{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YNHP5AFURMEXRY7OCSPNVK3VXF","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":"6d1b840661c430c556a86ffdd20af0bf76fc81dc1e951a1022c258c4a83dd055","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-06T12:08:31Z","title_canon_sha256":"e82a184d59ae743f0310387ffd49a48693b5d623d5163b87da92baff13aa178d"},"schema_version":"1.0","source":{"id":"1907.03121","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03121","created_at":"2026-07-05T01:58:39Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03121v2","created_at":"2026-07-05T01:58:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03121","created_at":"2026-07-05T01:58:39Z"},{"alias_kind":"pith_short_12","alias_value":"YNHP5AFURMEX","created_at":"2026-07-05T01:58:39Z"},{"alias_kind":"pith_short_16","alias_value":"YNHP5AFURMEXRY7O","created_at":"2026-07-05T01:58:39Z"},{"alias_kind":"pith_short_8","alias_value":"YNHP5AFU","created_at":"2026-07-05T01:58:39Z"}],"graph_snapshots":[{"event_id":"sha256:48473f1ac2f30aa10e5088aefdcf4589362f29574e5aad1219abe49c67cb6f18","target":"graph","created_at":"2026-07-05T01:58:39Z","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/1907.03121/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we present a vector field method for the study of solutions to massless relativistic transport equations. Compared to the methodologie developped by Fajman-Joudioux-Smulevici, we remove the Lorentz boosts of the commutation vector fields, which makes our method more suitable for the study of systems coupling a massless Vlasov equation with an equation which has a different speed of propagation. We also believe that our approach can be adapted more easily to the context of curved backgrounds.\n  In a second time, we apply our method in order to derive sharp decay estimates on th","authors_text":"L\\'eo Bigorgne","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-06T12:08:31Z","title":"A vector field method for massless relativistic transport equations and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03121","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":"sha256:5fd69fc2f46bb511b96f4d907be75a6735183a9b8fe5b56b6977787daf9e2a4d","target":"record","created_at":"2026-07-05T01:58:39Z","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":"6d1b840661c430c556a86ffdd20af0bf76fc81dc1e951a1022c258c4a83dd055","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-06T12:08:31Z","title_canon_sha256":"e82a184d59ae743f0310387ffd49a48693b5d623d5163b87da92baff13aa178d"},"schema_version":"1.0","source":{"id":"1907.03121","kind":"arxiv","version":2}},"canonical_sha256":"c34efe80b48b0978e3ee149edaab75b961d1717d72baacb0f7dd63aeb945f606","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c34efe80b48b0978e3ee149edaab75b961d1717d72baacb0f7dd63aeb945f606","first_computed_at":"2026-07-05T01:58:39.373660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:58:39.373660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ovpmaZaQMfiRPOmx3S3DrgwLGmIJZ3BK2XynyvtaH6Pf4V68VNc/uPh6hNlD5hh3xvVFbanbzKjcUiGhbnk/Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T01:58:39.374121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.03121","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fd69fc2f46bb511b96f4d907be75a6735183a9b8fe5b56b6977787daf9e2a4d","sha256:48473f1ac2f30aa10e5088aefdcf4589362f29574e5aad1219abe49c67cb6f18"],"state_sha256":"881fab73dd63cb860c483a1a55a2f062e2fdabc1002fcc42d332c5eda709e747"}