{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:6NO7NXXRPQXP67T6LXRGSC3JSO","short_pith_number":"pith:6NO7NXXR","canonical_record":{"source":{"id":"1903.03855","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-09T19:27:43Z","cross_cats_sorted":[],"title_canon_sha256":"44d566bbb5541c4aab6063b9e7d4855a7d611b7bd7c7080ba86c214cb0b09a76","abstract_canon_sha256":"005850323b9707d9264cf15bf249219c3ded7aad004dd825a7159919bae3645f"},"schema_version":"1.0"},"canonical_sha256":"f35df6def17c2eff7e7e5de2690b699390a8e55566f7a93604ddddc2a4acb3ea","source":{"kind":"arxiv","id":"1903.03855","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.03855","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1903.03855v3","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.03855","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"6NO7NXXRPQXP","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_16","alias_value":"6NO7NXXRPQXP67T6","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_8","alias_value":"6NO7NXXR","created_at":"2026-07-05T04:11:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:6NO7NXXRPQXP67T6LXRGSC3JSO","target":"record","payload":{"canonical_record":{"source":{"id":"1903.03855","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-09T19:27:43Z","cross_cats_sorted":[],"title_canon_sha256":"44d566bbb5541c4aab6063b9e7d4855a7d611b7bd7c7080ba86c214cb0b09a76","abstract_canon_sha256":"005850323b9707d9264cf15bf249219c3ded7aad004dd825a7159919bae3645f"},"schema_version":"1.0"},"canonical_sha256":"f35df6def17c2eff7e7e5de2690b699390a8e55566f7a93604ddddc2a4acb3ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:11:22.204994Z","signature_b64":"Ub9QzuBRGFxqLnineq1xUabLGIsSuspQIKjdOKGxFcrYRNcntnzb9qSVdH2eZ8G0eM+DDGyySd3iDd7SYScVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f35df6def17c2eff7e7e5de2690b699390a8e55566f7a93604ddddc2a4acb3ea","last_reissued_at":"2026-07-05T04:11:22.204584Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:11:22.204584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.03855","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"txbhjuV6lfXR6bbixZI2DAbNjWmQHmy0gH9AdIdE5SLJJtRDCTfwj0HVj2BpjAWXam0FeICnpHwwpqmQc057AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:43:09.434593Z"},"content_sha256":"822bfbac5510b31c0a1f703ae421fb30ad5731074a0ef1aac9838f65647ef49b","schema_version":"1.0","event_id":"sha256:822bfbac5510b31c0a1f703ae421fb30ad5731074a0ef1aac9838f65647ef49b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:6NO7NXXRPQXP67T6LXRGSC3JSO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gong Chen, Jiaqi Liu","submitted_at":"2019-03-09T19:27:43Z","abstract_excerpt":"The long time behavior of solutions to the defocusing modified Korteweg-de vries (MKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method of Deift and Zhou and its reformulation by Dieng and McLaughlin through $\\overline{\\partial}$-derivatives. To extend the asymptotics to solutions with initial data in lower regularity spaces, we apply a global approximation via PDE techniques."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03855","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.03855/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K3E3wCGstDSrARtdIG5qCmSz6hPx9LFzo9F6HbGYaCROLcH/Fhu7dGH0r0RMoMS1ACCR8FTPRpJ056XFcJI1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:43:09.435118Z"},"content_sha256":"8b995cd875bd7b10700ac2547f866e54e91ac1e3df9011dec37a476873f068a1","schema_version":"1.0","event_id":"sha256:8b995cd875bd7b10700ac2547f866e54e91ac1e3df9011dec37a476873f068a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NO7NXXRPQXP67T6LXRGSC3JSO/bundle.json","state_url":"https://pith.science/pith/6NO7NXXRPQXP67T6LXRGSC3JSO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NO7NXXRPQXP67T6LXRGSC3JSO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-11T11:43:09Z","links":{"resolver":"https://pith.science/pith/6NO7NXXRPQXP67T6LXRGSC3JSO","bundle":"https://pith.science/pith/6NO7NXXRPQXP67T6LXRGSC3JSO/bundle.json","state":"https://pith.science/pith/6NO7NXXRPQXP67T6LXRGSC3JSO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NO7NXXRPQXP67T6LXRGSC3JSO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6NO7NXXRPQXP67T6LXRGSC3JSO","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":"005850323b9707d9264cf15bf249219c3ded7aad004dd825a7159919bae3645f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-09T19:27:43Z","title_canon_sha256":"44d566bbb5541c4aab6063b9e7d4855a7d611b7bd7c7080ba86c214cb0b09a76"},"schema_version":"1.0","source":{"id":"1903.03855","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.03855","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1903.03855v3","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.03855","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"6NO7NXXRPQXP","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_16","alias_value":"6NO7NXXRPQXP67T6","created_at":"2026-07-05T04:11:22Z"},{"alias_kind":"pith_short_8","alias_value":"6NO7NXXR","created_at":"2026-07-05T04:11:22Z"}],"graph_snapshots":[{"event_id":"sha256:8b995cd875bd7b10700ac2547f866e54e91ac1e3df9011dec37a476873f068a1","target":"graph","created_at":"2026-07-05T04:11:22Z","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/1903.03855/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The long time behavior of solutions to the defocusing modified Korteweg-de vries (MKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method of Deift and Zhou and its reformulation by Dieng and McLaughlin through $\\overline{\\partial}$-derivatives. To extend the asymptotics to solutions with initial data in lower regularity spaces, we apply a global approximation via PDE techniques.","authors_text":"Gong Chen, Jiaqi Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-09T19:27:43Z","title":"Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03855","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":"sha256:822bfbac5510b31c0a1f703ae421fb30ad5731074a0ef1aac9838f65647ef49b","target":"record","created_at":"2026-07-05T04:11:22Z","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":"005850323b9707d9264cf15bf249219c3ded7aad004dd825a7159919bae3645f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-09T19:27:43Z","title_canon_sha256":"44d566bbb5541c4aab6063b9e7d4855a7d611b7bd7c7080ba86c214cb0b09a76"},"schema_version":"1.0","source":{"id":"1903.03855","kind":"arxiv","version":3}},"canonical_sha256":"f35df6def17c2eff7e7e5de2690b699390a8e55566f7a93604ddddc2a4acb3ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f35df6def17c2eff7e7e5de2690b699390a8e55566f7a93604ddddc2a4acb3ea","first_computed_at":"2026-07-05T04:11:22.204584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:11:22.204584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ub9QzuBRGFxqLnineq1xUabLGIsSuspQIKjdOKGxFcrYRNcntnzb9qSVdH2eZ8G0eM+DDGyySd3iDd7SYScVCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:11:22.204994Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.03855","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:822bfbac5510b31c0a1f703ae421fb30ad5731074a0ef1aac9838f65647ef49b","sha256:8b995cd875bd7b10700ac2547f866e54e91ac1e3df9011dec37a476873f068a1"],"state_sha256":"05ca3469154254a9ee89d8a87fc6c9ba3dd6b8d155379264c006d4c90a70cf57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wyViR9gp5Of0kd8ID7tcx84P+5+K/Kq8e5Ohg0yn1QEeMXhrYLpcTkKoa77KvArtO/OxRchSUhBi/vEvUnVEAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T11:43:09.439419Z","bundle_sha256":"d3f4136edfbad1fd54e308b7791884fe29d7c4c1cc027ead102cefe4351f060f"}}