{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GBWOSZNSF6WARPZVELBHJII7CR","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":"cbad2071281dbefa4758c2db2e5a89dc391d42741e5afa2436dfc4026f322fdb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-28T13:27:09Z","title_canon_sha256":"f7d5652dd969228de2f795279c1613161ca95e73df096a86c1bf80ddbe5c79bc"},"schema_version":"1.0","source":{"id":"1412.8165","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.8165","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"1412.8165v1","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8165","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"GBWOSZNSF6WA","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GBWOSZNSF6WARPZV","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GBWOSZNS","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:1b2d1efb28fd17755fc7acc0b3913133234caec6d6b39f7153339fe60defc17a","target":"graph","created_at":"2026-05-18T02:30:23Z","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 provide a simple proof of the existence of dark solitons of the defocusing cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity. Moreover, our proof allows for a broader class of inhomogeneities and gives some new properties of the solutions. We also apply our approach to the defocusing cubic-quintic nonlinear Schrodinger equation with a periodic potential.","authors_text":"Christos Sourdis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-28T13:27:09Z","title":"On the existence of dark solitons of the cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8165","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:b8a02b634fd25bf503b6c15f5d09d7315f82e685e63a2022a13424249c6da0a8","target":"record","created_at":"2026-05-18T02:30:23Z","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":"cbad2071281dbefa4758c2db2e5a89dc391d42741e5afa2436dfc4026f322fdb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-28T13:27:09Z","title_canon_sha256":"f7d5652dd969228de2f795279c1613161ca95e73df096a86c1bf80ddbe5c79bc"},"schema_version":"1.0","source":{"id":"1412.8165","kind":"arxiv","version":1}},"canonical_sha256":"306ce965b22fac08bf3522c274a11f144c5d90a2a6be65584e673966aac9d281","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"306ce965b22fac08bf3522c274a11f144c5d90a2a6be65584e673966aac9d281","first_computed_at":"2026-05-18T02:30:23.902603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:23.902603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZT3r7m60aFysM66oMca39jOeRWRWDuKCnryHlyjsxQMxJBrENwYnXXJ3VqHObyWve3qbgVFXF7ie3w5G5NxtBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:23.903361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.8165","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8a02b634fd25bf503b6c15f5d09d7315f82e685e63a2022a13424249c6da0a8","sha256:1b2d1efb28fd17755fc7acc0b3913133234caec6d6b39f7153339fe60defc17a"],"state_sha256":"01866e31825906dba2e8f40cb355066538846f475dc3329158162280cb759e50"}