{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KWBTIGN35T5IMA3TBVNKWZTIFL","short_pith_number":"pith:KWBTIGN3","canonical_record":{"source":{"id":"1410.5013","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-10-18T22:52:38Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"027818ae3fb5329f3e11a4430fd255faeb09c18c50f86a65e6d97424e1895138","abstract_canon_sha256":"829efc85f5f7601fbcc4235907e6cb05f65287c940e00c3cebe11c6fb74920be"},"schema_version":"1.0"},"canonical_sha256":"55833419bbecfa8603730d5aab66682ad046a8bf86e50080b41b025dc1959eb1","source":{"kind":"arxiv","id":"1410.5013","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5013","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5013v1","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5013","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"KWBTIGN35T5I","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KWBTIGN35T5IMA3T","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KWBTIGN3","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KWBTIGN35T5IMA3TBVNKWZTIFL","target":"record","payload":{"canonical_record":{"source":{"id":"1410.5013","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-10-18T22:52:38Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"027818ae3fb5329f3e11a4430fd255faeb09c18c50f86a65e6d97424e1895138","abstract_canon_sha256":"829efc85f5f7601fbcc4235907e6cb05f65287c940e00c3cebe11c6fb74920be"},"schema_version":"1.0"},"canonical_sha256":"55833419bbecfa8603730d5aab66682ad046a8bf86e50080b41b025dc1959eb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:47.218623Z","signature_b64":"S6BwUXd/wWQKoEUzs8c+d0YcyYI5L4ogJJtaHqe6uKQ9BQyqKS/tByPoz2/JLsxUjtQ5yLYWmVN94EnbY1nNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55833419bbecfa8603730d5aab66682ad046a8bf86e50080b41b025dc1959eb1","last_reissued_at":"2026-05-18T02:39:47.218180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:47.218180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.5013","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":"2026-05-18T02:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YaXsfh3RU/52W6EdY0okFnDM7cIbUZCLswnXETce7TezpYV/WVGuiC7c8kQgFYtYifEIWbgprzyVI2bto08+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:42:58.292029Z"},"content_sha256":"46b2263e6957b833218f72f23f29e88c96f638cfe93d3eb338100cc79f3552a1","schema_version":"1.0","event_id":"sha256:46b2263e6957b833218f72f23f29e88c96f638cfe93d3eb338100cc79f3552a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KWBTIGN35T5IMA3TBVNKWZTIFL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Darboux transformations, discrete integrable systems and related Yang-Baxter maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Sotiris Konstantinou-Rizos","submitted_at":"2014-10-18T22:52:38Z","abstract_excerpt":"In this thesis we study the Darboux transformations related to particular Lax operators of NLS type which are invariant under the action of the so-called reduction group. Specifically, we study the cases of: 1) the nonlinear Schr\\\"odinger equation (with no reduction), 2) the derivative nonlinear Schr\\\"odinger equation, where the corresponding Lax operator is invariant under the action of the $\\mathbb{Z}_2$-reduction group and 3) a deformation of the derivative nonlinear Schr\\\"odinger equation, associated to a Lax operator invariant under the action of the dihedral reduction group. These reduct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5013","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":"2026-05-18T02:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9r1bWq21rnvbRnIf7hpp93IYwdwMJWIzX6XQpoV5nq0PEvXmuDvfQVSYPivRV+ZmeOc29x4qyLFRFKNZtuy8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:42:58.292576Z"},"content_sha256":"68645f916dbc1f3cd7d452dab36f620b912cd36272eee4ac7c6b5f4365addf5c","schema_version":"1.0","event_id":"sha256:68645f916dbc1f3cd7d452dab36f620b912cd36272eee4ac7c6b5f4365addf5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KWBTIGN35T5IMA3TBVNKWZTIFL/bundle.json","state_url":"https://pith.science/pith/KWBTIGN35T5IMA3TBVNKWZTIFL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KWBTIGN35T5IMA3TBVNKWZTIFL/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":"2026-05-31T00:42:58Z","links":{"resolver":"https://pith.science/pith/KWBTIGN35T5IMA3TBVNKWZTIFL","bundle":"https://pith.science/pith/KWBTIGN35T5IMA3TBVNKWZTIFL/bundle.json","state":"https://pith.science/pith/KWBTIGN35T5IMA3TBVNKWZTIFL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KWBTIGN35T5IMA3TBVNKWZTIFL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KWBTIGN35T5IMA3TBVNKWZTIFL","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":"829efc85f5f7601fbcc4235907e6cb05f65287c940e00c3cebe11c6fb74920be","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-10-18T22:52:38Z","title_canon_sha256":"027818ae3fb5329f3e11a4430fd255faeb09c18c50f86a65e6d97424e1895138"},"schema_version":"1.0","source":{"id":"1410.5013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5013","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5013v1","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5013","created_at":"2026-05-18T02:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"KWBTIGN35T5I","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KWBTIGN35T5IMA3T","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KWBTIGN3","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:68645f916dbc1f3cd7d452dab36f620b912cd36272eee4ac7c6b5f4365addf5c","target":"graph","created_at":"2026-05-18T02:39:47Z","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 this thesis we study the Darboux transformations related to particular Lax operators of NLS type which are invariant under the action of the so-called reduction group. Specifically, we study the cases of: 1) the nonlinear Schr\\\"odinger equation (with no reduction), 2) the derivative nonlinear Schr\\\"odinger equation, where the corresponding Lax operator is invariant under the action of the $\\mathbb{Z}_2$-reduction group and 3) a deformation of the derivative nonlinear Schr\\\"odinger equation, associated to a Lax operator invariant under the action of the dihedral reduction group. These reduct","authors_text":"Sotiris Konstantinou-Rizos","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-10-18T22:52:38Z","title":"Darboux transformations, discrete integrable systems and related Yang-Baxter maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5013","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":"sha256:46b2263e6957b833218f72f23f29e88c96f638cfe93d3eb338100cc79f3552a1","target":"record","created_at":"2026-05-18T02:39:47Z","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":"829efc85f5f7601fbcc4235907e6cb05f65287c940e00c3cebe11c6fb74920be","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-10-18T22:52:38Z","title_canon_sha256":"027818ae3fb5329f3e11a4430fd255faeb09c18c50f86a65e6d97424e1895138"},"schema_version":"1.0","source":{"id":"1410.5013","kind":"arxiv","version":1}},"canonical_sha256":"55833419bbecfa8603730d5aab66682ad046a8bf86e50080b41b025dc1959eb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55833419bbecfa8603730d5aab66682ad046a8bf86e50080b41b025dc1959eb1","first_computed_at":"2026-05-18T02:39:47.218180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:47.218180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S6BwUXd/wWQKoEUzs8c+d0YcyYI5L4ogJJtaHqe6uKQ9BQyqKS/tByPoz2/JLsxUjtQ5yLYWmVN94EnbY1nNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:47.218623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46b2263e6957b833218f72f23f29e88c96f638cfe93d3eb338100cc79f3552a1","sha256:68645f916dbc1f3cd7d452dab36f620b912cd36272eee4ac7c6b5f4365addf5c"],"state_sha256":"a9a24cb3db9f9c523a3ba355422cd1169f62927b63c66331c71ea2997bc1d071"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38wHE/P/H8uIEp3706RWyw3yaWH3A+eUI80OmCBSjerhuOlenpyPYJIw/ZhwNojSgKxjtJjeZgq7bTRS/TfMBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:42:58.298753Z","bundle_sha256":"cd07c9aa6e2c0a7769020355c53d6d0855767d9a814ffb8eeec162c786cd17de"}}