{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5IIG4J5R6KJUESS4MM363PJA7L","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":"50a9ee72230cd098b22b3f02eaad1078324a4359ff6eac1fcfe14b33d45fa7ea","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-07T15:07:01Z","title_canon_sha256":"9ebf28d6dec88f474c02188ec44bee2411f449fe60a075b8a9c1b6156b4f0ae9"},"schema_version":"1.0","source":{"id":"1307.1873","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1873","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1873v4","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1873","created_at":"2026-05-18T00:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"5IIG4J5R6KJU","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5IIG4J5R6KJUESS4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5IIG4J5R","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:c95c0dedf69835bd9dc26cfff7485e2dac9b7afd0358fbd6771a3eafa2d36a9a","target":"graph","created_at":"2026-05-18T00:18:41Z","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 explore further the rarefaction wave-like solutions recently discussed in work of the second author with J. Colliander, T. Oh and G. Simpson for a model Hamiltonian dynamical system derived by Colliander-Keel-Staffilani-Takaoka-Tao to study frequency cascades in the cubic defocusing nonlinear Schr\\\"odinger equation on the torus.","authors_text":"Jeremy L. Marzuola, Sebastian Herr","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-07T15:07:01Z","title":"On discrete rarefaction waves in a nonlinear Schr\\\"odinger equation toy model for weak turbulence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1873","kind":"arxiv","version":4},"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":"sha256:1cf3489490e18f96a2a7c97e66c7e657cb2d1674c113039f5712feb365a4b53a","target":"record","created_at":"2026-05-18T00:18:41Z","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":"50a9ee72230cd098b22b3f02eaad1078324a4359ff6eac1fcfe14b33d45fa7ea","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-07T15:07:01Z","title_canon_sha256":"9ebf28d6dec88f474c02188ec44bee2411f449fe60a075b8a9c1b6156b4f0ae9"},"schema_version":"1.0","source":{"id":"1307.1873","kind":"arxiv","version":4}},"canonical_sha256":"ea106e27b1f293424a5c6337edbd20fafc1ca4b4f298eaafeb6eb547b213c349","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea106e27b1f293424a5c6337edbd20fafc1ca4b4f298eaafeb6eb547b213c349","first_computed_at":"2026-05-18T00:18:41.964549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:41.964549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l+buysjzbQ2vMb586bAQOQPYdYV2RIlewIqr4tTRFnEsZU2/t/02PJeFMfQHzCbV6jQx3EG7DOF6fVoBE4veDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:41.965013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1873","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cf3489490e18f96a2a7c97e66c7e657cb2d1674c113039f5712feb365a4b53a","sha256:c95c0dedf69835bd9dc26cfff7485e2dac9b7afd0358fbd6771a3eafa2d36a9a"],"state_sha256":"4af16b3e33efef02f1c1bce632ff2fb6691283baca9ba590eaed5ddc9896cf72"}