{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WIKICHR5OC74O2M6HJYGO2E2NB","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":"5807cc98368c72bd285c7b94de5bcd481f369fee56a659df59c6858d0bafa67b","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-21T14:03:48Z","title_canon_sha256":"055df4be6dadc3014149917a0e98a98ebe4055848c52ae10e197dfe0fa816c6b"},"schema_version":"1.0","source":{"id":"2304.10964","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.10964","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"2304.10964v3","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.10964","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"WIKICHR5OC74","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_16","alias_value":"WIKICHR5OC74O2M6","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_8","alias_value":"WIKICHR5","created_at":"2026-06-19T16:11:07Z"}],"graph_snapshots":[{"event_id":"sha256:facecb1514410e90db7ba267d75241f3bf30dea8c06fac34837537bd59d7beab","target":"graph","created_at":"2026-06-19T16:11:07Z","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/2304.10964/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss the Lugiato-Lefever equation and its variant with third-order dispersion, which are mathematical models used to describe how a light beam forms patterns within an optical cavity. It is mathematically demonstrated that the solutions of these equations follow the Talbot effect, which is a phenomenon of periodic self-imaging of an object under certain conditions of diffraction. The Talbot effect is regarded as the underlying cause of pattern formation in optical cavities.","authors_text":"Gunwoo Cho, Ihyeok Seo, Seongyeon Kim","cross_cats":["physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-21T14:03:48Z","title":"Talbot effect for the third order Lugiato-Lefever equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.10964","kind":"arxiv","version":3},"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:dd41e91fb710bd968be0a284edbf7915f2fe59a23a7a0f9a90830aa594b83ef1","target":"record","created_at":"2026-06-19T16:11:07Z","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":"5807cc98368c72bd285c7b94de5bcd481f369fee56a659df59c6858d0bafa67b","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-21T14:03:48Z","title_canon_sha256":"055df4be6dadc3014149917a0e98a98ebe4055848c52ae10e197dfe0fa816c6b"},"schema_version":"1.0","source":{"id":"2304.10964","kind":"arxiv","version":3}},"canonical_sha256":"b214811e3d70bfc7699e3a7067689a686cf94b503278fb761bb23b4bcb411eec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b214811e3d70bfc7699e3a7067689a686cf94b503278fb761bb23b4bcb411eec","first_computed_at":"2026-06-19T16:11:07.592620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:07.592620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xJZiEbHg/Gs6mObk6DB7kpX2C/My2GNzHhQGrkhjOj+eCXUb89xXmdxxjHQ7AoU5zNf3xVdBUe0m++2gVHXyDA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:07.593006Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.10964","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd41e91fb710bd968be0a284edbf7915f2fe59a23a7a0f9a90830aa594b83ef1","sha256:facecb1514410e90db7ba267d75241f3bf30dea8c06fac34837537bd59d7beab"],"state_sha256":"9b0bdfc190945e83c91aa5c85d3f8e768b30f54e78bc0abe5284270ed8e77689"}