{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JK3ZDCDA3SFG6CUVESAWXK5HKI","short_pith_number":"pith:JK3ZDCDA","canonical_record":{"source":{"id":"1601.04317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-01-17T17:42:07Z","cross_cats_sorted":["nlin.PS","physics.data-an","physics.flu-dyn","physics.optics"],"title_canon_sha256":"751cb2805f99fd34594dfd7d9bd3a5fd20b3e623b6eea56d63df7209b92b8ada","abstract_canon_sha256":"9920dbcac4c572c81030a976895ac9a04aef7c03c8e2e0e0445a61e01c81322e"},"schema_version":"1.0"},"canonical_sha256":"4ab7918860dc8a6f0a9524816baba7520adcb84d11b75ecd00c45d8e422515a9","source":{"kind":"arxiv","id":"1601.04317","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04317","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04317v1","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04317","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"pith_short_12","alias_value":"JK3ZDCDA3SFG","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JK3ZDCDA3SFG6CUV","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JK3ZDCDA","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JK3ZDCDA3SFG6CUVESAWXK5HKI","target":"record","payload":{"canonical_record":{"source":{"id":"1601.04317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-01-17T17:42:07Z","cross_cats_sorted":["nlin.PS","physics.data-an","physics.flu-dyn","physics.optics"],"title_canon_sha256":"751cb2805f99fd34594dfd7d9bd3a5fd20b3e623b6eea56d63df7209b92b8ada","abstract_canon_sha256":"9920dbcac4c572c81030a976895ac9a04aef7c03c8e2e0e0445a61e01c81322e"},"schema_version":"1.0"},"canonical_sha256":"4ab7918860dc8a6f0a9524816baba7520adcb84d11b75ecd00c45d8e422515a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:12.215047Z","signature_b64":"EQmWeQnH6JOUqY4Epa6h51Q9pHW7019cUOoMRDFOqANkX8yl+rLzPZpLJtUp2/MA/ttCwOhLGQfkmyM5cyBWBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ab7918860dc8a6f0a9524816baba7520adcb84d11b75ecd00c45d8e422515a9","last_reissued_at":"2026-05-18T01:08:12.214456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:12.214456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.04317","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":"2026-05-18T01:08:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hC91Yzk0a1KijJOR05OB+oyiBEtn1X39xeOm2owF1/y8fhNuV98yErlMv4AP2XVQbEdxLmsZVmAQvU4J25IiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:58:20.187743Z"},"content_sha256":"a2c7c97e80924cb37ddb7effa05c26e946cc12bc99731bd46114b5767b1d63b1","schema_version":"1.0","event_id":"sha256:a2c7c97e80924cb37ddb7effa05c26e946cc12bc99731bd46114b5767b1d63b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JK3ZDCDA3SFG6CUVESAWXK5HKI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Origin of heavy tail statistics in equations of the Nonlinear Schr\\\"odinger type: an exact result","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS","physics.data-an","physics.flu-dyn","physics.optics"],"primary_cat":"nlin.CD","authors_text":"D. Proment, G. El, M. Onorato, P. Suret, S. Randoux","submitted_at":"2016-01-17T17:42:07Z","abstract_excerpt":"We study the formation of extreme events in incoherent systems described by envelope equations, such as the Nonliner Schr\\\"odinger equation. We derive an identity that relates the evolution of the kurtosis (a measure of the relevance of the tails in a probability density function) of the wave amplitude to the rate of change of the width of the Fourier spectrum of the wave field. The result is exact for all dispersive systems characterized by a nonlinear term of the form of the one contained in the Nonlinear Schr\\\"odinger equation. Numerical simulations are also performed to confirm our finding"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04317","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":"2026-05-18T01:08:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KZMBNxZ5xueIcJ3z8FJ03ksYCk8hydOWXN5NmDfYUDfR/7hxdDWR/C6V3MiQtr9TNV7OHa2H/btpki83apGHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:58:20.188446Z"},"content_sha256":"3bff83db0df3c96dd11e832103483550c2812e5816b8eba7e9fd8bef2dde0059","schema_version":"1.0","event_id":"sha256:3bff83db0df3c96dd11e832103483550c2812e5816b8eba7e9fd8bef2dde0059"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JK3ZDCDA3SFG6CUVESAWXK5HKI/bundle.json","state_url":"https://pith.science/pith/JK3ZDCDA3SFG6CUVESAWXK5HKI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JK3ZDCDA3SFG6CUVESAWXK5HKI/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":"2026-05-25T16:58:20Z","links":{"resolver":"https://pith.science/pith/JK3ZDCDA3SFG6CUVESAWXK5HKI","bundle":"https://pith.science/pith/JK3ZDCDA3SFG6CUVESAWXK5HKI/bundle.json","state":"https://pith.science/pith/JK3ZDCDA3SFG6CUVESAWXK5HKI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JK3ZDCDA3SFG6CUVESAWXK5HKI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JK3ZDCDA3SFG6CUVESAWXK5HKI","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":"9920dbcac4c572c81030a976895ac9a04aef7c03c8e2e0e0445a61e01c81322e","cross_cats_sorted":["nlin.PS","physics.data-an","physics.flu-dyn","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-01-17T17:42:07Z","title_canon_sha256":"751cb2805f99fd34594dfd7d9bd3a5fd20b3e623b6eea56d63df7209b92b8ada"},"schema_version":"1.0","source":{"id":"1601.04317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04317","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04317v1","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04317","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"pith_short_12","alias_value":"JK3ZDCDA3SFG","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JK3ZDCDA3SFG6CUV","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JK3ZDCDA","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:3bff83db0df3c96dd11e832103483550c2812e5816b8eba7e9fd8bef2dde0059","target":"graph","created_at":"2026-05-18T01:08:12Z","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 study the formation of extreme events in incoherent systems described by envelope equations, such as the Nonliner Schr\\\"odinger equation. We derive an identity that relates the evolution of the kurtosis (a measure of the relevance of the tails in a probability density function) of the wave amplitude to the rate of change of the width of the Fourier spectrum of the wave field. The result is exact for all dispersive systems characterized by a nonlinear term of the form of the one contained in the Nonlinear Schr\\\"odinger equation. Numerical simulations are also performed to confirm our finding","authors_text":"D. Proment, G. El, M. Onorato, P. Suret, S. Randoux","cross_cats":["nlin.PS","physics.data-an","physics.flu-dyn","physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-01-17T17:42:07Z","title":"Origin of heavy tail statistics in equations of the Nonlinear Schr\\\"odinger type: an exact result"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04317","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:a2c7c97e80924cb37ddb7effa05c26e946cc12bc99731bd46114b5767b1d63b1","target":"record","created_at":"2026-05-18T01:08:12Z","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":"9920dbcac4c572c81030a976895ac9a04aef7c03c8e2e0e0445a61e01c81322e","cross_cats_sorted":["nlin.PS","physics.data-an","physics.flu-dyn","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-01-17T17:42:07Z","title_canon_sha256":"751cb2805f99fd34594dfd7d9bd3a5fd20b3e623b6eea56d63df7209b92b8ada"},"schema_version":"1.0","source":{"id":"1601.04317","kind":"arxiv","version":1}},"canonical_sha256":"4ab7918860dc8a6f0a9524816baba7520adcb84d11b75ecd00c45d8e422515a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ab7918860dc8a6f0a9524816baba7520adcb84d11b75ecd00c45d8e422515a9","first_computed_at":"2026-05-18T01:08:12.214456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:12.214456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EQmWeQnH6JOUqY4Epa6h51Q9pHW7019cUOoMRDFOqANkX8yl+rLzPZpLJtUp2/MA/ttCwOhLGQfkmyM5cyBWBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:12.215047Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2c7c97e80924cb37ddb7effa05c26e946cc12bc99731bd46114b5767b1d63b1","sha256:3bff83db0df3c96dd11e832103483550c2812e5816b8eba7e9fd8bef2dde0059"],"state_sha256":"39cc44b568f9539354e290401d80a268f38048f09a93f564af5feb50dc17a979"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ecM+lkZE3vNix819NhTP4UgYo684oJAB2utIzOcZNIS4Njs1bm3tK2FPCDUcsnMKebhBTdsOC6Qw5fTNO9EFAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:58:20.191880Z","bundle_sha256":"76ab1038308f3f84142c33023c46cf56d30c7bb2749a0bd60758d38994601289"}}