{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LC5WVO2ZFT4LSQIONV3U3OZWXN","short_pith_number":"pith:LC5WVO2Z","canonical_record":{"source":{"id":"1406.6749","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2014-06-26T02:18:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d6f448a6205f326bb6dc09a112a301de03f8a7981db357b8b815e0433be74739","abstract_canon_sha256":"5cdd4c4bb105297161a8d5c864bae7cf2ae0055c8b563b4b9d6a6f036b1650e0"},"schema_version":"1.0"},"canonical_sha256":"58bb6abb592cf8b9410e6d774dbb36bb588923b58bc4e66e8247bb7f44aa5ea5","source":{"kind":"arxiv","id":"1406.6749","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6749","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6749v1","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6749","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"LC5WVO2ZFT4L","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"LC5WVO2ZFT4LSQIO","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"LC5WVO2Z","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LC5WVO2ZFT4LSQIONV3U3OZWXN","target":"record","payload":{"canonical_record":{"source":{"id":"1406.6749","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2014-06-26T02:18:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d6f448a6205f326bb6dc09a112a301de03f8a7981db357b8b815e0433be74739","abstract_canon_sha256":"5cdd4c4bb105297161a8d5c864bae7cf2ae0055c8b563b4b9d6a6f036b1650e0"},"schema_version":"1.0"},"canonical_sha256":"58bb6abb592cf8b9410e6d774dbb36bb588923b58bc4e66e8247bb7f44aa5ea5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:33.816075Z","signature_b64":"3gjaQemVUJ8MAwnpb6TvE+IiZk64nE9UUoGkTbGtDSa4F61yHy5A5KXlzgrzS/znLx+0I3SF3dsPEqspYG43Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58bb6abb592cf8b9410e6d774dbb36bb588923b58bc4e66e8247bb7f44aa5ea5","last_reissued_at":"2026-05-18T01:55:33.815576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:33.815576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.6749","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":"2026-05-18T01:55:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FDeNztQI/5eB1dFlK7uhD5oU+sJziodbbiQulQ6BPzDCjFLUejT3oqThNcMqA3CscBMrPnZe1vcvGSuVcksAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:58:44.893637Z"},"content_sha256":"751be1cecb76e68f9203d1db7be6ce50e3a402a7c5caed419cf0fe96c79a923f","schema_version":"1.0","event_id":"sha256:751be1cecb76e68f9203d1db7be6ce50e3a402a7c5caed419cf0fe96c79a923f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LC5WVO2ZFT4LSQIONV3U3OZWXN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cusp solitons to the long-short waves equation and the $\\bar\\partial$-dressing method","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Junyi Zhu, Yonghui Kuang","submitted_at":"2014-06-26T02:18:16Z","abstract_excerpt":"The dressing method based on $3\\times3$ matrix $\\bar{\\partial}$-problem is extended to study the long-short waves equation with the cases $\\sigma=\\pm1$. The soliton solutions for the long-short wave equation for $\\sigma=\\pm1$ are given by means of the properties of Cauchy matrix. It is shown that the long-short wave equation for $\\sigma=1$ has the cusp solitons."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6749","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":"2026-05-18T01:55:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hRHTUxiEFF0DxvMxm3YSZ+IWrw/WQQpSoFXkK6BdkUA1bR0AqxcxJxamWMz2ComhOYKH4XomGajRwgFzOVE4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:58:44.893989Z"},"content_sha256":"00bf21cfa91ec392083cb3f4a552132b8924c3b4d3d43317b901ebe6f0d8826b","schema_version":"1.0","event_id":"sha256:00bf21cfa91ec392083cb3f4a552132b8924c3b4d3d43317b901ebe6f0d8826b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LC5WVO2ZFT4LSQIONV3U3OZWXN/bundle.json","state_url":"https://pith.science/pith/LC5WVO2ZFT4LSQIONV3U3OZWXN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LC5WVO2ZFT4LSQIONV3U3OZWXN/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":"2026-07-02T12:58:44Z","links":{"resolver":"https://pith.science/pith/LC5WVO2ZFT4LSQIONV3U3OZWXN","bundle":"https://pith.science/pith/LC5WVO2ZFT4LSQIONV3U3OZWXN/bundle.json","state":"https://pith.science/pith/LC5WVO2ZFT4LSQIONV3U3OZWXN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LC5WVO2ZFT4LSQIONV3U3OZWXN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LC5WVO2ZFT4LSQIONV3U3OZWXN","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":"5cdd4c4bb105297161a8d5c864bae7cf2ae0055c8b563b4b9d6a6f036b1650e0","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2014-06-26T02:18:16Z","title_canon_sha256":"d6f448a6205f326bb6dc09a112a301de03f8a7981db357b8b815e0433be74739"},"schema_version":"1.0","source":{"id":"1406.6749","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6749","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6749v1","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6749","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"LC5WVO2ZFT4L","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"LC5WVO2ZFT4LSQIO","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"LC5WVO2Z","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:00bf21cfa91ec392083cb3f4a552132b8924c3b4d3d43317b901ebe6f0d8826b","target":"graph","created_at":"2026-05-18T01:55:33Z","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":"The dressing method based on $3\\times3$ matrix $\\bar{\\partial}$-problem is extended to study the long-short waves equation with the cases $\\sigma=\\pm1$. The soliton solutions for the long-short wave equation for $\\sigma=\\pm1$ are given by means of the properties of Cauchy matrix. It is shown that the long-short wave equation for $\\sigma=1$ has the cusp solitons.","authors_text":"Junyi Zhu, Yonghui Kuang","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2014-06-26T02:18:16Z","title":"Cusp solitons to the long-short waves equation and the $\\bar\\partial$-dressing method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6749","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":"sha256:751be1cecb76e68f9203d1db7be6ce50e3a402a7c5caed419cf0fe96c79a923f","target":"record","created_at":"2026-05-18T01:55:33Z","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":"5cdd4c4bb105297161a8d5c864bae7cf2ae0055c8b563b4b9d6a6f036b1650e0","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2014-06-26T02:18:16Z","title_canon_sha256":"d6f448a6205f326bb6dc09a112a301de03f8a7981db357b8b815e0433be74739"},"schema_version":"1.0","source":{"id":"1406.6749","kind":"arxiv","version":1}},"canonical_sha256":"58bb6abb592cf8b9410e6d774dbb36bb588923b58bc4e66e8247bb7f44aa5ea5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58bb6abb592cf8b9410e6d774dbb36bb588923b58bc4e66e8247bb7f44aa5ea5","first_computed_at":"2026-05-18T01:55:33.815576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:33.815576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3gjaQemVUJ8MAwnpb6TvE+IiZk64nE9UUoGkTbGtDSa4F61yHy5A5KXlzgrzS/znLx+0I3SF3dsPEqspYG43Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:33.816075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6749","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:751be1cecb76e68f9203d1db7be6ce50e3a402a7c5caed419cf0fe96c79a923f","sha256:00bf21cfa91ec392083cb3f4a552132b8924c3b4d3d43317b901ebe6f0d8826b"],"state_sha256":"a68b12c56889b33e442d0cd1599a2d37cf46c3ba28e6a637c4cf5d8d275cc2d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gt73zTC2qPTcW6Dds2kWaQUsW/cyK+RuIA9FtWaTzJkdrMA6TdaklRVFVth7NdaXnW9F0N5s6p5YqZDdPlHVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T12:58:44.895979Z","bundle_sha256":"d85d8deab1104e7b025427ffc04bb71a825f8594b67cde1d2920ac9aba127431"}}