{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DZE3SROTNAF64WUHUYIAK6LQKS","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":"6bf34f97f0b63d7622341f9370d9647e8a3c32a92616a3e9ce2b7af0d6a3722c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-08T17:39:29Z","title_canon_sha256":"c67f38f146e6dc5c4dc87e7b6adeec22d839693c6f44cb2bac93b238a013839f"},"schema_version":"1.0","source":{"id":"1612.02738","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02738","created_at":"2026-05-18T00:47:42Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02738v3","created_at":"2026-05-18T00:47:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02738","created_at":"2026-05-18T00:47:42Z"},{"alias_kind":"pith_short_12","alias_value":"DZE3SROTNAF6","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DZE3SROTNAF64WUH","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DZE3SROT","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:30577f459db1e3fb3d8f96ac3e3ff5f96e2eb43e43e3790d662098da45a9771f","target":"graph","created_at":"2026-05-18T00:47:42Z","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":"This paper is concerned with time global behavior of solutions to nonlinear Schr\\\"odinger equation with a non-vanishing condition at the spatial infinity. Under a non-vanishing condition, it would be expected that the behavior is determined by the shape of the nonlinear term around the non-vanishing state. To observe this phenomenon, we introduce a generalized version of the Gross-Pitaevskii equation, which is a typical equation involving a non-vanishing condition, by modifying the shape of nonlinearity around the non-vanishing state. It turns out that, if the nonlinearity decays fast as a sol","authors_text":"Hayato Miyazaki, Satoshi Masaki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-08T17:39:29Z","title":"Global behavior of solutions to generalized Gross-Pitaevskii equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02738","kind":"arxiv","version":3},"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":"sha256:34b381f323b69ec95a240cadc449651cd5fbc5abe5a33d858fffc3fbce150178","target":"record","created_at":"2026-05-18T00:47:42Z","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":"6bf34f97f0b63d7622341f9370d9647e8a3c32a92616a3e9ce2b7af0d6a3722c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-08T17:39:29Z","title_canon_sha256":"c67f38f146e6dc5c4dc87e7b6adeec22d839693c6f44cb2bac93b238a013839f"},"schema_version":"1.0","source":{"id":"1612.02738","kind":"arxiv","version":3}},"canonical_sha256":"1e49b945d3680bee5a87a610057970549e7f23c394889bc609000aa52fd8eda4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e49b945d3680bee5a87a610057970549e7f23c394889bc609000aa52fd8eda4","first_computed_at":"2026-05-18T00:47:42.316402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:42.316402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ttWs1LknnlsNff892+rtRqfC6DVOUPgyG7GbYyd7FMcTbLy8wQgqu8TJnERSguBSsKwVg0Rn3oCJVs7kg03uDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:42.317240Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02738","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34b381f323b69ec95a240cadc449651cd5fbc5abe5a33d858fffc3fbce150178","sha256:30577f459db1e3fb3d8f96ac3e3ff5f96e2eb43e43e3790d662098da45a9771f"],"state_sha256":"a32ec554097f5e66131c0c052278ba18e9a301671c43bd0f4047d33a7b81daba"}