{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DVIQIBNITMH46UDWJQAPCO4CGW","short_pith_number":"pith:DVIQIBNI","canonical_record":{"source":{"id":"1609.03391","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-09-12T13:35:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0731345f585c2a1bc5f9fa1ac63c2116b2bf7a1f078b6a4c095d5d7e7f67330c","abstract_canon_sha256":"014dc627f7a76a4d92e9a6bc8c63323db0f5acdd11720934826a68d21c44f4ea"},"schema_version":"1.0"},"canonical_sha256":"1d510405a89b0fcf50764c00f13b8235bd9280f4d2f13d72afc5c65d381427aa","source":{"kind":"arxiv","id":"1609.03391","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03391","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03391v3","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03391","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"pith_short_12","alias_value":"DVIQIBNITMH4","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DVIQIBNITMH46UDW","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DVIQIBNI","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DVIQIBNITMH46UDWJQAPCO4CGW","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03391","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-09-12T13:35:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0731345f585c2a1bc5f9fa1ac63c2116b2bf7a1f078b6a4c095d5d7e7f67330c","abstract_canon_sha256":"014dc627f7a76a4d92e9a6bc8c63323db0f5acdd11720934826a68d21c44f4ea"},"schema_version":"1.0"},"canonical_sha256":"1d510405a89b0fcf50764c00f13b8235bd9280f4d2f13d72afc5c65d381427aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:10.750835Z","signature_b64":"23boELs9oGymKuJYmrg2ZWD52sMIty7RcX50xbPWev8KJwvZ1GOSaeI5EY0va66r5z7GNE+DdEz5D+ZdSlKDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d510405a89b0fcf50764c00f13b8235bd9280f4d2f13d72afc5c65d381427aa","last_reissued_at":"2026-05-18T00:47:10.749965Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:10.749965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03391","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":"2026-05-18T00:47:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"frH+/oNjkWZ0pzJNV5ImMPKpc6oEKY1pqzQ6TPnjx8/vS6fGlE6R3sqTBWcILE2uB/MnQhNvqqmtg5C78Kv2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:57:07.968013Z"},"content_sha256":"c8577d48d547ceda66f8266f642421eff0ebb6c884c55e2252403dadc6ed38a2","schema_version":"1.0","event_id":"sha256:c8577d48d547ceda66f8266f642421eff0ebb6c884c55e2252403dadc6ed38a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DVIQIBNITMH46UDWJQAPCO4CGW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"NLS breathers, rogue waves, and solutions of the Lyapunov equation for Jordan blocks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Folkert M\\\"uller-Hoissen, Oleksandr Chvartatskyi","submitted_at":"2016-09-12T13:35:29Z","abstract_excerpt":"The infinite families of Peregrine, Akhmediev and Kuznetsov-Ma breather solutions of the focusing Nonlinear Schroedinger (NLS) equation are obtained via a matrix version of the Darboux transformation, with a spectral matrix of the form of a Jordan block. The structure of these solutions is essentially determined by the corresponding solution of the Lyapunov equation. In particular, regularity follows from properties of the Lyapunov equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03391","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":"2026-05-18T00:47:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRfpa5eIJirLQLO60MG6v0B5iUczSkJZEx7DF9p+AESL0neKPFc4cYyDSzFCgAe/4S+WneEKNDKl/xJFy9lMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:57:07.968379Z"},"content_sha256":"43bff30ee3b536f4d0b43197911ba41762a5bbe51a80c80ce953487fead43763","schema_version":"1.0","event_id":"sha256:43bff30ee3b536f4d0b43197911ba41762a5bbe51a80c80ce953487fead43763"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DVIQIBNITMH46UDWJQAPCO4CGW/bundle.json","state_url":"https://pith.science/pith/DVIQIBNITMH46UDWJQAPCO4CGW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DVIQIBNITMH46UDWJQAPCO4CGW/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":"2026-06-23T16:57:07Z","links":{"resolver":"https://pith.science/pith/DVIQIBNITMH46UDWJQAPCO4CGW","bundle":"https://pith.science/pith/DVIQIBNITMH46UDWJQAPCO4CGW/bundle.json","state":"https://pith.science/pith/DVIQIBNITMH46UDWJQAPCO4CGW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DVIQIBNITMH46UDWJQAPCO4CGW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DVIQIBNITMH46UDWJQAPCO4CGW","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":"014dc627f7a76a4d92e9a6bc8c63323db0f5acdd11720934826a68d21c44f4ea","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-09-12T13:35:29Z","title_canon_sha256":"0731345f585c2a1bc5f9fa1ac63c2116b2bf7a1f078b6a4c095d5d7e7f67330c"},"schema_version":"1.0","source":{"id":"1609.03391","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03391","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03391v3","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03391","created_at":"2026-05-18T00:47:10Z"},{"alias_kind":"pith_short_12","alias_value":"DVIQIBNITMH4","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DVIQIBNITMH46UDW","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DVIQIBNI","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:43bff30ee3b536f4d0b43197911ba41762a5bbe51a80c80ce953487fead43763","target":"graph","created_at":"2026-05-18T00:47:10Z","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 infinite families of Peregrine, Akhmediev and Kuznetsov-Ma breather solutions of the focusing Nonlinear Schroedinger (NLS) equation are obtained via a matrix version of the Darboux transformation, with a spectral matrix of the form of a Jordan block. The structure of these solutions is essentially determined by the corresponding solution of the Lyapunov equation. In particular, regularity follows from properties of the Lyapunov equation.","authors_text":"Folkert M\\\"uller-Hoissen, Oleksandr Chvartatskyi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-09-12T13:35:29Z","title":"NLS breathers, rogue waves, and solutions of the Lyapunov equation for Jordan blocks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03391","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:c8577d48d547ceda66f8266f642421eff0ebb6c884c55e2252403dadc6ed38a2","target":"record","created_at":"2026-05-18T00:47:10Z","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":"014dc627f7a76a4d92e9a6bc8c63323db0f5acdd11720934826a68d21c44f4ea","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-09-12T13:35:29Z","title_canon_sha256":"0731345f585c2a1bc5f9fa1ac63c2116b2bf7a1f078b6a4c095d5d7e7f67330c"},"schema_version":"1.0","source":{"id":"1609.03391","kind":"arxiv","version":3}},"canonical_sha256":"1d510405a89b0fcf50764c00f13b8235bd9280f4d2f13d72afc5c65d381427aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d510405a89b0fcf50764c00f13b8235bd9280f4d2f13d72afc5c65d381427aa","first_computed_at":"2026-05-18T00:47:10.749965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:10.749965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"23boELs9oGymKuJYmrg2ZWD52sMIty7RcX50xbPWev8KJwvZ1GOSaeI5EY0va66r5z7GNE+DdEz5D+ZdSlKDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:10.750835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03391","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8577d48d547ceda66f8266f642421eff0ebb6c884c55e2252403dadc6ed38a2","sha256:43bff30ee3b536f4d0b43197911ba41762a5bbe51a80c80ce953487fead43763"],"state_sha256":"068997dc75b6a9e6efaa648d7b790fca541192f63b28afd6d14478b298ad996a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"csn6MTbIpDhXzXluVgGqM9/5Arj01q95GFb6+hENtisGSkkgZAfdiF5GQEnYmaRD5M6Dapxhr1hib8RaFoyqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:57:07.970432Z","bundle_sha256":"ec18dedd8af39a411a51e4a23271ff5bbdd84b454781974d73c74c020b9f9c81"}}