{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EYS7P7EOWP2MHG5MBJGPA6XQLG","short_pith_number":"pith:EYS7P7EO","canonical_record":{"source":{"id":"1711.01588","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-11-05T13:52:24Z","cross_cats_sorted":[],"title_canon_sha256":"520e10a821304dd71cc34c372d53fbe73b94b2968188cf0213e05daf27def7c9","abstract_canon_sha256":"dad7de5e76966ba517545e49e2b44c290de58f4ee5bf6c00a0021a2ff4f11802"},"schema_version":"1.0"},"canonical_sha256":"2625f7fc8eb3f4c39bac0a4cf07af059aaed011a5c23e73507ec80ef951ba9bc","source":{"kind":"arxiv","id":"1711.01588","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01588","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01588v2","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01588","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"pith_short_12","alias_value":"EYS7P7EOWP2M","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EYS7P7EOWP2MHG5M","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EYS7P7EO","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EYS7P7EOWP2MHG5MBJGPA6XQLG","target":"record","payload":{"canonical_record":{"source":{"id":"1711.01588","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-11-05T13:52:24Z","cross_cats_sorted":[],"title_canon_sha256":"520e10a821304dd71cc34c372d53fbe73b94b2968188cf0213e05daf27def7c9","abstract_canon_sha256":"dad7de5e76966ba517545e49e2b44c290de58f4ee5bf6c00a0021a2ff4f11802"},"schema_version":"1.0"},"canonical_sha256":"2625f7fc8eb3f4c39bac0a4cf07af059aaed011a5c23e73507ec80ef951ba9bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:40.667923Z","signature_b64":"QblNC/ftXnU/stJAR/t3FiBsOVP9u5VeOqSrw9QTkxfjIaOTGOKMrSNb4LkbItIL0TSjC2Mh0Gr+Uvjc4i8MAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2625f7fc8eb3f4c39bac0a4cf07af059aaed011a5c23e73507ec80ef951ba9bc","last_reissued_at":"2026-05-18T00:29:40.667280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:40.667280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.01588","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":"2026-05-18T00:29:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LHYZcP2h3RxlSN168WkRZpEkKSFvdMRjvDpeUNIZ4xc3f5bbWwoh4gd7/httjM+srDnrpkeECjw1rBMm/lsWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:49:54.949647Z"},"content_sha256":"0890d06fcd66b76ec29618e311bebd55d7ab34fe805bcde17eba527664ce00d0","schema_version":"1.0","event_id":"sha256:0890d06fcd66b76ec29618e311bebd55d7ab34fe805bcde17eba527664ce00d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EYS7P7EOWP2MHG5MBJGPA6XQLG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlocal Modified KdV Equations and Their Soliton Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Asl{\\i} Pekcan, Metin G\\\"urses","submitted_at":"2017-11-05T13:52:24Z","abstract_excerpt":"We study the nonlocal modified Korteweg-de Vries (mKdV) equations obtained from AKNS scheme by Ablowitz-Musslimani type nonlocal reductions. We first find soliton solutions of the coupled mKdV system by using the Hirota direct method. Then by using the Ablowitz-Musslimani reduction formulas, we find one-, two-, and three-soliton solutions of local and nonlocal complex mKdV and mKdV equations. The soliton solutions of these equations are of two types. We give one-soliton solutions of both types and present only first type of two- and three-soliton solutions. We illustrate our soliton solutions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01588","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":""},"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":"2026-05-18T00:29:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vebyv1tPMbh/Q/M3fP2QFo+DwLSELmjSlC1k0m71U2l2TgqJ+/r24EU6cbdT18ZcN1uStjX35PHhNVyhMdACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:49:54.950306Z"},"content_sha256":"57bb7ee1da3f82e2aeb65f8886f7ef8d21f788660232f0d5f209cfafed1b02fd","schema_version":"1.0","event_id":"sha256:57bb7ee1da3f82e2aeb65f8886f7ef8d21f788660232f0d5f209cfafed1b02fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EYS7P7EOWP2MHG5MBJGPA6XQLG/bundle.json","state_url":"https://pith.science/pith/EYS7P7EOWP2MHG5MBJGPA6XQLG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EYS7P7EOWP2MHG5MBJGPA6XQLG/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":"2026-05-30T00:49:54Z","links":{"resolver":"https://pith.science/pith/EYS7P7EOWP2MHG5MBJGPA6XQLG","bundle":"https://pith.science/pith/EYS7P7EOWP2MHG5MBJGPA6XQLG/bundle.json","state":"https://pith.science/pith/EYS7P7EOWP2MHG5MBJGPA6XQLG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EYS7P7EOWP2MHG5MBJGPA6XQLG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EYS7P7EOWP2MHG5MBJGPA6XQLG","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":"dad7de5e76966ba517545e49e2b44c290de58f4ee5bf6c00a0021a2ff4f11802","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-11-05T13:52:24Z","title_canon_sha256":"520e10a821304dd71cc34c372d53fbe73b94b2968188cf0213e05daf27def7c9"},"schema_version":"1.0","source":{"id":"1711.01588","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01588","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01588v2","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01588","created_at":"2026-05-18T00:29:40Z"},{"alias_kind":"pith_short_12","alias_value":"EYS7P7EOWP2M","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EYS7P7EOWP2MHG5M","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EYS7P7EO","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:57bb7ee1da3f82e2aeb65f8886f7ef8d21f788660232f0d5f209cfafed1b02fd","target":"graph","created_at":"2026-05-18T00:29:40Z","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":"We study the nonlocal modified Korteweg-de Vries (mKdV) equations obtained from AKNS scheme by Ablowitz-Musslimani type nonlocal reductions. We first find soliton solutions of the coupled mKdV system by using the Hirota direct method. Then by using the Ablowitz-Musslimani reduction formulas, we find one-, two-, and three-soliton solutions of local and nonlocal complex mKdV and mKdV equations. The soliton solutions of these equations are of two types. We give one-soliton solutions of both types and present only first type of two- and three-soliton solutions. We illustrate our soliton solutions ","authors_text":"Asl{\\i} Pekcan, Metin G\\\"urses","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-11-05T13:52:24Z","title":"Nonlocal Modified KdV Equations and Their Soliton Solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01588","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":"sha256:0890d06fcd66b76ec29618e311bebd55d7ab34fe805bcde17eba527664ce00d0","target":"record","created_at":"2026-05-18T00:29:40Z","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":"dad7de5e76966ba517545e49e2b44c290de58f4ee5bf6c00a0021a2ff4f11802","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-11-05T13:52:24Z","title_canon_sha256":"520e10a821304dd71cc34c372d53fbe73b94b2968188cf0213e05daf27def7c9"},"schema_version":"1.0","source":{"id":"1711.01588","kind":"arxiv","version":2}},"canonical_sha256":"2625f7fc8eb3f4c39bac0a4cf07af059aaed011a5c23e73507ec80ef951ba9bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2625f7fc8eb3f4c39bac0a4cf07af059aaed011a5c23e73507ec80ef951ba9bc","first_computed_at":"2026-05-18T00:29:40.667280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:40.667280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QblNC/ftXnU/stJAR/t3FiBsOVP9u5VeOqSrw9QTkxfjIaOTGOKMrSNb4LkbItIL0TSjC2Mh0Gr+Uvjc4i8MAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:40.667923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.01588","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0890d06fcd66b76ec29618e311bebd55d7ab34fe805bcde17eba527664ce00d0","sha256:57bb7ee1da3f82e2aeb65f8886f7ef8d21f788660232f0d5f209cfafed1b02fd"],"state_sha256":"611c8fda6ffec30ef4638d207a7609db130e8ac0fd628ca97115821a7b8db9dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wCqSJpcbvCzE/0+QaEIl2kIywUEhrZ/rpMyfHm5IVdwKpQaxTNwK25bMJiKr3cEzEeNkk5cART0Xt/SsXBfyCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T00:49:54.953785Z","bundle_sha256":"d6d9af349ce2c95d3797db7f062da36925c0b0040c8eaf1d369abdfdce597d96"}}