{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LW3GWL4XXPKI4UI2CHWLERNXVI","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":"e4c79a7c6173af1082c293ba7e21170f472130137b5cfdb1e924fc4d4a2fdf2a","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-09T11:28:42Z","title_canon_sha256":"24ce9ffeff38ce7548dbfcf59c934e3062e75caf58f9133f7b1c64f9fd3cd0b0"},"schema_version":"1.0","source":{"id":"1407.2438","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2438","created_at":"2026-05-18T00:43:36Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2438v2","created_at":"2026-05-18T00:43:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2438","created_at":"2026-05-18T00:43:36Z"},{"alias_kind":"pith_short_12","alias_value":"LW3GWL4XXPKI","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LW3GWL4XXPKI4UI2","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LW3GWL4X","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:c4ffa3a9d1290c55af0075154b7824724f585fc0e0d420d81a4e7e594f29b1ec","target":"graph","created_at":"2026-05-18T00:43:36Z","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 prove finite time supercritical blowup in a parity-time-symmetric system of the two coupled nonlinear Schr\\\"odinger (NLS) equations. One of the equations contains gain and the other one contains dissipation such that strengths of the gain and dissipation are equal. We address two cases: in the first model all nonlinear coefficients (i.e. the ones describing self-action and non-linear coupling) correspond to attractive (focusing) nonlinearities, and in the second case the NLS equation with gain has attractive nonlinearity while the NLS equation with dissipation has repulsive (defocusing) non","authors_text":"Dmitry A. Zezyulin, Jo\\~ao-Paulo Dias, M\\'ario Figueira, Vladimir V. Konotop","cross_cats":["physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-09T11:28:42Z","title":"Supercritical blowup in coupled parity-time-symmetric nonlinear Schr\\\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2438","kind":"arxiv","version":2},"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":"sha256:53edb127cc6324dec3a0dded388b06a31f1d28463c6f136e52414dbacbd0505a","target":"record","created_at":"2026-05-18T00:43:36Z","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":"e4c79a7c6173af1082c293ba7e21170f472130137b5cfdb1e924fc4d4a2fdf2a","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-09T11:28:42Z","title_canon_sha256":"24ce9ffeff38ce7548dbfcf59c934e3062e75caf58f9133f7b1c64f9fd3cd0b0"},"schema_version":"1.0","source":{"id":"1407.2438","kind":"arxiv","version":2}},"canonical_sha256":"5db66b2f97bbd48e511a11ecb245b7aa1529acc2601ba5946fd6e887dbc37cba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5db66b2f97bbd48e511a11ecb245b7aa1529acc2601ba5946fd6e887dbc37cba","first_computed_at":"2026-05-18T00:43:36.270195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:36.270195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zpOIejBSJyandQ/iVKFKOQjv3gfxPL9mnGpp9SgoiJ6k0tJvG2/2a4aQUEUDpqWjX2fXgCfsVj+lW4tWInPBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:36.270613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2438","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53edb127cc6324dec3a0dded388b06a31f1d28463c6f136e52414dbacbd0505a","sha256:c4ffa3a9d1290c55af0075154b7824724f585fc0e0d420d81a4e7e594f29b1ec"],"state_sha256":"1f62c49ace4d884ba5ed9500501a09f1d72c8c549bd47eb036492c55fe563124"}