4L4FVL5XSUEGFI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness of the solution to the 2D Vlasov-Navier-Stokes system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ayman Moussa, Daniel Han-Kwan, \\'Evelyne Miot, Iv\\'an Moyano","submitted_at":"2017-10-20T06:39:42Z","abstract_excerpt":"We prove a uniqueness result for weak solutions to the Vlasov-Navier-Stokes system in two dimensions, both in the whole space and in the periodic case, under a mild decay condition on the initial distribution function. The main result is achieved by combining methods from optimal transportation (introduced in this context by G. Loeper) with the use of Hardy's maximal function, in order to obtain some fine Wassestein-like estimates for the difference of two solutions of the Vlasov equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07427","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":"2026-05-18T00:32:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMRxbehYlyB+kMm9535gycfcIqHxa59eD9esFlJlLcvkHTzxptveV6NJxJy9euknppFhkblW22912h51AwS8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:17:24.392709Z"},"content_sha256":"db7169bd4221d36c15426e43ab1c5ab6a07ad08eda21f6b2739e59572d5f48d5","schema_version":"1.0","event_id":"sha256:db7169bd4221d36c15426e43ab1c5ab6a07ad08eda21f6b2739e59572d5f48d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQDZW4XOOAOD4L4FVL5XSUEGFI/bundle.json","state_url":"https://pith.science/pith/UQDZW4XOOAOD4L4FVL5XSUEGFI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQDZW4XOOAOD4L4FVL5XSUEGFI/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":"2026-05-31T02:17:24Z","links":{"resolver":"https://pith.science/pith/UQDZW4XOOAOD4L4FVL5XSUEGFI","bundle":"https://pith.science/pith/UQDZW4XOOAOD4L4FVL5XSUEGFI/bundle.json","state":"https://pith.science/pith/UQDZW4XOOAOD4L4FVL5XSUEGFI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQDZW4XOOAOD4L4FVL5XSUEGFI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UQDZW4XOOAOD4L4FVL5XSUEGFI","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":"013e2a49a3c0281015b1c6a93c30b18fae59dbadd75b028f763299f60c1353a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-20T06:39:42Z","title_canon_sha256":"4f9a72d3b4b4a3c32187dacf55763d3e9d998558e00035affcca75a9acad84c6"},"schema_version":"1.0","source":{"id":"1710.07427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.07427","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"arxiv_version","alias_value":"1710.07427v1","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07427","created_at":"2026-05-18T00:32:24Z"},{"alias_kind":"pith_short_12","alias_value":"UQDZW4XOOAOD","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UQDZW4XOOAOD4L4F","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UQDZW4XO","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:db7169bd4221d36c15426e43ab1c5ab6a07ad08eda21f6b2739e59572d5f48d5","target":"graph","created_at":"2026-05-18T00:32:24Z","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 prove a uniqueness result for weak solutions to the Vlasov-Navier-Stokes system in two dimensions, both in the whole space and in the periodic case, under a mild decay condition on the initial distribution function. The main result is achieved by combining methods from optimal transportation (introduced in this context by G. Loeper) with the use of Hardy's maximal function, in order to obtain some fine Wassestein-like estimates for the difference of two solutions of the Vlasov equation.","authors_text":"Ayman Moussa, Daniel Han-Kwan, \\'Evelyne Miot, Iv\\'an Moyano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-20T06:39:42Z","title":"Uniqueness of the solution to the 2D Vlasov-Navier-Stokes system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07427","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":"sha256:0be5e07c14e4d53742a815c0ea1826f2686373c27b7ce364e41f475a158a166b","target":"record","created_at":"2026-05-18T00:32:24Z","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":"013e2a49a3c0281015b1c6a93c30b18fae59dbadd75b028f763299f60c1353a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-20T06:39:42Z","title_canon_sha256":"4f9a72d3b4b4a3c32187dacf55763d3e9d998558e00035affcca75a9acad84c6"},"schema_version":"1.0","source":{"id":"1710.07427","kind":"arxiv","version":1}},"canonical_sha256":"a4079b72ee701c3e2f85aafb7950862a04747d33a49dabe40ec2c19f2579f8ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4079b72ee701c3e2f85aafb7950862a04747d33a49dabe40ec2c19f2579f8ba","first_computed_at":"2026-05-18T00:32:24.841176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:24.841176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wcqAmFN0Ik+bG32T26IBc+Fcko1QwG3+j8pYv0XXSwGyC5vKMc38Cq37172rQkpw0OCD0g4n0RndMSJwxCb9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:24.841844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.07427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0be5e07c14e4d53742a815c0ea1826f2686373c27b7ce364e41f475a158a166b","sha256:db7169bd4221d36c15426e43ab1c5ab6a07ad08eda21f6b2739e59572d5f48d5"],"state_sha256":"dc342210913643b35873c4b781b385353bff27e2323e8f15bfa9ca6215818c1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"auWQ1Y6xIkT+lF4k1rLB/LOerSvApSXDyhdq3NfxdWAEA5kX/z8PEZPioddZxX+B9L3+9668OF8mWpnSKHInDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:17:24.395948Z","bundle_sha256":"ea006204e82101c159a6603f9bb9c6622d776d37f0aeebda82eed483e597f393"}}