{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ACWX7DDATA55YSAVP6RYYA2RHL","short_pith_number":"pith:ACWX7DDA","canonical_record":{"source":{"id":"1903.04878","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-12T12:56:16Z","cross_cats_sorted":[],"title_canon_sha256":"b60e39f18ff6a91ef827eb9df0eb09577f12b0d77d8ffa1138f1503507e0eb6b","abstract_canon_sha256":"a4217fddafd97e807ca6bc3d5f726cfa53ea87400f25734719498492e748f37c"},"schema_version":"1.0"},"canonical_sha256":"00ad7f8c60983bdc48157fa38c03513afca8e58e6315ca6f6dd53bd8a0f307c8","source":{"kind":"arxiv","id":"1903.04878","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04878","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04878v2","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04878","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"pith_short_12","alias_value":"ACWX7DDATA55","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"ACWX7DDATA55YSAV","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"ACWX7DDA","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ACWX7DDATA55YSAVP6RYYA2RHL","target":"record","payload":{"canonical_record":{"source":{"id":"1903.04878","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-12T12:56:16Z","cross_cats_sorted":[],"title_canon_sha256":"b60e39f18ff6a91ef827eb9df0eb09577f12b0d77d8ffa1138f1503507e0eb6b","abstract_canon_sha256":"a4217fddafd97e807ca6bc3d5f726cfa53ea87400f25734719498492e748f37c"},"schema_version":"1.0"},"canonical_sha256":"00ad7f8c60983bdc48157fa38c03513afca8e58e6315ca6f6dd53bd8a0f307c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:49.823663Z","signature_b64":"icjeRMRXybJF3t86MPg8vrzWDh2JOqU/C8h0HKR0rNeQHjNkPb7mvWW6FY68j8ZSL6ei7wsPkYNba9d/QtKoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00ad7f8c60983bdc48157fa38c03513afca8e58e6315ca6f6dd53bd8a0f307c8","last_reissued_at":"2026-05-17T23:49:49.823229Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:49.823229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.04878","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":"2026-05-17T23:49:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CByX0WEOdeA3ynMqGHeUlQ0S3Mzwo+G1KLoE3o28nt02FaJJrktY41Cltf6OmWldbg86q9RIpc0ffd9l25YDDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T02:40:36.377825Z"},"content_sha256":"1693f66eda17582c798293a627b1a47ff14df6f958dd58db978bc9a4a3af1a22","schema_version":"1.0","event_id":"sha256:1693f66eda17582c798293a627b1a47ff14df6f958dd58db978bc9a4a3af1a22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ACWX7DDATA55YSAVP6RYYA2RHL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Onsager type conjecture and renormalized solutions for the relativistic Vlasov Maxwell system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claude Bardos, Nicolas Besse, Toan T. Nguyen","submitted_at":"2019-03-12T12:56:16Z","abstract_excerpt":"In this paper we give a proof of an Onsager type conjecture on conservation of energy and entropies of weak solutions to the relativistic Vlasov--Maxwell equations. As concerns the regularity of weak solutions, say in Sobolev spaces $W^{\\alpha,p}$, we determine Onsager type exponents $\\alpha$ that guarantee the conservation of all entropies. In particular, the Onsager exponent $\\alpha$ is smaller than $\\alpha = 1/3$ established for fluid models. Entropies conservation is equivalent to the renormalization property, which have been introduced by DiPerna--Lions for studying well-posedness of pass"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04878","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":"2026-05-17T23:49:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmCNKevQmtXO7TSq3xgFcoyp+DLZcXfVZhnZdp3Fj+PxSutisnMeNelly1LIgSBYIKpnngsN07Qc7JPWJJ54DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T02:40:36.378471Z"},"content_sha256":"ef4ad48194522f2cf08839ae67d5c245631b27df8ae3319139413c4b636e25dd","schema_version":"1.0","event_id":"sha256:ef4ad48194522f2cf08839ae67d5c245631b27df8ae3319139413c4b636e25dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ACWX7DDATA55YSAVP6RYYA2RHL/bundle.json","state_url":"https://pith.science/pith/ACWX7DDATA55YSAVP6RYYA2RHL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ACWX7DDATA55YSAVP6RYYA2RHL/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":"2026-08-22T02:40:36Z","links":{"resolver":"https://pith.science/pith/ACWX7DDATA55YSAVP6RYYA2RHL","bundle":"https://pith.science/pith/ACWX7DDATA55YSAVP6RYYA2RHL/bundle.json","state":"https://pith.science/pith/ACWX7DDATA55YSAVP6RYYA2RHL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ACWX7DDATA55YSAVP6RYYA2RHL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ACWX7DDATA55YSAVP6RYYA2RHL","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":"a4217fddafd97e807ca6bc3d5f726cfa53ea87400f25734719498492e748f37c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-12T12:56:16Z","title_canon_sha256":"b60e39f18ff6a91ef827eb9df0eb09577f12b0d77d8ffa1138f1503507e0eb6b"},"schema_version":"1.0","source":{"id":"1903.04878","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04878","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04878v2","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04878","created_at":"2026-05-17T23:49:49Z"},{"alias_kind":"pith_short_12","alias_value":"ACWX7DDATA55","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"ACWX7DDATA55YSAV","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"ACWX7DDA","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:ef4ad48194522f2cf08839ae67d5c245631b27df8ae3319139413c4b636e25dd","target":"graph","created_at":"2026-05-17T23:49:49Z","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":"In this paper we give a proof of an Onsager type conjecture on conservation of energy and entropies of weak solutions to the relativistic Vlasov--Maxwell equations. As concerns the regularity of weak solutions, say in Sobolev spaces $W^{\\alpha,p}$, we determine Onsager type exponents $\\alpha$ that guarantee the conservation of all entropies. In particular, the Onsager exponent $\\alpha$ is smaller than $\\alpha = 1/3$ established for fluid models. Entropies conservation is equivalent to the renormalization property, which have been introduced by DiPerna--Lions for studying well-posedness of pass","authors_text":"Claude Bardos, Nicolas Besse, Toan T. Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-12T12:56:16Z","title":"Onsager type conjecture and renormalized solutions for the relativistic Vlasov Maxwell system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04878","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":"sha256:1693f66eda17582c798293a627b1a47ff14df6f958dd58db978bc9a4a3af1a22","target":"record","created_at":"2026-05-17T23:49:49Z","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":"a4217fddafd97e807ca6bc3d5f726cfa53ea87400f25734719498492e748f37c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-12T12:56:16Z","title_canon_sha256":"b60e39f18ff6a91ef827eb9df0eb09577f12b0d77d8ffa1138f1503507e0eb6b"},"schema_version":"1.0","source":{"id":"1903.04878","kind":"arxiv","version":2}},"canonical_sha256":"00ad7f8c60983bdc48157fa38c03513afca8e58e6315ca6f6dd53bd8a0f307c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00ad7f8c60983bdc48157fa38c03513afca8e58e6315ca6f6dd53bd8a0f307c8","first_computed_at":"2026-05-17T23:49:49.823229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:49.823229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"icjeRMRXybJF3t86MPg8vrzWDh2JOqU/C8h0HKR0rNeQHjNkPb7mvWW6FY68j8ZSL6ei7wsPkYNba9d/QtKoAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:49.823663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.04878","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1693f66eda17582c798293a627b1a47ff14df6f958dd58db978bc9a4a3af1a22","sha256:ef4ad48194522f2cf08839ae67d5c245631b27df8ae3319139413c4b636e25dd"],"state_sha256":"bbb92b31310489cc33741e95300595b9c73058ff02c0e929aead457daaefaef3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSnXHo2/g5L3GizlqmVDFThyQpiyvnDkXtpmQpbnkp+G3fA07VZTr85oVJiXarMInypUrtN38fgKqB29vSDPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T02:40:36.383763Z","bundle_sha256":"1126d275eed2acceb29a7f1c50d18c94e0c5a8cdeb932ad8c4e870530bc4907b"}}