{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FZ2IKHTC22PYZLBP3E24ZKCCUY","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":"eeea3d50f1a4a7b13878862963f9bb1bf8a3054c690fde2ac8142f01429752b6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-18T08:58:56Z","title_canon_sha256":"6311d587e258ee708055d143ff37db31bcdd2b7d6fe05263b967e18f5376da30"},"schema_version":"1.0","source":{"id":"1304.5056","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5056","created_at":"2026-05-18T03:27:31Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5056v2","created_at":"2026-05-18T03:27:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5056","created_at":"2026-05-18T03:27:31Z"},{"alias_kind":"pith_short_12","alias_value":"FZ2IKHTC22PY","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FZ2IKHTC22PYZLBP","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FZ2IKHTC","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:81de92cc85412350da1d3fe62da715317853c498d8e69b5dabee7469188feaf4","target":"graph","created_at":"2026-05-18T03:27:31Z","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":"As a continuation of our previous work on the subject, we prove new measure invariance results for the Benjamin-Ono equation. The measures are associated with conservation laws whose leading term is a fractional Sobolev norm of order larger or equal than 5/2. The new ingredient, compared with the case of conservation laws whose leading term is an integer Sobolev norm of order larger or equal than 3 (that has been studied in our previous work), is the use of suitable orthogonality relations satisfied by multilinear products of centered complex independent gaussian variables. We also give some p","authors_text":"Nicola Visciglia, Nikolay Tzvetkov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-18T08:58:56Z","title":"Invariant measures and long time behaviour for the Benjamin-Ono equation II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5056","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:c24ba2dd655e2ca1a03a469022503227efc0dbd7d02eb13fecb2a73b5c50dbb8","target":"record","created_at":"2026-05-18T03:27:31Z","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":"eeea3d50f1a4a7b13878862963f9bb1bf8a3054c690fde2ac8142f01429752b6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-18T08:58:56Z","title_canon_sha256":"6311d587e258ee708055d143ff37db31bcdd2b7d6fe05263b967e18f5376da30"},"schema_version":"1.0","source":{"id":"1304.5056","kind":"arxiv","version":2}},"canonical_sha256":"2e74851e62d69f8cac2fd935cca842a601a185aedfde950dcd79e2d3a0724aed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e74851e62d69f8cac2fd935cca842a601a185aedfde950dcd79e2d3a0724aed","first_computed_at":"2026-05-18T03:27:31.824089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:31.824089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tcrOksRklb41u8cDHqArGSHqEFFiKZH+8PERpH9ThdlTI95ry1cQoNrmA9qeJevZxykzKWT6g6IDXWghUpWbCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:31.824962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5056","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c24ba2dd655e2ca1a03a469022503227efc0dbd7d02eb13fecb2a73b5c50dbb8","sha256:81de92cc85412350da1d3fe62da715317853c498d8e69b5dabee7469188feaf4"],"state_sha256":"7b0c83f0b5c8e304ed27ee66a31f6c265e8b7f0b72edfa300859f0e27e58dfc8"}