{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:C3RCTUY3AVHQU75DQGTWGVIMAP","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":"f0b080550986745e0a15dec0355692f22660393d4384d40aceaa43ab7480e093","cross_cats_sorted":["nlin.SI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-02T00:50:26Z","title_canon_sha256":"a4347626f16e8d55fbf38a983ace33d8f8940218dde5c79ceadd57a648bb2ca6"},"schema_version":"1.0","source":{"id":"2606.02989","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02989","created_at":"2026-06-03T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02989v1","created_at":"2026-06-03T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02989","created_at":"2026-06-03T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"C3RCTUY3AVHQ","created_at":"2026-06-03T01:05:28Z"},{"alias_kind":"pith_short_16","alias_value":"C3RCTUY3AVHQU75D","created_at":"2026-06-03T01:05:28Z"},{"alias_kind":"pith_short_8","alias_value":"C3RCTUY3","created_at":"2026-06-03T01:05:28Z"}],"graph_snapshots":[{"event_id":"sha256:3c5cb042cb7370beab774a0481c2dd05a3e4b4e61d5225d58ccdebb8bc1796d1","target":"graph","created_at":"2026-06-03T01:05:28Z","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/2606.02989/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We obtain the leading term in the solution of the Cauchy problem for the Benjamin-Ono equation in the limit $t\\to+\\infty$ with $x=O(t^{1/2})$. We show that the rate of decay exceeds that of self-similar solutions and obtain an explicit universal profile for the decaying solution, relating it to the linearization of the profile equation for self-similar solutions. The proof assumes a class of rational initial data $u_0$ in $L^2(\\mathbb{R})\\cap L^1(\\mathbb{R})$ that exhibit generic behavior of the reflection coefficient at the origin.","authors_text":"Louise Gassot, Patrick G\\'erard, Peter D. Miller","cross_cats":["nlin.SI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-02T00:50:26Z","title":"The Benjamin-Ono Equation in the Long-Time Limit: Linearized Self-Similar Universality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02989","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":"sha256:13a50e41b26f9b8aa90ccc29e18b7651e767daff7a607deb44cee89b8b254b8d","target":"record","created_at":"2026-06-03T01:05:28Z","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":"f0b080550986745e0a15dec0355692f22660393d4384d40aceaa43ab7480e093","cross_cats_sorted":["nlin.SI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-02T00:50:26Z","title_canon_sha256":"a4347626f16e8d55fbf38a983ace33d8f8940218dde5c79ceadd57a648bb2ca6"},"schema_version":"1.0","source":{"id":"2606.02989","kind":"arxiv","version":1}},"canonical_sha256":"16e229d31b054f0a7fa381a763550c03c355d9561f324f66acf9c174e6403856","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16e229d31b054f0a7fa381a763550c03c355d9561f324f66acf9c174e6403856","first_computed_at":"2026-06-03T01:05:28.631410Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:28.631410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0H8Tfgw6NLMI8MT3VWSvIQFytkoE781KdqdSKBhD+elCRoiOkX96n2Lp264RQUj5xuvKbck1ZefWdjftoxUFBg==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:28.631823Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02989","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13a50e41b26f9b8aa90ccc29e18b7651e767daff7a607deb44cee89b8b254b8d","sha256:3c5cb042cb7370beab774a0481c2dd05a3e4b4e61d5225d58ccdebb8bc1796d1"],"state_sha256":"130f2b98b450acf996952d290daa7ac4db6490120918f07cadce3a273930f852"}