{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:S7RM264GPL6WCHLBGSTN5MTXJ7","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":"ffd1f0f1c37b4c23fbb227b278d96b4829299eafd8d6036e7c5f5a4d83645a60","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-03T17:45:43Z","title_canon_sha256":"ede3189410dd94bd14a4dec0f0250aced478dccb3a5e2f917d3a331f7aa782ba"},"schema_version":"1.0","source":{"id":"2608.02567","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.02567","created_at":"2026-08-04T02:44:09Z"},{"alias_kind":"arxiv_version","alias_value":"2608.02567v1","created_at":"2026-08-04T02:44:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.02567","created_at":"2026-08-04T02:44:09Z"},{"alias_kind":"pith_short_12","alias_value":"S7RM264GPL6W","created_at":"2026-08-04T02:44:09Z"},{"alias_kind":"pith_short_16","alias_value":"S7RM264GPL6WCHLB","created_at":"2026-08-04T02:44:09Z"},{"alias_kind":"pith_short_8","alias_value":"S7RM264G","created_at":"2026-08-04T02:44:09Z"}],"graph_snapshots":[{"event_id":"sha256:d5d23d987221e35451ddcc05e0feadd9f66b9b672ec93f22c66a37f14a41ae7d","target":"graph","created_at":"2026-08-04T02:44:09Z","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/2608.02567/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the Talbot effect for the periodic Benjamin--Ono equation with rough initial data. Using the smoothing theorem of G\\'erard--Kappeler--Topalov for Tao's gauge transform, we reduce the singularity analysis to an explicit quadratic gauge profile. For general bounded-variation data we obtain a rational-time gauge-Hardy representation. For a natural subclass of Talbot-admissible data, whose initial gauge profile has only finitely many edge singularities, this representation becomes a finite sum of logarithmic kernels and one-jump kernels, up to a continuous remainder. We show that finite-j","authors_text":"Xi Chen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-03T17:45:43Z","title":"Talbot effect for the periodic Benjamin--Ono equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02567","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:e65c50e5112a06891cfb6f6af6bb4ed3c83642596741ad34cd38900207ff7464","target":"record","created_at":"2026-08-04T02:44:09Z","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":"ffd1f0f1c37b4c23fbb227b278d96b4829299eafd8d6036e7c5f5a4d83645a60","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-03T17:45:43Z","title_canon_sha256":"ede3189410dd94bd14a4dec0f0250aced478dccb3a5e2f917d3a331f7aa782ba"},"schema_version":"1.0","source":{"id":"2608.02567","kind":"arxiv","version":1}},"canonical_sha256":"97e2cd7b867afd611d6134a6deb2774fef773192f201eae49d39eabdd1a6c5cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97e2cd7b867afd611d6134a6deb2774fef773192f201eae49d39eabdd1a6c5cc","first_computed_at":"2026-08-04T02:44:09.133671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:44:09.133671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cGQRtHLkDzFQ7j044wJq31L5AO8jfND01cgg+zphoJV5z207lH1+o5MCmXHiqD8jYfKKV1s/h6wG0IF9VINxCA==","signature_status":"signed_v1","signed_at":"2026-08-04T02:44:09.136009Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.02567","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e65c50e5112a06891cfb6f6af6bb4ed3c83642596741ad34cd38900207ff7464","sha256:d5d23d987221e35451ddcc05e0feadd9f66b9b672ec93f22c66a37f14a41ae7d"],"state_sha256":"02153277ed0231191801b0e07a008ab165f36ae47c1a0d3da0fb6f3a50327b93"}