{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TJBKCDEZPPFEH3RTOFBSIUJI27","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":"31e747058f7c904959592dc9763623b3c4159efa1c4b72ef7ce516c7885bc71b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-24T17:46:19Z","title_canon_sha256":"a596dd54e1cfb99b2ffc22e88d14df4a7e6b67d0c075c206100f96577adecbff"},"schema_version":"1.0","source":{"id":"1109.5291","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5291","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5291v2","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5291","created_at":"2026-05-18T03:51:48Z"},{"alias_kind":"pith_short_12","alias_value":"TJBKCDEZPPFE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TJBKCDEZPPFEH3RT","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TJBKCDEZ","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:ad56249e6cef2e821810700b333eb29cb70ef16b98384555d0a18ffe59103c40","target":"graph","created_at":"2026-05-18T03:51:48Z","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":"Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.","authors_text":"N. Tzvetkov, N. Visciglia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-24T17:46:19Z","title":"Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5291","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":"sha256:835cfca35b7695535fb0d92abb2ce0aaa0d2d0f12af18e4978b218262b682c5f","target":"record","created_at":"2026-05-18T03:51:48Z","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":"31e747058f7c904959592dc9763623b3c4159efa1c4b72ef7ce516c7885bc71b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-24T17:46:19Z","title_canon_sha256":"a596dd54e1cfb99b2ffc22e88d14df4a7e6b67d0c075c206100f96577adecbff"},"schema_version":"1.0","source":{"id":"1109.5291","kind":"arxiv","version":2}},"canonical_sha256":"9a42a10c997bca43ee337143245128d7fb04e5d9a608eb095a6f261c51be85b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a42a10c997bca43ee337143245128d7fb04e5d9a608eb095a6f261c51be85b9","first_computed_at":"2026-05-18T03:51:48.780099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:48.780099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YEe0jtdz0dbOJQIpIx2egDwJNhHtwv5OrrJMXorz6ATcNWKLcwvlDkH+UfKXk8FQjX2tZvI+HerJrEXXWcMnBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:48.781032Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5291","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:835cfca35b7695535fb0d92abb2ce0aaa0d2d0f12af18e4978b218262b682c5f","sha256:ad56249e6cef2e821810700b333eb29cb70ef16b98384555d0a18ffe59103c40"],"state_sha256":"108db2e701debe547e0098f83cf69eb703426df7a3c375b18943504cd572bffc"}