{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:NVTZS32IQU22COYPX577RE6JTD","short_pith_number":"pith:NVTZS32I","canonical_record":{"source":{"id":"2110.08763","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2021-10-17T08:51:00Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"dd628294d644302cf8412b858cdca3b27b52d53012ff300547ffa3ee67776003","abstract_canon_sha256":"8805e4e7a3affcb519d219e59819b1af960f589cce4fae5d3986adbc3080916b"},"schema_version":"1.0"},"canonical_sha256":"6d67996f488535a13b0fbf7ff893c998cc704d941bbaad96bb084be0d19753c7","source":{"kind":"arxiv","id":"2110.08763","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.08763","created_at":"2026-07-05T04:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"2110.08763v2","created_at":"2026-07-05T04:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.08763","created_at":"2026-07-05T04:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"NVTZS32IQU22","created_at":"2026-07-05T04:00:59Z"},{"alias_kind":"pith_short_16","alias_value":"NVTZS32IQU22COYP","created_at":"2026-07-05T04:00:59Z"},{"alias_kind":"pith_short_8","alias_value":"NVTZS32I","created_at":"2026-07-05T04:00:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:NVTZS32IQU22COYPX577RE6JTD","target":"record","payload":{"canonical_record":{"source":{"id":"2110.08763","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2021-10-17T08:51:00Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"dd628294d644302cf8412b858cdca3b27b52d53012ff300547ffa3ee67776003","abstract_canon_sha256":"8805e4e7a3affcb519d219e59819b1af960f589cce4fae5d3986adbc3080916b"},"schema_version":"1.0"},"canonical_sha256":"6d67996f488535a13b0fbf7ff893c998cc704d941bbaad96bb084be0d19753c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:00:59.176797Z","signature_b64":"qwDITpEMEPPMmzyYCFnGF2OzLclg589lDih7onyNgphDwhulcn9cFAudEePjI5UhtWRL/XUwojl/gy4Km1+7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d67996f488535a13b0fbf7ff893c998cc704d941bbaad96bb084be0d19753c7","last_reissued_at":"2026-07-05T04:00:59.176352Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:00:59.176352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.08763","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KbKuessBsxKEcFRvZfUI5E99gZp0bFZg85EQGxlqf6v5f8Wb1Z2hKz0sBUD4kKCdPR/3uGobsAVAILnqftiRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T10:56:07.938010Z"},"content_sha256":"e00ba9a082068627015bd46cb93058804aa802bff62256903133d18d89e940ea","schema_version":"1.0","event_id":"sha256:e00ba9a082068627015bd46cb93058804aa802bff62256903133d18d89e940ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:NVTZS32IQU22COYPX577RE6JTD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral analysis and long-time asymptotics of complex mKdV equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"nlin.SI","authors_text":"Hong-Yi Zhang, Yu-Feng Zhang","submitted_at":"2021-10-17T08:51:00Z","abstract_excerpt":"In this paper, we obtain the long-time asymptotics of complex mKdV equation via Defit-Zhou method (Non-linear steepest descent method). The Cauchy problem of complex mKdV equation is transformed into the corresponding Riemann-Hilbert problem on the basis of the Lax pair and the scattering matrix. After that Riemann-Hilbert problems are converted through a decomposition of the matrix-valued spectral function and factorizations of the jump matrix for Riemann-Hilbert problem. Finally, by solving the last model problem, the long-time asymptotics of complex mKdV equation are derived."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.08763","kind":"arxiv","version":2},"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/2110.08763/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":"2026-07-05T04:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3F3tsUxp1jamkvccaseRU8IsRodDOPpt+5998u+sSXB6+cpcecExloCzI5800GVNsT7D0a8xcjtQnXZm8KVvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T10:56:07.938526Z"},"content_sha256":"35529e70ef6a81f445e22a1f536cabcce7d90e687ea36168d0d0df3defaf9b26","schema_version":"1.0","event_id":"sha256:35529e70ef6a81f445e22a1f536cabcce7d90e687ea36168d0d0df3defaf9b26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NVTZS32IQU22COYPX577RE6JTD/bundle.json","state_url":"https://pith.science/pith/NVTZS32IQU22COYPX577RE6JTD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NVTZS32IQU22COYPX577RE6JTD/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":"2026-08-19T10:56:07Z","links":{"resolver":"https://pith.science/pith/NVTZS32IQU22COYPX577RE6JTD","bundle":"https://pith.science/pith/NVTZS32IQU22COYPX577RE6JTD/bundle.json","state":"https://pith.science/pith/NVTZS32IQU22COYPX577RE6JTD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NVTZS32IQU22COYPX577RE6JTD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:NVTZS32IQU22COYPX577RE6JTD","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":"8805e4e7a3affcb519d219e59819b1af960f589cce4fae5d3986adbc3080916b","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2021-10-17T08:51:00Z","title_canon_sha256":"dd628294d644302cf8412b858cdca3b27b52d53012ff300547ffa3ee67776003"},"schema_version":"1.0","source":{"id":"2110.08763","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.08763","created_at":"2026-07-05T04:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"2110.08763v2","created_at":"2026-07-05T04:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.08763","created_at":"2026-07-05T04:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"NVTZS32IQU22","created_at":"2026-07-05T04:00:59Z"},{"alias_kind":"pith_short_16","alias_value":"NVTZS32IQU22COYP","created_at":"2026-07-05T04:00:59Z"},{"alias_kind":"pith_short_8","alias_value":"NVTZS32I","created_at":"2026-07-05T04:00:59Z"}],"graph_snapshots":[{"event_id":"sha256:35529e70ef6a81f445e22a1f536cabcce7d90e687ea36168d0d0df3defaf9b26","target":"graph","created_at":"2026-07-05T04:00:59Z","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/2110.08763/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we obtain the long-time asymptotics of complex mKdV equation via Defit-Zhou method (Non-linear steepest descent method). The Cauchy problem of complex mKdV equation is transformed into the corresponding Riemann-Hilbert problem on the basis of the Lax pair and the scattering matrix. After that Riemann-Hilbert problems are converted through a decomposition of the matrix-valued spectral function and factorizations of the jump matrix for Riemann-Hilbert problem. Finally, by solving the last model problem, the long-time asymptotics of complex mKdV equation are derived.","authors_text":"Hong-Yi Zhang, Yu-Feng Zhang","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2021-10-17T08:51:00Z","title":"Spectral analysis and long-time asymptotics of complex mKdV equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.08763","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:e00ba9a082068627015bd46cb93058804aa802bff62256903133d18d89e940ea","target":"record","created_at":"2026-07-05T04:00:59Z","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":"8805e4e7a3affcb519d219e59819b1af960f589cce4fae5d3986adbc3080916b","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2021-10-17T08:51:00Z","title_canon_sha256":"dd628294d644302cf8412b858cdca3b27b52d53012ff300547ffa3ee67776003"},"schema_version":"1.0","source":{"id":"2110.08763","kind":"arxiv","version":2}},"canonical_sha256":"6d67996f488535a13b0fbf7ff893c998cc704d941bbaad96bb084be0d19753c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d67996f488535a13b0fbf7ff893c998cc704d941bbaad96bb084be0d19753c7","first_computed_at":"2026-07-05T04:00:59.176352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:00:59.176352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qwDITpEMEPPMmzyYCFnGF2OzLclg589lDih7onyNgphDwhulcn9cFAudEePjI5UhtWRL/XUwojl/gy4Km1+7BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:00:59.176797Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.08763","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e00ba9a082068627015bd46cb93058804aa802bff62256903133d18d89e940ea","sha256:35529e70ef6a81f445e22a1f536cabcce7d90e687ea36168d0d0df3defaf9b26"],"state_sha256":"1759b0ceaa9ef64d8880ed7bb9db73f44b9069286a147f9b9f9a134f10e0bc5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IykpyRC1NtrBB+txr/dy/TaUHvF0Cnyo7twXjkhK149qRdNYTjft8//3wdC3SanH1QMSx6b8HGB0SR4ZDW1KCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T10:56:07.943085Z","bundle_sha256":"aca7962c7557e090b90579ab95f1236c2556d97d68e25c23ac853a6238126fcb"}}