{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:DSJWPEAIQWF4LJ2JFWMRB2EIOX","short_pith_number":"pith:DSJWPEAI","canonical_record":{"source":{"id":"hep-th/0610006","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2006-10-02T18:42:39Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"5e08357b70ed046a16111e8b5892bc1c7cc67df65847e0c27b408a00db1b49a3","abstract_canon_sha256":"4ca7f73f0e123ad2891c3c5a66667392b00a6981dff8890bfaf74dfc04216c50"},"schema_version":"1.0"},"canonical_sha256":"1c93679008858bc5a7492d9910e88875d549671e02a1b8120eab4861dc91a9ef","source":{"kind":"arxiv","id":"hep-th/0610006","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0610006","created_at":"2026-05-18T04:38:26Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0610006v3","created_at":"2026-05-18T04:38:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0610006","created_at":"2026-05-18T04:38:26Z"},{"alias_kind":"pith_short_12","alias_value":"DSJWPEAIQWF4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DSJWPEAIQWF4LJ2J","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DSJWPEAI","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:DSJWPEAIQWF4LJ2JFWMRB2EIOX","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0610006","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2006-10-02T18:42:39Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"title_canon_sha256":"5e08357b70ed046a16111e8b5892bc1c7cc67df65847e0c27b408a00db1b49a3","abstract_canon_sha256":"4ca7f73f0e123ad2891c3c5a66667392b00a6981dff8890bfaf74dfc04216c50"},"schema_version":"1.0"},"canonical_sha256":"1c93679008858bc5a7492d9910e88875d549671e02a1b8120eab4861dc91a9ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:26.435590Z","signature_b64":"OkoAbQtERNT9HDbpiv2o5SE0BzIGNHQnYxtnew4slaDUWYTvJMKYzrNjWrLHQFC1xN5O3rtvnRlKMxm89A0WBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c93679008858bc5a7492d9910e88875d549671e02a1b8120eab4861dc91a9ef","last_reissued_at":"2026-05-18T04:38:26.435007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:26.435007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0610006","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:38:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xtO7DNsXLP+rpPWsw5jj6fKku1p1u6QJNgpjoxbRU19JRkod/MDBAR7V1Cz2Jqf8mzmVe4GPI6PmkAFQgnckDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:13:29.545729Z"},"content_sha256":"9473835f02138e5e4e0b1f946ac16d177db6958ffce972c9b717b5f6b87f25f8","schema_version":"1.0","event_id":"sha256:9473835f02138e5e4e0b1f946ac16d177db6958ffce972c9b717b5f6b87f25f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:DSJWPEAIQWF4LJ2JFWMRB2EIOX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies","license":"","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"hep-th","authors_text":"Masashi Hamanaka","submitted_at":"2006-10-02T18:42:39Z","abstract_excerpt":"We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic behavior of the multi-soliton solutions and found that the asymptotic configurations in soliton scattering process can be all the same as commutative ones, that is, the configuration of N-soliton solution has N isolated localized energy densities and the each solitary wave-packet preserves its shape and velocity in the scattering process. The phase shifts are also the sam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0610006","kind":"arxiv","version":3},"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":"2026-05-18T04:38:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EOaJ4KjY+5DhlQUxKQ6OyADv4pJSP2U6HUpTa8yG/gyMxe3OBo9AYrfe6WOo5jorYD5Y/puttn9Il1BP6XC7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:13:29.546076Z"},"content_sha256":"3c4072d61199293207a6dac7aa3039af3ab56b0dc85b84dd3dc3b8f2483b4126","schema_version":"1.0","event_id":"sha256:3c4072d61199293207a6dac7aa3039af3ab56b0dc85b84dd3dc3b8f2483b4126"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DSJWPEAIQWF4LJ2JFWMRB2EIOX/bundle.json","state_url":"https://pith.science/pith/DSJWPEAIQWF4LJ2JFWMRB2EIOX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DSJWPEAIQWF4LJ2JFWMRB2EIOX/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":"2026-07-03T13:13:29Z","links":{"resolver":"https://pith.science/pith/DSJWPEAIQWF4LJ2JFWMRB2EIOX","bundle":"https://pith.science/pith/DSJWPEAIQWF4LJ2JFWMRB2EIOX/bundle.json","state":"https://pith.science/pith/DSJWPEAIQWF4LJ2JFWMRB2EIOX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DSJWPEAIQWF4LJ2JFWMRB2EIOX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:DSJWPEAIQWF4LJ2JFWMRB2EIOX","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":"4ca7f73f0e123ad2891c3c5a66667392b00a6981dff8890bfaf74dfc04216c50","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"","primary_cat":"hep-th","submitted_at":"2006-10-02T18:42:39Z","title_canon_sha256":"5e08357b70ed046a16111e8b5892bc1c7cc67df65847e0c27b408a00db1b49a3"},"schema_version":"1.0","source":{"id":"hep-th/0610006","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0610006","created_at":"2026-05-18T04:38:26Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0610006v3","created_at":"2026-05-18T04:38:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0610006","created_at":"2026-05-18T04:38:26Z"},{"alias_kind":"pith_short_12","alias_value":"DSJWPEAIQWF4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DSJWPEAIQWF4LJ2J","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DSJWPEAI","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:3c4072d61199293207a6dac7aa3039af3ab56b0dc85b84dd3dc3b8f2483b4126","target":"graph","created_at":"2026-05-18T04:38:26Z","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 exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic behavior of the multi-soliton solutions and found that the asymptotic configurations in soliton scattering process can be all the same as commutative ones, that is, the configuration of N-soliton solution has N isolated localized energy densities and the each solitary wave-packet preserves its shape and velocity in the scattering process. The phase shifts are also the sam","authors_text":"Masashi Hamanaka","cross_cats":["math-ph","math.MP","nlin.SI"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2006-10-02T18:42:39Z","title":"Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0610006","kind":"arxiv","version":3},"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":"sha256:9473835f02138e5e4e0b1f946ac16d177db6958ffce972c9b717b5f6b87f25f8","target":"record","created_at":"2026-05-18T04:38:26Z","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":"4ca7f73f0e123ad2891c3c5a66667392b00a6981dff8890bfaf74dfc04216c50","cross_cats_sorted":["math-ph","math.MP","nlin.SI"],"license":"","primary_cat":"hep-th","submitted_at":"2006-10-02T18:42:39Z","title_canon_sha256":"5e08357b70ed046a16111e8b5892bc1c7cc67df65847e0c27b408a00db1b49a3"},"schema_version":"1.0","source":{"id":"hep-th/0610006","kind":"arxiv","version":3}},"canonical_sha256":"1c93679008858bc5a7492d9910e88875d549671e02a1b8120eab4861dc91a9ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c93679008858bc5a7492d9910e88875d549671e02a1b8120eab4861dc91a9ef","first_computed_at":"2026-05-18T04:38:26.435007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:26.435007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OkoAbQtERNT9HDbpiv2o5SE0BzIGNHQnYxtnew4slaDUWYTvJMKYzrNjWrLHQFC1xN5O3rtvnRlKMxm89A0WBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:26.435590Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0610006","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9473835f02138e5e4e0b1f946ac16d177db6958ffce972c9b717b5f6b87f25f8","sha256:3c4072d61199293207a6dac7aa3039af3ab56b0dc85b84dd3dc3b8f2483b4126"],"state_sha256":"a0b1802b93a73be8a87d2120eb3fac0bcc184a5af8de7fc13e63404eb64cc000"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gt76bi1C8SZssXwQOxRL22PdWIU7IBz5OxfCHkTZcO7uBcWD7BwmlHwc4Rzg/y5ie4XD4BcrpcHPHnC6ITBtBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T13:13:29.547997Z","bundle_sha256":"a9919cf06dfdd6333df587c0de4fb772cfa4f84802662c2fce2426764e62f44b"}}