{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QVFQCNTMNQITXSSXANPKOCFFZE","short_pith_number":"pith:QVFQCNTM","canonical_record":{"source":{"id":"1304.2619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-09T14:45:20Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"c6efdd3086843565b99cc9fbf583c47bfe51e3d7fa9ce85a71429f2f5d39305f","abstract_canon_sha256":"2695286793e1a417b5e431e03e9a7bb634db5b5f3d3ce4c1c01db868762e661e"},"schema_version":"1.0"},"canonical_sha256":"854b01366c6c113bca57035ea708a5c90181e63437f8c8e8640869ff8740a4d5","source":{"kind":"arxiv","id":"1304.2619","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2619","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2619v1","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2619","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"pith_short_12","alias_value":"QVFQCNTMNQIT","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QVFQCNTMNQITXSSX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QVFQCNTM","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QVFQCNTMNQITXSSXANPKOCFFZE","target":"record","payload":{"canonical_record":{"source":{"id":"1304.2619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-09T14:45:20Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"c6efdd3086843565b99cc9fbf583c47bfe51e3d7fa9ce85a71429f2f5d39305f","abstract_canon_sha256":"2695286793e1a417b5e431e03e9a7bb634db5b5f3d3ce4c1c01db868762e661e"},"schema_version":"1.0"},"canonical_sha256":"854b01366c6c113bca57035ea708a5c90181e63437f8c8e8640869ff8740a4d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:31.281605Z","signature_b64":"l8/k6TY06trLR04amnlQx6/epQsufT9DmN6W7x8YDNHurZBq493g8qhuySoPfrOFgldbw3Ix3uTf1KVJen4tAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"854b01366c6c113bca57035ea708a5c90181e63437f8c8e8640869ff8740a4d5","last_reissued_at":"2026-05-18T03:28:31.280775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:31.280775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.2619","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+pn1DbKhbV6VvodJl6lUqcCxGRtVwUiub9kmpNx84c+uUlgYGu6A9PzIglWsYwoN4qlsGhdDLLc3fRtHV5WbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:59:02.154067Z"},"content_sha256":"23aaa0c4a633c39079c246601250e6a7f06fb3787a9893024f1668f45ca70f56","schema_version":"1.0","event_id":"sha256:23aaa0c4a633c39079c246601250e6a7f06fb3787a9893024f1668f45ca70f56"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QVFQCNTMNQITXSSXANPKOCFFZE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An explicit formula for the cubic Szeg\\\"o equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Patrick G\\'erard (LM-Orsay), Sandrine Grellier (MAPMO)","submitted_at":"2013-04-09T14:45:20Z","abstract_excerpt":"We derive an explicit formula for the general solution of the cubic Szeg\\\"o equation and of the evolution equation of the corresponding hierarchy. As an application, we prove that all the solutions corresponding to finite rank Hankel operators are quasiperiodic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2619","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7oWtM1D6H/YQT7SGe/gydv3ykOCRjVKTxp4VqIWvSmZzZrEcHoUIYnx1umNs+5uiZhIWit+EiPqCsLAvGJuJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:59:02.154914Z"},"content_sha256":"69b65276755836e1d3cb1f1024ad056d726692fd610895ab1cf0fb2216cbec4a","schema_version":"1.0","event_id":"sha256:69b65276755836e1d3cb1f1024ad056d726692fd610895ab1cf0fb2216cbec4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVFQCNTMNQITXSSXANPKOCFFZE/bundle.json","state_url":"https://pith.science/pith/QVFQCNTMNQITXSSXANPKOCFFZE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVFQCNTMNQITXSSXANPKOCFFZE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-20T05:59:02Z","links":{"resolver":"https://pith.science/pith/QVFQCNTMNQITXSSXANPKOCFFZE","bundle":"https://pith.science/pith/QVFQCNTMNQITXSSXANPKOCFFZE/bundle.json","state":"https://pith.science/pith/QVFQCNTMNQITXSSXANPKOCFFZE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVFQCNTMNQITXSSXANPKOCFFZE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QVFQCNTMNQITXSSXANPKOCFFZE","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":"2695286793e1a417b5e431e03e9a7bb634db5b5f3d3ce4c1c01db868762e661e","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-09T14:45:20Z","title_canon_sha256":"c6efdd3086843565b99cc9fbf583c47bfe51e3d7fa9ce85a71429f2f5d39305f"},"schema_version":"1.0","source":{"id":"1304.2619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2619","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2619v1","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2619","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"pith_short_12","alias_value":"QVFQCNTMNQIT","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QVFQCNTMNQITXSSX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QVFQCNTM","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:69b65276755836e1d3cb1f1024ad056d726692fd610895ab1cf0fb2216cbec4a","target":"graph","created_at":"2026-05-18T03:28:31Z","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":"We derive an explicit formula for the general solution of the cubic Szeg\\\"o equation and of the evolution equation of the corresponding hierarchy. As an application, we prove that all the solutions corresponding to finite rank Hankel operators are quasiperiodic.","authors_text":"Patrick G\\'erard (LM-Orsay), Sandrine Grellier (MAPMO)","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-09T14:45:20Z","title":"An explicit formula for the cubic Szeg\\\"o equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2619","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":"sha256:23aaa0c4a633c39079c246601250e6a7f06fb3787a9893024f1668f45ca70f56","target":"record","created_at":"2026-05-18T03:28:31Z","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":"2695286793e1a417b5e431e03e9a7bb634db5b5f3d3ce4c1c01db868762e661e","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-09T14:45:20Z","title_canon_sha256":"c6efdd3086843565b99cc9fbf583c47bfe51e3d7fa9ce85a71429f2f5d39305f"},"schema_version":"1.0","source":{"id":"1304.2619","kind":"arxiv","version":1}},"canonical_sha256":"854b01366c6c113bca57035ea708a5c90181e63437f8c8e8640869ff8740a4d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"854b01366c6c113bca57035ea708a5c90181e63437f8c8e8640869ff8740a4d5","first_computed_at":"2026-05-18T03:28:31.280775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:31.280775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l8/k6TY06trLR04amnlQx6/epQsufT9DmN6W7x8YDNHurZBq493g8qhuySoPfrOFgldbw3Ix3uTf1KVJen4tAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:31.281605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23aaa0c4a633c39079c246601250e6a7f06fb3787a9893024f1668f45ca70f56","sha256:69b65276755836e1d3cb1f1024ad056d726692fd610895ab1cf0fb2216cbec4a"],"state_sha256":"c037ab4f8d2b4b71d6383c88048e00c5c5bd00862ecbc1fe76dbd4da1c4e0908"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gWQ+Ux6y5Qj0xi7Ohuz1m4lhedl1QDCrkMahiM/CcZNeZFyUOmf0STSAjo43Hmtq4PCfLX2AUVzJ3b+heajPCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T05:59:02.158908Z","bundle_sha256":"b1945d8123fed7a81e93de8eee4d9cb92ab3617b2341d02b094ae7f00531294f"}}