{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KR27EELXQZMKRNEILV3BBTGUEN","short_pith_number":"pith:KR27EELX","canonical_record":{"source":{"id":"1412.0318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-01T01:03:04Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d380c461dc42dbba89520e3abf1030a76b9cb49d703df3185b598b9bbf935730","abstract_canon_sha256":"60d926208f8debbe7b668a6cc58e8f803b755f64043c892cc6bc037100277efa"},"schema_version":"1.0"},"canonical_sha256":"5475f211778658a8b4885d7610ccd4234bafbd9d5d9ddd20f6ddff55c052668e","source":{"kind":"arxiv","id":"1412.0318","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0318","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0318v1","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0318","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"pith_short_12","alias_value":"KR27EELXQZMK","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KR27EELXQZMKRNEI","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KR27EELX","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KR27EELXQZMKRNEILV3BBTGUEN","target":"record","payload":{"canonical_record":{"source":{"id":"1412.0318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-01T01:03:04Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d380c461dc42dbba89520e3abf1030a76b9cb49d703df3185b598b9bbf935730","abstract_canon_sha256":"60d926208f8debbe7b668a6cc58e8f803b755f64043c892cc6bc037100277efa"},"schema_version":"1.0"},"canonical_sha256":"5475f211778658a8b4885d7610ccd4234bafbd9d5d9ddd20f6ddff55c052668e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:05.757369Z","signature_b64":"9IUWEKM+iCiGXk292BmHbw3EfNhqaH/drT16PwlmI11Avi7jNAWMpL9vCynlbIsHaoTQcB91sf5mrxOuCK+cBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5475f211778658a8b4885d7610ccd4234bafbd9d5d9ddd20f6ddff55c052668e","last_reissued_at":"2026-05-18T00:31:05.756758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:05.756758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.0318","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":"2026-05-18T00:31:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FO6XdLjG0ZenegWovkLHLnS1DtHPaVeOnnI3xvDiFVlvemZjnsNpl1BbW6VL38KD2qULaVolq1qG2z0b50yPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:03:36.258644Z"},"content_sha256":"201b7925e2c7ebe6a0473dd999441e67f0c76b2f65e4a597ab133d3760202093","schema_version":"1.0","event_id":"sha256:201b7925e2c7ebe6a0473dd999441e67f0c76b2f65e4a597ab133d3760202093"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KR27EELXQZMKRNEILV3BBTGUEN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Formation of three-dimensional surface waves on deep-water using elliptic solutions of nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"physics.flu-dyn","authors_text":"Frederique Drullion, Shahrdad G. Sajjadi, Stefan C. Mancas","submitted_at":"2014-12-01T01:03:04Z","abstract_excerpt":"A review of three-dimensional waves on deep-water is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these three-dimensional waves is given through cubic nonlinear Schr\\\"odinger equation. The periodic solutions of the cubic nonlinear Schr\\\"odinger equation are found using Weierstrass elliptic $\\wp$ functions. It is shown that the classification of solutions depends on the boundary conditions, wavenumber and frequency. For certain parameters, Weierstrass $\\wp$ functions are reduced to periodic, hyperboli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0318","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":"2026-05-18T00:31:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sLzsxTao8X3/JpLGZaIcnYdGVWoSEs98DsHJFnCVOa9nMqaDqdAy0tPX+6FeSq9Yk3CvWIg22ABSGZveDU6MBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:03:36.258995Z"},"content_sha256":"4b2e78667633f9e86eaa89ece92fdb0d68aa6835d198a7bd0a9967ef4052fe34","schema_version":"1.0","event_id":"sha256:4b2e78667633f9e86eaa89ece92fdb0d68aa6835d198a7bd0a9967ef4052fe34"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KR27EELXQZMKRNEILV3BBTGUEN/bundle.json","state_url":"https://pith.science/pith/KR27EELXQZMKRNEILV3BBTGUEN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KR27EELXQZMKRNEILV3BBTGUEN/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":"2026-06-23T06:03:36Z","links":{"resolver":"https://pith.science/pith/KR27EELXQZMKRNEILV3BBTGUEN","bundle":"https://pith.science/pith/KR27EELXQZMKRNEILV3BBTGUEN/bundle.json","state":"https://pith.science/pith/KR27EELXQZMKRNEILV3BBTGUEN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KR27EELXQZMKRNEILV3BBTGUEN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KR27EELXQZMKRNEILV3BBTGUEN","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":"60d926208f8debbe7b668a6cc58e8f803b755f64043c892cc6bc037100277efa","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-01T01:03:04Z","title_canon_sha256":"d380c461dc42dbba89520e3abf1030a76b9cb49d703df3185b598b9bbf935730"},"schema_version":"1.0","source":{"id":"1412.0318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0318","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0318v1","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0318","created_at":"2026-05-18T00:31:05Z"},{"alias_kind":"pith_short_12","alias_value":"KR27EELXQZMK","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KR27EELXQZMKRNEI","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KR27EELX","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:4b2e78667633f9e86eaa89ece92fdb0d68aa6835d198a7bd0a9967ef4052fe34","target":"graph","created_at":"2026-05-18T00:31:05Z","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":"A review of three-dimensional waves on deep-water is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these three-dimensional waves is given through cubic nonlinear Schr\\\"odinger equation. The periodic solutions of the cubic nonlinear Schr\\\"odinger equation are found using Weierstrass elliptic $\\wp$ functions. It is shown that the classification of solutions depends on the boundary conditions, wavenumber and frequency. For certain parameters, Weierstrass $\\wp$ functions are reduced to periodic, hyperboli","authors_text":"Frederique Drullion, Shahrdad G. Sajjadi, Stefan C. Mancas","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-01T01:03:04Z","title":"Formation of three-dimensional surface waves on deep-water using elliptic solutions of nonlinear Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0318","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":"sha256:201b7925e2c7ebe6a0473dd999441e67f0c76b2f65e4a597ab133d3760202093","target":"record","created_at":"2026-05-18T00:31:05Z","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":"60d926208f8debbe7b668a6cc58e8f803b755f64043c892cc6bc037100277efa","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2014-12-01T01:03:04Z","title_canon_sha256":"d380c461dc42dbba89520e3abf1030a76b9cb49d703df3185b598b9bbf935730"},"schema_version":"1.0","source":{"id":"1412.0318","kind":"arxiv","version":1}},"canonical_sha256":"5475f211778658a8b4885d7610ccd4234bafbd9d5d9ddd20f6ddff55c052668e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5475f211778658a8b4885d7610ccd4234bafbd9d5d9ddd20f6ddff55c052668e","first_computed_at":"2026-05-18T00:31:05.756758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:05.756758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9IUWEKM+iCiGXk292BmHbw3EfNhqaH/drT16PwlmI11Avi7jNAWMpL9vCynlbIsHaoTQcB91sf5mrxOuCK+cBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:05.757369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:201b7925e2c7ebe6a0473dd999441e67f0c76b2f65e4a597ab133d3760202093","sha256:4b2e78667633f9e86eaa89ece92fdb0d68aa6835d198a7bd0a9967ef4052fe34"],"state_sha256":"66aa01239438f5a7a39b56c794e976f24569e815a84b94fc6317367d56b7173f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4F+vL7mqCbrNCxgG5hKosUzEx1Jzpoy/KHSrjAN2n6/EVy93Zjwp6ZWuJJ7KfMBt/iKMX4xsKOgsZ/DsTiH5DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:03:36.260943Z","bundle_sha256":"fcf73e45f3d2a3f467cbeaad9d811dbcb6e839c1eef54c6abfceb5bff726ccb2"}}