{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AYUMARJPHR36BCOJNLBTJCURBK","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":"a8bab804fe11d8fcc384f50a6ea01773dfef1cf15cb50945590970f916b3b1d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-11-09T16:02:07Z","title_canon_sha256":"858ec1c9dc0a86990d4ae8b6851ef7eab2cd372a80264d3a3938e2b7832a728c"},"schema_version":"1.0","source":{"id":"2511.06432","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.06432","created_at":"2026-06-09T02:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"2511.06432v4","created_at":"2026-06-09T02:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.06432","created_at":"2026-06-09T02:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"AYUMARJPHR36","created_at":"2026-06-09T02:07:12Z"},{"alias_kind":"pith_short_16","alias_value":"AYUMARJPHR36BCOJ","created_at":"2026-06-09T02:07:12Z"},{"alias_kind":"pith_short_8","alias_value":"AYUMARJP","created_at":"2026-06-09T02:07:12Z"}],"graph_snapshots":[{"event_id":"sha256:e073b96adc4a5dbdf41274294f003d594d7da635b37b501a5de90b8930f28972","target":"graph","created_at":"2026-06-09T02:07:12Z","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/2511.06432/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the long time behavior of solutions to the defocusing Calogero--Moser derivative nonlinear Schr\\\"odinger equation (CM-DNLS). Using the G\\'erard-type explicit formula, we prove the scattering result of solutions to this equation with initial data in $H_{+}^{1,\\alpha}(\\mathbb{R}): = \\{u \\in H_{+}^1(\\mathbb{R}): |x|^{\\alpha} u \\in L^2(\\mathbb{R})\\}$ with some $\\alpha>0$. We also characterize the scattering term using the distorted Fourier transform associated with the Lax operator. This is one of the first works that apply the G\\'erard-type explicit formula to study the lo","authors_text":"Xi Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-11-09T16:02:07Z","title":"Scattering of the defocusing Calogero--Moser derivative nonlinear Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.06432","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":"sha256:623cd6d1fee6c3f3dcc43415e3d825250df35b11f067dee685c5cfccf5cbeae8","target":"record","created_at":"2026-06-09T02:07:12Z","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":"a8bab804fe11d8fcc384f50a6ea01773dfef1cf15cb50945590970f916b3b1d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-11-09T16:02:07Z","title_canon_sha256":"858ec1c9dc0a86990d4ae8b6851ef7eab2cd372a80264d3a3938e2b7832a728c"},"schema_version":"1.0","source":{"id":"2511.06432","kind":"arxiv","version":4}},"canonical_sha256":"0628c0452f3c77e089c96ac3348a910a9964d1ec6ac44db3095fa1d3c5fd02d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0628c0452f3c77e089c96ac3348a910a9964d1ec6ac44db3095fa1d3c5fd02d8","first_computed_at":"2026-06-09T02:07:12.577437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:12.577437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T+UORoHceHuPVUAdLp1X9/xwfnAMiiqwwjHWWsw9kps56Xa+dl6ALuVCoO2VCXwBYyHmpaYuoG0lHYu1Cd+xAQ==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:12.578092Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.06432","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:623cd6d1fee6c3f3dcc43415e3d825250df35b11f067dee685c5cfccf5cbeae8","sha256:e073b96adc4a5dbdf41274294f003d594d7da635b37b501a5de90b8930f28972"],"state_sha256":"47e5ae500a98e39f5cf7d00ec5b3ce288fb59ebc89661f7c617791dd8acbf486"}