{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QAQJZVANCKLJFJNPU7K6RTVOIN","short_pith_number":"pith:QAQJZVAN","canonical_record":{"source":{"id":"1704.02557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-04-09T02:54:45Z","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.PS","physics.optics"],"title_canon_sha256":"719e7b315a382ef2e7be4f8d424ae464e5e7285df9e27a6d0c400f71f0017943","abstract_canon_sha256":"34fbc213504cadeb95e9fe045664747ec1ff69a0563a55e3109addfb11ed0ae6"},"schema_version":"1.0"},"canonical_sha256":"80209cd40d129692a5afa7d5e8ceae4370599ffc9977e91701e182b7000ca9e4","source":{"kind":"arxiv","id":"1704.02557","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02557","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02557v1","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02557","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"pith_short_12","alias_value":"QAQJZVANCKLJ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QAQJZVANCKLJFJNP","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QAQJZVAN","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QAQJZVANCKLJFJNPU7K6RTVOIN","target":"record","payload":{"canonical_record":{"source":{"id":"1704.02557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-04-09T02:54:45Z","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.PS","physics.optics"],"title_canon_sha256":"719e7b315a382ef2e7be4f8d424ae464e5e7285df9e27a6d0c400f71f0017943","abstract_canon_sha256":"34fbc213504cadeb95e9fe045664747ec1ff69a0563a55e3109addfb11ed0ae6"},"schema_version":"1.0"},"canonical_sha256":"80209cd40d129692a5afa7d5e8ceae4370599ffc9977e91701e182b7000ca9e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:11.946963Z","signature_b64":"yqMF6Gq6KOtNPbHDY/BPjd36DieKG2ie0HLNLCoKLpAjC+Wl+jP71otncsMeXkdhIoi1HbJPg/drL2aUznsmAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80209cd40d129692a5afa7d5e8ceae4370599ffc9977e91701e182b7000ca9e4","last_reissued_at":"2026-05-18T00:46:11.946544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:11.946544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.02557","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tXXWX74MyTcrF5dG/wDdN5VpiLwa876meaaH+SEqRsuySXfNI6asMED3Bn6qTDwZLypvlSH5M4WG7FUMzyanCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:45:39.139748Z"},"content_sha256":"8c735660027cf39ed01f7bc6f29dd14ceb8e6bfc4835c3eaa0d26ee5b6e31008","schema_version":"1.0","event_id":"sha256:8c735660027cf39ed01f7bc6f29dd14ceb8e6bfc4835c3eaa0d26ee5b6e31008"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QAQJZVANCKLJFJNPU7K6RTVOIN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrodinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","nlin.PS","physics.optics"],"primary_cat":"nlin.SI","authors_text":"Xiao-Yong Wen, Yunqing Yang, Zhenya Yan","submitted_at":"2017-04-09T02:54:45Z","abstract_excerpt":"In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrodinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc. and may be useful to study "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02557","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:46:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aTZmZ5A2dIzbl0oEeeNWFBfvoNtt84eplmFKluZsWcfp55bTJ7FZlK2bfHbAbqlQto3pK6YkApatcvn4ik/GDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:45:39.140108Z"},"content_sha256":"99b60b785d3e2068ec37f0692fa47e001da5d9e31de6fd9ec3b682864c84d119","schema_version":"1.0","event_id":"sha256:99b60b785d3e2068ec37f0692fa47e001da5d9e31de6fd9ec3b682864c84d119"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QAQJZVANCKLJFJNPU7K6RTVOIN/bundle.json","state_url":"https://pith.science/pith/QAQJZVANCKLJFJNPU7K6RTVOIN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QAQJZVANCKLJFJNPU7K6RTVOIN/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":"2026-06-05T11:45:39Z","links":{"resolver":"https://pith.science/pith/QAQJZVANCKLJFJNPU7K6RTVOIN","bundle":"https://pith.science/pith/QAQJZVANCKLJFJNPU7K6RTVOIN/bundle.json","state":"https://pith.science/pith/QAQJZVANCKLJFJNPU7K6RTVOIN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QAQJZVANCKLJFJNPU7K6RTVOIN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QAQJZVANCKLJFJNPU7K6RTVOIN","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":"34fbc213504cadeb95e9fe045664747ec1ff69a0563a55e3109addfb11ed0ae6","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.PS","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-04-09T02:54:45Z","title_canon_sha256":"719e7b315a382ef2e7be4f8d424ae464e5e7285df9e27a6d0c400f71f0017943"},"schema_version":"1.0","source":{"id":"1704.02557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02557","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02557v1","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02557","created_at":"2026-05-18T00:46:11Z"},{"alias_kind":"pith_short_12","alias_value":"QAQJZVANCKLJ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QAQJZVANCKLJFJNP","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QAQJZVAN","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:99b60b785d3e2068ec37f0692fa47e001da5d9e31de6fd9ec3b682864c84d119","target":"graph","created_at":"2026-05-18T00:46:11Z","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":"In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrodinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc. and may be useful to study ","authors_text":"Xiao-Yong Wen, Yunqing Yang, Zhenya Yan","cross_cats":["math-ph","math.AP","math.MP","nlin.PS","physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-04-09T02:54:45Z","title":"Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrodinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02557","kind":"arxiv","version":1},"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":"sha256:8c735660027cf39ed01f7bc6f29dd14ceb8e6bfc4835c3eaa0d26ee5b6e31008","target":"record","created_at":"2026-05-18T00:46:11Z","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":"34fbc213504cadeb95e9fe045664747ec1ff69a0563a55e3109addfb11ed0ae6","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.PS","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-04-09T02:54:45Z","title_canon_sha256":"719e7b315a382ef2e7be4f8d424ae464e5e7285df9e27a6d0c400f71f0017943"},"schema_version":"1.0","source":{"id":"1704.02557","kind":"arxiv","version":1}},"canonical_sha256":"80209cd40d129692a5afa7d5e8ceae4370599ffc9977e91701e182b7000ca9e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80209cd40d129692a5afa7d5e8ceae4370599ffc9977e91701e182b7000ca9e4","first_computed_at":"2026-05-18T00:46:11.946544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:11.946544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yqMF6Gq6KOtNPbHDY/BPjd36DieKG2ie0HLNLCoKLpAjC+Wl+jP71otncsMeXkdhIoi1HbJPg/drL2aUznsmAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:11.946963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c735660027cf39ed01f7bc6f29dd14ceb8e6bfc4835c3eaa0d26ee5b6e31008","sha256:99b60b785d3e2068ec37f0692fa47e001da5d9e31de6fd9ec3b682864c84d119"],"state_sha256":"228ff894f40f86d85f9acfba523d240a508f72ad451104d4434d27df350ad44b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bHGvinMoS4IsLLmEsUAHt16spQ4HiwqUKtZ6RGJJvVDjSNmrKRVaiOjH66Zt1tdkcWK/fNHi2mT0PVutoyHSBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:45:39.142193Z","bundle_sha256":"a1914a21589dd85b007b62203d550b98c30a696735d50e8e9114c6a2e1cc82ca"}}