{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NFGQD2KMROZNUHZXZFNNCDV6BJ","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":"edf7f9929bce9e79fbb676a02b5b63920975a768acb42da30c4302421afc0ee2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2025-12-26T03:03:29Z","title_canon_sha256":"769901d2c89a49bd6f815861059163b090f819f53d40b0a0c03e8627702d4160"},"schema_version":"1.0","source":{"id":"2512.21841","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.21841","created_at":"2026-06-23T01:11:59Z"},{"alias_kind":"arxiv_version","alias_value":"2512.21841v2","created_at":"2026-06-23T01:11:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.21841","created_at":"2026-06-23T01:11:59Z"},{"alias_kind":"pith_short_12","alias_value":"NFGQD2KMROZN","created_at":"2026-06-23T01:11:59Z"},{"alias_kind":"pith_short_16","alias_value":"NFGQD2KMROZNUHZX","created_at":"2026-06-23T01:11:59Z"},{"alias_kind":"pith_short_8","alias_value":"NFGQD2KM","created_at":"2026-06-23T01:11:59Z"}],"graph_snapshots":[{"event_id":"sha256:be1117b6854a06d4b031aaac6e3589d07760b7efb8998a6b606dd11e26606216","target":"graph","created_at":"2026-06-23T01:11:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2512.21841/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Manakov system is a two-component nonlinear Schr\\\"odinger equation. In this paper, we derive a long-time asymptotic formula for the solution of the defocusing Manakov system with nonzero boundary conditions and provide a detailed proof. We first formulate the inverse problem as a $3\\times3$ matrix Riemann--Hilbert problem. We then carry out the Deift--Zhou steepest descent analysis for this Riemann--Hilbert problem and obtain the long-time asymptotics in the space-time soliton region. In this region, the leading order of the solution takes the form of a modulated multisoliton. Apart from t","authors_text":"Haibing Zhang, Jiao Wei, Xianguo Geng","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2025-12-26T03:03:29Z","title":"Large-time asymptotics for the defocusing Manakov system on a nonzero background"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.21841","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":"sha256:2a48deaa991d140f4e30a84da28335f9432b5540b5d8fc4ba2adab833813a735","target":"record","created_at":"2026-06-23T01:11:59Z","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":"edf7f9929bce9e79fbb676a02b5b63920975a768acb42da30c4302421afc0ee2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2025-12-26T03:03:29Z","title_canon_sha256":"769901d2c89a49bd6f815861059163b090f819f53d40b0a0c03e8627702d4160"},"schema_version":"1.0","source":{"id":"2512.21841","kind":"arxiv","version":2}},"canonical_sha256":"694d01e94c8bb2da1f37c95ad10ebe0a45bddc6de43646b0e428f5d40eb31bc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"694d01e94c8bb2da1f37c95ad10ebe0a45bddc6de43646b0e428f5d40eb31bc8","first_computed_at":"2026-06-23T01:11:59.708538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T01:11:59.708538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RAN0TYle7z/YQPpOZd1nsYfM8D7DHmeDwi5/WQeUxF6+iCcdgadwFQ5h2+0wFAFZuRHtKoRby0x38Rq0TQXpBQ==","signature_status":"signed_v1","signed_at":"2026-06-23T01:11:59.709232Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.21841","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a48deaa991d140f4e30a84da28335f9432b5540b5d8fc4ba2adab833813a735","sha256:be1117b6854a06d4b031aaac6e3589d07760b7efb8998a6b606dd11e26606216"],"state_sha256":"00b3a10295078323988a9d286f1bc4d0298d2b5d42b939fea9d8260340d1e30e"}