{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HQEAHZ5PUENNWG663LZJ5RXN7I","short_pith_number":"pith:HQEAHZ5P","canonical_record":{"source":{"id":"1208.3259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-08-16T01:21:08Z","cross_cats_sorted":[],"title_canon_sha256":"0d63327121e02484a7eb3945acee06ce23fae74df5ac2df8f2ca0feca111ee8c","abstract_canon_sha256":"1e1c8f03990fba6989afdf0205a06733817fc8b01e7a4479eaccfaa77b646ad4"},"schema_version":"1.0"},"canonical_sha256":"3c0803e7afa11adb1bdedaf29ec6edfa1aeb3f0d068df066e138943df28400d2","source":{"kind":"arxiv","id":"1208.3259","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3259","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3259v1","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3259","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"pith_short_12","alias_value":"HQEAHZ5PUENN","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HQEAHZ5PUENNWG66","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HQEAHZ5P","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HQEAHZ5PUENNWG663LZJ5RXN7I","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-08-16T01:21:08Z","cross_cats_sorted":[],"title_canon_sha256":"0d63327121e02484a7eb3945acee06ce23fae74df5ac2df8f2ca0feca111ee8c","abstract_canon_sha256":"1e1c8f03990fba6989afdf0205a06733817fc8b01e7a4479eaccfaa77b646ad4"},"schema_version":"1.0"},"canonical_sha256":"3c0803e7afa11adb1bdedaf29ec6edfa1aeb3f0d068df066e138943df28400d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:36.391167Z","signature_b64":"YXHETauDDuAlx2nrK1G+yFnn58aHImuHQ2P2EIIcc+Xg90Koq8+O5GEXwseleju8GkELN6BKyDYiA8NIB8rXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c0803e7afa11adb1bdedaf29ec6edfa1aeb3f0d068df066e138943df28400d2","last_reissued_at":"2026-05-18T03:48:36.390721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:36.390721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3259","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":"2026-05-18T03:48:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lDSbizX2prAKTVXTGYimFwOKFCukLKit9lUf9cTvp90DsiAaPxhhQNal7HF9Y3R0miwNbgJFTssd6ZVH6tS8Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T13:35:27.682886Z"},"content_sha256":"fdb42b3a17f115f05cb08e5446b02c6bedd2fc4525e0e6c4d2a3a7bdad4322c3","schema_version":"1.0","event_id":"sha256:fdb42b3a17f115f05cb08e5446b02c6bedd2fc4525e0e6c4d2a3a7bdad4322c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HQEAHZ5PUENNWG663LZJ5RXN7I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interactions among different types of nonlinear waves described by the Kadomtsev-Petviashvili Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Chun-li Chen, Sen-yue Lou, Xue-Ping Cheng","submitted_at":"2012-08-16T01:21:08Z","abstract_excerpt":"In nonlinear physics, the interactions among solitons are well studied thanks to the multiple soliton solutions can be obtained by various effective methods. However, it is very difficult to study interactions among different types of nonlinear waves such as the solitons (or solitary waves), the cnoidal periodic waves and Painlev\\'e waves. In this paper, the nonlocal symmetries related to the Darboux transformations (DT) of the Kadomtsev-Petviashvili (KP) equation is localized after imbedding the original system to an enlarged one. Then the DT is used to find the corresponding group invariant "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3259","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":"2026-05-18T03:48:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qr/k4y16BRGlBhb5XWZiTyiYr0eJPnXZi5EioksVN+TJf8dmw8BaW585mnLr7fPnLe2JKlYnVS8TPsHXMdMYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T13:35:27.683230Z"},"content_sha256":"483e4df41e6c88780764f656233f15089cd6d2d88387eaf00218c5f5fb430420","schema_version":"1.0","event_id":"sha256:483e4df41e6c88780764f656233f15089cd6d2d88387eaf00218c5f5fb430420"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HQEAHZ5PUENNWG663LZJ5RXN7I/bundle.json","state_url":"https://pith.science/pith/HQEAHZ5PUENNWG663LZJ5RXN7I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HQEAHZ5PUENNWG663LZJ5RXN7I/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":"2026-06-24T13:35:27Z","links":{"resolver":"https://pith.science/pith/HQEAHZ5PUENNWG663LZJ5RXN7I","bundle":"https://pith.science/pith/HQEAHZ5PUENNWG663LZJ5RXN7I/bundle.json","state":"https://pith.science/pith/HQEAHZ5PUENNWG663LZJ5RXN7I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HQEAHZ5PUENNWG663LZJ5RXN7I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HQEAHZ5PUENNWG663LZJ5RXN7I","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":"1e1c8f03990fba6989afdf0205a06733817fc8b01e7a4479eaccfaa77b646ad4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-08-16T01:21:08Z","title_canon_sha256":"0d63327121e02484a7eb3945acee06ce23fae74df5ac2df8f2ca0feca111ee8c"},"schema_version":"1.0","source":{"id":"1208.3259","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3259","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3259v1","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3259","created_at":"2026-05-18T03:48:36Z"},{"alias_kind":"pith_short_12","alias_value":"HQEAHZ5PUENN","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HQEAHZ5PUENNWG66","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HQEAHZ5P","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:483e4df41e6c88780764f656233f15089cd6d2d88387eaf00218c5f5fb430420","target":"graph","created_at":"2026-05-18T03:48:36Z","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 nonlinear physics, the interactions among solitons are well studied thanks to the multiple soliton solutions can be obtained by various effective methods. However, it is very difficult to study interactions among different types of nonlinear waves such as the solitons (or solitary waves), the cnoidal periodic waves and Painlev\\'e waves. In this paper, the nonlocal symmetries related to the Darboux transformations (DT) of the Kadomtsev-Petviashvili (KP) equation is localized after imbedding the original system to an enlarged one. Then the DT is used to find the corresponding group invariant ","authors_text":"Chun-li Chen, Sen-yue Lou, Xue-Ping Cheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-08-16T01:21:08Z","title":"Interactions among different types of nonlinear waves described by the Kadomtsev-Petviashvili Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3259","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:fdb42b3a17f115f05cb08e5446b02c6bedd2fc4525e0e6c4d2a3a7bdad4322c3","target":"record","created_at":"2026-05-18T03:48:36Z","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":"1e1c8f03990fba6989afdf0205a06733817fc8b01e7a4479eaccfaa77b646ad4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-08-16T01:21:08Z","title_canon_sha256":"0d63327121e02484a7eb3945acee06ce23fae74df5ac2df8f2ca0feca111ee8c"},"schema_version":"1.0","source":{"id":"1208.3259","kind":"arxiv","version":1}},"canonical_sha256":"3c0803e7afa11adb1bdedaf29ec6edfa1aeb3f0d068df066e138943df28400d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c0803e7afa11adb1bdedaf29ec6edfa1aeb3f0d068df066e138943df28400d2","first_computed_at":"2026-05-18T03:48:36.390721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:36.390721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YXHETauDDuAlx2nrK1G+yFnn58aHImuHQ2P2EIIcc+Xg90Koq8+O5GEXwseleju8GkELN6BKyDYiA8NIB8rXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:36.391167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3259","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdb42b3a17f115f05cb08e5446b02c6bedd2fc4525e0e6c4d2a3a7bdad4322c3","sha256:483e4df41e6c88780764f656233f15089cd6d2d88387eaf00218c5f5fb430420"],"state_sha256":"023f92a3d1e34d7785b39e64d9e66f5e421b2c1d71e0c98c82f0607e2b6575c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dCbW6N+YtktFJ2OiB3xrBrO86z8WvCupFZx3sODBTVe8moWtBuGkfHuZ4O0wLOnmGBE+9trwVr4jrlM8HarIBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T13:35:27.685049Z","bundle_sha256":"43fce9d6375c21ae2b2f919dc20582470d8816901fa13d9f926900149ae09284"}}