{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YYMAYAIP44C77HGXGDDAGVGPQC","short_pith_number":"pith:YYMAYAIP","canonical_record":{"source":{"id":"1307.0619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-02T08:19:40Z","cross_cats_sorted":[],"title_canon_sha256":"acb4535a2eff12a6b1578b74d27e2e96051d2d035e31cbc5e671c697ca732c40","abstract_canon_sha256":"66759aeb9d5b4c41ee99b722a92eedaa851e5e5c336ce7e920cee8abc78f89bb"},"schema_version":"1.0"},"canonical_sha256":"c6180c010fe705ff9cd730c60354cf80aa3955c49c1ef91a9d93dbff4e6ae16e","source":{"kind":"arxiv","id":"1307.0619","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0619","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0619v1","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0619","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"pith_short_12","alias_value":"YYMAYAIP44C7","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YYMAYAIP44C77HGX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YYMAYAIP","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YYMAYAIP44C77HGXGDDAGVGPQC","target":"record","payload":{"canonical_record":{"source":{"id":"1307.0619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-02T08:19:40Z","cross_cats_sorted":[],"title_canon_sha256":"acb4535a2eff12a6b1578b74d27e2e96051d2d035e31cbc5e671c697ca732c40","abstract_canon_sha256":"66759aeb9d5b4c41ee99b722a92eedaa851e5e5c336ce7e920cee8abc78f89bb"},"schema_version":"1.0"},"canonical_sha256":"c6180c010fe705ff9cd730c60354cf80aa3955c49c1ef91a9d93dbff4e6ae16e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:25.115612Z","signature_b64":"XpeFKSQnsqlsNUTaX2yVCjH2gFY27fOGt0tFYtIAb6JDfqN60zspnOFv9M2Dyferdhvp9yeBzo5OR2He0jyFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6180c010fe705ff9cd730c60354cf80aa3955c49c1ef91a9d93dbff4e6ae16e","last_reissued_at":"2026-05-18T03:19:25.114901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:25.114901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.0619","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":"2026-05-18T03:19:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5+QPSG501OgTFNRyyfSJqFifHBRh6FtQR8d8eFvEOVxmUxNPVmNSIAO0YOfJCY/X3VH+TeJd6gIJPFp2A9ELAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:03:04.143615Z"},"content_sha256":"669ace09f0f25256d3dc9516c0a05df66fb15cc7600a9b5d575e9830780c47cd","schema_version":"1.0","event_id":"sha256:669ace09f0f25256d3dc9516c0a05df66fb15cc7600a9b5d575e9830780c47cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YYMAYAIP44C77HGXGDDAGVGPQC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the use of normal forms in the propagation of random waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anne-Sophie de Suzzoni","submitted_at":"2013-07-02T08:19:40Z","abstract_excerpt":"We consider the evolution of the correlations between the Fourier coeficients of a solution of the Kamdostev-Petviavshvili II equation when these coefficients are initially independent random variables. We use the structure of normal forms of the equation to prove that those correlations remain small until times of order $\\varepsilon^{-5/3}$ or $\\varepsilon^{-2}$ depending on the quantity considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0619","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":"2026-05-18T03:19:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jr3rrAQ8c6iolG+M2Oh7WjocfSLCKOBF4Qfu5K4pHjA/TI6GAWD5aejtzgu+Gu+ePlpQaQz2GgNV9hKWDX7bAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:03:04.144260Z"},"content_sha256":"2850529da6da226e57e75ced701f0d096086d8e08bf5e1c2ef16e6e916e4d250","schema_version":"1.0","event_id":"sha256:2850529da6da226e57e75ced701f0d096086d8e08bf5e1c2ef16e6e916e4d250"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYMAYAIP44C77HGXGDDAGVGPQC/bundle.json","state_url":"https://pith.science/pith/YYMAYAIP44C77HGXGDDAGVGPQC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYMAYAIP44C77HGXGDDAGVGPQC/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":"2026-05-29T15:03:04Z","links":{"resolver":"https://pith.science/pith/YYMAYAIP44C77HGXGDDAGVGPQC","bundle":"https://pith.science/pith/YYMAYAIP44C77HGXGDDAGVGPQC/bundle.json","state":"https://pith.science/pith/YYMAYAIP44C77HGXGDDAGVGPQC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYMAYAIP44C77HGXGDDAGVGPQC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YYMAYAIP44C77HGXGDDAGVGPQC","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":"66759aeb9d5b4c41ee99b722a92eedaa851e5e5c336ce7e920cee8abc78f89bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-02T08:19:40Z","title_canon_sha256":"acb4535a2eff12a6b1578b74d27e2e96051d2d035e31cbc5e671c697ca732c40"},"schema_version":"1.0","source":{"id":"1307.0619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0619","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0619v1","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0619","created_at":"2026-05-18T03:19:25Z"},{"alias_kind":"pith_short_12","alias_value":"YYMAYAIP44C7","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YYMAYAIP44C77HGX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YYMAYAIP","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:2850529da6da226e57e75ced701f0d096086d8e08bf5e1c2ef16e6e916e4d250","target":"graph","created_at":"2026-05-18T03:19:25Z","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 consider the evolution of the correlations between the Fourier coeficients of a solution of the Kamdostev-Petviavshvili II equation when these coefficients are initially independent random variables. We use the structure of normal forms of the equation to prove that those correlations remain small until times of order $\\varepsilon^{-5/3}$ or $\\varepsilon^{-2}$ depending on the quantity considered.","authors_text":"Anne-Sophie de Suzzoni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-02T08:19:40Z","title":"On the use of normal forms in the propagation of random waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0619","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":"sha256:669ace09f0f25256d3dc9516c0a05df66fb15cc7600a9b5d575e9830780c47cd","target":"record","created_at":"2026-05-18T03:19:25Z","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":"66759aeb9d5b4c41ee99b722a92eedaa851e5e5c336ce7e920cee8abc78f89bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-02T08:19:40Z","title_canon_sha256":"acb4535a2eff12a6b1578b74d27e2e96051d2d035e31cbc5e671c697ca732c40"},"schema_version":"1.0","source":{"id":"1307.0619","kind":"arxiv","version":1}},"canonical_sha256":"c6180c010fe705ff9cd730c60354cf80aa3955c49c1ef91a9d93dbff4e6ae16e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6180c010fe705ff9cd730c60354cf80aa3955c49c1ef91a9d93dbff4e6ae16e","first_computed_at":"2026-05-18T03:19:25.114901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:25.114901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XpeFKSQnsqlsNUTaX2yVCjH2gFY27fOGt0tFYtIAb6JDfqN60zspnOFv9M2Dyferdhvp9yeBzo5OR2He0jyFDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:25.115612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:669ace09f0f25256d3dc9516c0a05df66fb15cc7600a9b5d575e9830780c47cd","sha256:2850529da6da226e57e75ced701f0d096086d8e08bf5e1c2ef16e6e916e4d250"],"state_sha256":"14efa0d4f4753e6eb1872c552b2aba24f3f68357e07fac57da73396cbceeb669"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iA6jhZIB2Ok0fgPFks6eoZBFM61YUVskMq/D7/o1ar/BPftsVd2mFIXBxXgQr7Epe3CHLGgAB84n+AsgCStlAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:03:04.147593Z","bundle_sha256":"851bc9c5820da0e5ddec3db64b52843e05c69ea2059682d8feecfabce58a3aa2"}}