{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NZAYSNQ6LAYT3OP4NJATAT42GL","short_pith_number":"pith:NZAYSNQ6","canonical_record":{"source":{"id":"1411.5856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-11-21T13:02:25Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"c5e88bb70069de145d56e583a4de4f941b59e53b7fe7aaeeb991a6b95bb3d8ae","abstract_canon_sha256":"adc070e1aa574da31e4e5f56d259babb4fb419c5ad704d4d6289286a50e81a0f"},"schema_version":"1.0"},"canonical_sha256":"6e4189361e58313db9fc6a41304f9a32d71faaebba629b143024405d9795874d","source":{"kind":"arxiv","id":"1411.5856","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5856","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5856v1","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5856","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"NZAYSNQ6LAYT","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NZAYSNQ6LAYT3OP4","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NZAYSNQ6","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NZAYSNQ6LAYT3OP4NJATAT42GL","target":"record","payload":{"canonical_record":{"source":{"id":"1411.5856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-11-21T13:02:25Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"c5e88bb70069de145d56e583a4de4f941b59e53b7fe7aaeeb991a6b95bb3d8ae","abstract_canon_sha256":"adc070e1aa574da31e4e5f56d259babb4fb419c5ad704d4d6289286a50e81a0f"},"schema_version":"1.0"},"canonical_sha256":"6e4189361e58313db9fc6a41304f9a32d71faaebba629b143024405d9795874d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:33.305131Z","signature_b64":"D1a2vgnSOvQKCwKzET5xwmysE1VlYuoB0IegegSe6Sqp9IabbsQV4kSEHyO9TgQWB6Qp4ONTzUyuhw1+vPRzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e4189361e58313db9fc6a41304f9a32d71faaebba629b143024405d9795874d","last_reissued_at":"2026-05-18T01:55:33.304518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:33.304518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.5856","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":"4vhH6XnJkfk/OSxAk52Vbn9IhsLhkJmN9llAIMVY2FcTXj/uiG8NT1ANlEdSOzPg4NNesjjJBSTUnebWAvdJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:43:38.184190Z"},"content_sha256":"9e9db0c473d3854d407330640f426bb8a32e81ef5a320428557afc4c676632fd","schema_version":"1.0","event_id":"sha256:9e9db0c473d3854d407330640f426bb8a32e81ef5a320428557afc4c676632fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NZAYSNQ6LAYT3OP4NJATAT42GL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical points, Lauricella functions and Whitham-type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"nlin.SI","authors_text":"B. Konopelchenko, W.K. Schief, Y. Kodama","submitted_at":"2014-11-21T13:02:25Z","abstract_excerpt":"A large class of semi-Hamiltonian systems of hydrodynamic type is interpreted as the equations governing families of critical points of functions obeying the classical linear Darboux equations for conjugate nets.The distinguished role of the Euler-Poisson-Darboux equations and associated Lauricella-type functions is emphasised. In particular, it is shown that the classical g-phase Whitham equations for the KdV and NLS equations are obtained via a g-fold iterated Darboux-type transformation generated by appropriate Lauricella functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5856","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":"z40pDMKcy//XvNkiYycTbuoyzi1NPdWxnenaDplKcqn94fofXMQvMZ/8zbqjF2Cd7c9r8oFaopsAzzhfCbqFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:43:38.184802Z"},"content_sha256":"6571075247b5975362f7647f7954d44f736f0dee4cdd25c79b894f086cb418c5","schema_version":"1.0","event_id":"sha256:6571075247b5975362f7647f7954d44f736f0dee4cdd25c79b894f086cb418c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZAYSNQ6LAYT3OP4NJATAT42GL/bundle.json","state_url":"https://pith.science/pith/NZAYSNQ6LAYT3OP4NJATAT42GL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZAYSNQ6LAYT3OP4NJATAT42GL/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":"2026-05-27T19:43:38Z","links":{"resolver":"https://pith.science/pith/NZAYSNQ6LAYT3OP4NJATAT42GL","bundle":"https://pith.science/pith/NZAYSNQ6LAYT3OP4NJATAT42GL/bundle.json","state":"https://pith.science/pith/NZAYSNQ6LAYT3OP4NJATAT42GL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZAYSNQ6LAYT3OP4NJATAT42GL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NZAYSNQ6LAYT3OP4NJATAT42GL","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":"adc070e1aa574da31e4e5f56d259babb4fb419c5ad704d4d6289286a50e81a0f","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-11-21T13:02:25Z","title_canon_sha256":"c5e88bb70069de145d56e583a4de4f941b59e53b7fe7aaeeb991a6b95bb3d8ae"},"schema_version":"1.0","source":{"id":"1411.5856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5856","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5856v1","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5856","created_at":"2026-05-18T01:55:33Z"},{"alias_kind":"pith_short_12","alias_value":"NZAYSNQ6LAYT","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NZAYSNQ6LAYT3OP4","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NZAYSNQ6","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:6571075247b5975362f7647f7954d44f736f0dee4cdd25c79b894f086cb418c5","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":"A large class of semi-Hamiltonian systems of hydrodynamic type is interpreted as the equations governing families of critical points of functions obeying the classical linear Darboux equations for conjugate nets.The distinguished role of the Euler-Poisson-Darboux equations and associated Lauricella-type functions is emphasised. In particular, it is shown that the classical g-phase Whitham equations for the KdV and NLS equations are obtained via a g-fold iterated Darboux-type transformation generated by appropriate Lauricella functions.","authors_text":"B. Konopelchenko, W.K. Schief, Y. Kodama","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-11-21T13:02:25Z","title":"Critical points, Lauricella functions and Whitham-type equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5856","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":"sha256:9e9db0c473d3854d407330640f426bb8a32e81ef5a320428557afc4c676632fd","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":"adc070e1aa574da31e4e5f56d259babb4fb419c5ad704d4d6289286a50e81a0f","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-11-21T13:02:25Z","title_canon_sha256":"c5e88bb70069de145d56e583a4de4f941b59e53b7fe7aaeeb991a6b95bb3d8ae"},"schema_version":"1.0","source":{"id":"1411.5856","kind":"arxiv","version":1}},"canonical_sha256":"6e4189361e58313db9fc6a41304f9a32d71faaebba629b143024405d9795874d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e4189361e58313db9fc6a41304f9a32d71faaebba629b143024405d9795874d","first_computed_at":"2026-05-18T01:55:33.304518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:33.304518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D1a2vgnSOvQKCwKzET5xwmysE1VlYuoB0IegegSe6Sqp9IabbsQV4kSEHyO9TgQWB6Qp4ONTzUyuhw1+vPRzBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:33.305131Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e9db0c473d3854d407330640f426bb8a32e81ef5a320428557afc4c676632fd","sha256:6571075247b5975362f7647f7954d44f736f0dee4cdd25c79b894f086cb418c5"],"state_sha256":"36278f4ae973887fffb39ff621689f8ce7c6837161b743ea7195d557bec938ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1szXwUgI6VKYyoDgkZKuYwG4hd8RzEbNnVKENzlfzWRT2/CvKwNbQWY1F8zY8F5iY2D7KK2nkU5nZFdxGfbTBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:43:38.187902Z","bundle_sha256":"bbe1d2070087ace4af0aeaa4833af949adb3261bee5f35fbfba7a42ea09feee6"}}