{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XPGAMKISZOHARJBRNUHAKYSTPJ","short_pith_number":"pith:XPGAMKIS","canonical_record":{"source":{"id":"1612.06723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-12-20T15:59:18Z","cross_cats_sorted":[],"title_canon_sha256":"f4f67f0cd7c64ba4d7bbac2b9d23f94ddac7e1ec6c399037efbca90b62745715","abstract_canon_sha256":"4658a9d4104c9ae8978793fd3f6c4ba7d16c778e2238782fd31e83a167709d4a"},"schema_version":"1.0"},"canonical_sha256":"bbcc062912cb8e08a4316d0e0562537a523613543f9ae60c6f4cd113528bca77","source":{"kind":"arxiv","id":"1612.06723","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06723","created_at":"2026-05-18T00:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06723v1","created_at":"2026-05-18T00:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06723","created_at":"2026-05-18T00:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"XPGAMKISZOHA","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XPGAMKISZOHARJBR","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XPGAMKIS","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XPGAMKISZOHARJBRNUHAKYSTPJ","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-12-20T15:59:18Z","cross_cats_sorted":[],"title_canon_sha256":"f4f67f0cd7c64ba4d7bbac2b9d23f94ddac7e1ec6c399037efbca90b62745715","abstract_canon_sha256":"4658a9d4104c9ae8978793fd3f6c4ba7d16c778e2238782fd31e83a167709d4a"},"schema_version":"1.0"},"canonical_sha256":"bbcc062912cb8e08a4316d0e0562537a523613543f9ae60c6f4cd113528bca77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:21.587080Z","signature_b64":"eXUkfiTqY3jYEi3ZvEtKXwjTovGBN8U17sDL7QwuAHbH7qxtGFkyGbN6iB6zPCfUVXOjAsDlkdikMU6xFYnkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbcc062912cb8e08a4316d0e0562537a523613543f9ae60c6f4cd113528bca77","last_reissued_at":"2026-05-18T00:54:21.586632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:21.586632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06723","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":"2026-05-18T00:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cqxl3vwKjFLOtbzIl8GW2bUufcyG9Iy9r4yGOmJdBSnF8CUBZt8l6N2+/TyF5zDubvpIdOApmxUcUUVTThfcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:49:28.353996Z"},"content_sha256":"0f90159616038fefa97b088a46c897a8ac0b8eb51454134a532be08fb725b837","schema_version":"1.0","event_id":"sha256:0f90159616038fefa97b088a46c897a8ac0b8eb51454134a532be08fb725b837"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XPGAMKISZOHARJBRNUHAKYSTPJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integrable nonlocal complex mKdV equation: soliton solution and gauge equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Li-Yuan Ma, Shou-Feng Shen, Zuo-nong Zhu","submitted_at":"2016-12-20T15:59:18Z","abstract_excerpt":"In this paper, we prove that the nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity, 29, 915-946 (2016)] is gauge equivalent to a spin-like model. From the gauge equivalence, one can see that there exists significant difference between the nonlocal complex mKdV equation and the classical complex mKdV equation. Through constructing the Darboux transformation(DT) for nonlocal complex mKdV equation, a variety of exact solutions including dark soliton, W-type soliton, M-type soliton and periodic solutions are derived."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06723","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":"2026-05-18T00:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1RnXZxsZxkE0HCjCTq0Nqa228AMGvIUCp7FSwwlAr8qmBjtcsqvTmz99qGI7S0d90GgjYCI+HkGKVFcfbLKqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:49:28.354616Z"},"content_sha256":"4d33e8665e058aa624e2f3ab8b7c10ba6f6ea34312fef1a84bbf2abd3acfd28f","schema_version":"1.0","event_id":"sha256:4d33e8665e058aa624e2f3ab8b7c10ba6f6ea34312fef1a84bbf2abd3acfd28f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XPGAMKISZOHARJBRNUHAKYSTPJ/bundle.json","state_url":"https://pith.science/pith/XPGAMKISZOHARJBRNUHAKYSTPJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XPGAMKISZOHARJBRNUHAKYSTPJ/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":"2026-06-07T01:49:28Z","links":{"resolver":"https://pith.science/pith/XPGAMKISZOHARJBRNUHAKYSTPJ","bundle":"https://pith.science/pith/XPGAMKISZOHARJBRNUHAKYSTPJ/bundle.json","state":"https://pith.science/pith/XPGAMKISZOHARJBRNUHAKYSTPJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XPGAMKISZOHARJBRNUHAKYSTPJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XPGAMKISZOHARJBRNUHAKYSTPJ","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":"4658a9d4104c9ae8978793fd3f6c4ba7d16c778e2238782fd31e83a167709d4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-12-20T15:59:18Z","title_canon_sha256":"f4f67f0cd7c64ba4d7bbac2b9d23f94ddac7e1ec6c399037efbca90b62745715"},"schema_version":"1.0","source":{"id":"1612.06723","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06723","created_at":"2026-05-18T00:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06723v1","created_at":"2026-05-18T00:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06723","created_at":"2026-05-18T00:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"XPGAMKISZOHA","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XPGAMKISZOHARJBR","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XPGAMKIS","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:4d33e8665e058aa624e2f3ab8b7c10ba6f6ea34312fef1a84bbf2abd3acfd28f","target":"graph","created_at":"2026-05-18T00:54:21Z","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, we prove that the nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity, 29, 915-946 (2016)] is gauge equivalent to a spin-like model. From the gauge equivalence, one can see that there exists significant difference between the nonlocal complex mKdV equation and the classical complex mKdV equation. Through constructing the Darboux transformation(DT) for nonlocal complex mKdV equation, a variety of exact solutions including dark soliton, W-type soliton, M-type soliton and periodic solutions are derived.","authors_text":"Li-Yuan Ma, Shou-Feng Shen, Zuo-nong Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-12-20T15:59:18Z","title":"Integrable nonlocal complex mKdV equation: soliton solution and gauge equivalence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06723","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":"sha256:0f90159616038fefa97b088a46c897a8ac0b8eb51454134a532be08fb725b837","target":"record","created_at":"2026-05-18T00:54:21Z","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":"4658a9d4104c9ae8978793fd3f6c4ba7d16c778e2238782fd31e83a167709d4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-12-20T15:59:18Z","title_canon_sha256":"f4f67f0cd7c64ba4d7bbac2b9d23f94ddac7e1ec6c399037efbca90b62745715"},"schema_version":"1.0","source":{"id":"1612.06723","kind":"arxiv","version":1}},"canonical_sha256":"bbcc062912cb8e08a4316d0e0562537a523613543f9ae60c6f4cd113528bca77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbcc062912cb8e08a4316d0e0562537a523613543f9ae60c6f4cd113528bca77","first_computed_at":"2026-05-18T00:54:21.586632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:21.586632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eXUkfiTqY3jYEi3ZvEtKXwjTovGBN8U17sDL7QwuAHbH7qxtGFkyGbN6iB6zPCfUVXOjAsDlkdikMU6xFYnkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:21.587080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06723","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f90159616038fefa97b088a46c897a8ac0b8eb51454134a532be08fb725b837","sha256:4d33e8665e058aa624e2f3ab8b7c10ba6f6ea34312fef1a84bbf2abd3acfd28f"],"state_sha256":"fe1fb034918d648774aa88e6ee165b084b2fd3cf7cf731eb68bfa51fdfd2c8d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DGBoyglYjySDzvX1AxddsX4win0+Jg65y5vexorjRcyU+AL8opoHVPKeAp6oS4RzSw+piXw1qHrZSetCGz+tAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T01:49:28.358355Z","bundle_sha256":"ab15daa6bfecd99f6b080313e12f76b43a8a5457001ac1ac7a82c222f039ce43"}}