{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SAYBCAOA7CGVWFECJTFZOVX5JQ","short_pith_number":"pith:SAYBCAOA","canonical_record":{"source":{"id":"1110.2990","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-13T16:15:06Z","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"title_canon_sha256":"864ddc409b3d6c93171f85e3d8af0ea64cd6c1b2070d7b3f95cfa31ec14bd2b7","abstract_canon_sha256":"1ab44adcbbeb428774f471887b6066f27324f432f1460117e183fcfa73645ddf"},"schema_version":"1.0"},"canonical_sha256":"90301101c0f88d5b14824ccb9756fd4c2cec00180c8331ab94501b4492c65295","source":{"kind":"arxiv","id":"1110.2990","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2990","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2990v2","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2990","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"SAYBCAOA7CGV","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SAYBCAOA7CGVWFEC","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SAYBCAOA","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SAYBCAOA7CGVWFECJTFZOVX5JQ","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2990","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-13T16:15:06Z","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"title_canon_sha256":"864ddc409b3d6c93171f85e3d8af0ea64cd6c1b2070d7b3f95cfa31ec14bd2b7","abstract_canon_sha256":"1ab44adcbbeb428774f471887b6066f27324f432f1460117e183fcfa73645ddf"},"schema_version":"1.0"},"canonical_sha256":"90301101c0f88d5b14824ccb9756fd4c2cec00180c8331ab94501b4492c65295","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:12.673759Z","signature_b64":"RNBLwuZRsjbIA792VlePNJDFR76YxP6hn/YMv2jC4b2I7z+nX7VmeqHfPoSnN2uGidbn8PYjbtxhx73yHnfXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90301101c0f88d5b14824ccb9756fd4c2cec00180c8331ab94501b4492c65295","last_reissued_at":"2026-05-18T02:00:12.673061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:12.673061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2990","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":"2026-05-18T02:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"veGG1SWs5fFEKmh0C8uH4FrFg+nyvRDdzWFNgwtgChEj7z0WerLnt48DPi8YsUL6eV8q3ZZYh9zspYEdyDwDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:44:25.004119Z"},"content_sha256":"c506e7a998643911065a54b20c245035233501275d87cfcf5c9a33bb0d25dd24","schema_version":"1.0","event_id":"sha256:c506e7a998643911065a54b20c245035233501275d87cfcf5c9a33bb0d25dd24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SAYBCAOA7CGVWFECJTFZOVX5JQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector Nonlinear Schr\\\"odinger Equation on the half-line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Q. C. Zhang, V. Caudrelier","submitted_at":"2011-10-13T16:15:06Z","abstract_excerpt":"We investigate the Manakov model or, more generally, the vector nonlinear Schr\\\"odinger equation on the half-line. Using a B\\\"acklund transformation method, two classes of integrable boundary conditions are derived: mixed Neumann/Dirichlet and Robin boundary conditions. Integrability is shown by constructing a generating function for the conserved quantities. We apply a nonlinear mirror image technique to construct the inverse scattering method with these boundary conditions. The important feature in the reconstruction formula for the fields is the symmetry property of the scattering data emer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2990","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":"2026-05-18T02:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rGqKdXmbTmHwiOhK2qamGASe7vqY9jp6JO/0hTQ6bEGUfnXenaRWm0KSgRFX1Xq8wRoTWnPr6gGhmsSDIe8SDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:44:25.004492Z"},"content_sha256":"ad8697b28c9145e92ee735a920c11bed02ad7aad3cb5221a39be3c46aa28b752","schema_version":"1.0","event_id":"sha256:ad8697b28c9145e92ee735a920c11bed02ad7aad3cb5221a39be3c46aa28b752"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SAYBCAOA7CGVWFECJTFZOVX5JQ/bundle.json","state_url":"https://pith.science/pith/SAYBCAOA7CGVWFECJTFZOVX5JQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SAYBCAOA7CGVWFECJTFZOVX5JQ/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":"2026-06-01T13:44:25Z","links":{"resolver":"https://pith.science/pith/SAYBCAOA7CGVWFECJTFZOVX5JQ","bundle":"https://pith.science/pith/SAYBCAOA7CGVWFECJTFZOVX5JQ/bundle.json","state":"https://pith.science/pith/SAYBCAOA7CGVWFECJTFZOVX5JQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SAYBCAOA7CGVWFECJTFZOVX5JQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SAYBCAOA7CGVWFECJTFZOVX5JQ","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":"1ab44adcbbeb428774f471887b6066f27324f432f1460117e183fcfa73645ddf","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-13T16:15:06Z","title_canon_sha256":"864ddc409b3d6c93171f85e3d8af0ea64cd6c1b2070d7b3f95cfa31ec14bd2b7"},"schema_version":"1.0","source":{"id":"1110.2990","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2990","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2990v2","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2990","created_at":"2026-05-18T02:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"SAYBCAOA7CGV","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SAYBCAOA7CGVWFEC","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SAYBCAOA","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:ad8697b28c9145e92ee735a920c11bed02ad7aad3cb5221a39be3c46aa28b752","target":"graph","created_at":"2026-05-18T02:00:12Z","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 investigate the Manakov model or, more generally, the vector nonlinear Schr\\\"odinger equation on the half-line. Using a B\\\"acklund transformation method, two classes of integrable boundary conditions are derived: mixed Neumann/Dirichlet and Robin boundary conditions. Integrability is shown by constructing a generating function for the conserved quantities. We apply a nonlinear mirror image technique to construct the inverse scattering method with these boundary conditions. The important feature in the reconstruction formula for the fields is the symmetry property of the scattering data emer","authors_text":"Q. C. Zhang, V. Caudrelier","cross_cats":["hep-th","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-13T16:15:06Z","title":"Vector Nonlinear Schr\\\"odinger Equation on the half-line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2990","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:c506e7a998643911065a54b20c245035233501275d87cfcf5c9a33bb0d25dd24","target":"record","created_at":"2026-05-18T02:00:12Z","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":"1ab44adcbbeb428774f471887b6066f27324f432f1460117e183fcfa73645ddf","cross_cats_sorted":["hep-th","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-13T16:15:06Z","title_canon_sha256":"864ddc409b3d6c93171f85e3d8af0ea64cd6c1b2070d7b3f95cfa31ec14bd2b7"},"schema_version":"1.0","source":{"id":"1110.2990","kind":"arxiv","version":2}},"canonical_sha256":"90301101c0f88d5b14824ccb9756fd4c2cec00180c8331ab94501b4492c65295","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90301101c0f88d5b14824ccb9756fd4c2cec00180c8331ab94501b4492c65295","first_computed_at":"2026-05-18T02:00:12.673061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:12.673061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RNBLwuZRsjbIA792VlePNJDFR76YxP6hn/YMv2jC4b2I7z+nX7VmeqHfPoSnN2uGidbn8PYjbtxhx73yHnfXAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:12.673759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2990","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c506e7a998643911065a54b20c245035233501275d87cfcf5c9a33bb0d25dd24","sha256:ad8697b28c9145e92ee735a920c11bed02ad7aad3cb5221a39be3c46aa28b752"],"state_sha256":"fe983f854d846d9cc71137294b646b85b3be0620658072f27ec9a87bf53c7d0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9RLBW69Z8v+GVqe4FAN6K4BDiMjelmXZViURjuxlNsAbPkJOWNDu03BYqGZKMX5WpWPo4oTegBt4OohZ9P7JCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:44:25.006327Z","bundle_sha256":"25e9c18662eaf1c90e84e3312183c2431a125c5f396843343c9b199eeca6a804"}}