{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:KY6O7AFHTBFWLLSC7SADSD27ZT","short_pith_number":"pith:KY6O7AFH","schema_version":"1.0","canonical_sha256":"563cef80a7984b65ae42fc80390f5fccf4ad2a094bd39fba2945399f23288d11","source":{"kind":"arxiv","id":"0905.2219","version":1},"attestation_state":"computed","paper":{"title":"Generalisations of the Camassa-Holm equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Vladimir Novikov","submitted_at":"2009-05-13T23:22:10Z","abstract_excerpt":"We classify generalised Camassa-Holm type equations which possess infinite hierarchies of higher symmetries. We show that the obtained equations can be treated as negative flows of integrable quasi-linear scalar evolution equations of orders 2, 3 and 5. We present the corresponding Lax representations or linearisation transformations for these equations. Some of the obtained equations seem to be new."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0905.2219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2009-05-13T23:22:10Z","cross_cats_sorted":[],"title_canon_sha256":"ec6c4c084ec3a23c47e5abed6cb2f815ae69cdf6748a7098f5c0bb0be7f6caa3","abstract_canon_sha256":"a8ef014d3407ef3e38d014adce6ceecc5c7dd00059b3e2e1d31cadc0ab312be4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:42:34.595142Z","signature_b64":"w+xxrRNkPaM7xvnhDk/XdcJwEt+wrriQqEScpH9cnyaG2EMDHfrjaAn5I0b6zskfnX2B1iln8nmugJV1tqIAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"563cef80a7984b65ae42fc80390f5fccf4ad2a094bd39fba2945399f23288d11","last_reissued_at":"2026-07-04T15:42:34.594625Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:42:34.594625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalisations of the Camassa-Holm equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Vladimir Novikov","submitted_at":"2009-05-13T23:22:10Z","abstract_excerpt":"We classify generalised Camassa-Holm type equations which possess infinite hierarchies of higher symmetries. We show that the obtained equations can be treated as negative flows of integrable quasi-linear scalar evolution equations of orders 2, 3 and 5. We present the corresponding Lax representations or linearisation transformations for these equations. Some of the obtained equations seem to be new."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2219","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0905.2219/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0905.2219","created_at":"2026-07-04T15:42:34.594693+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.2219v1","created_at":"2026-07-04T15:42:34.594693+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.2219","created_at":"2026-07-04T15:42:34.594693+00:00"},{"alias_kind":"pith_short_12","alias_value":"KY6O7AFHTBFW","created_at":"2026-07-04T15:42:34.594693+00:00"},{"alias_kind":"pith_short_16","alias_value":"KY6O7AFHTBFWLLSC","created_at":"2026-07-04T15:42:34.594693+00:00"},{"alias_kind":"pith_short_8","alias_value":"KY6O7AFH","created_at":"2026-07-04T15:42:34.594693+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KY6O7AFHTBFWLLSC7SADSD27ZT","json":"https://pith.science/pith/KY6O7AFHTBFWLLSC7SADSD27ZT.json","graph_json":"https://pith.science/api/pith-number/KY6O7AFHTBFWLLSC7SADSD27ZT/graph.json","events_json":"https://pith.science/api/pith-number/KY6O7AFHTBFWLLSC7SADSD27ZT/events.json","paper":"https://pith.science/paper/KY6O7AFH"},"agent_actions":{"view_html":"https://pith.science/pith/KY6O7AFHTBFWLLSC7SADSD27ZT","download_json":"https://pith.science/pith/KY6O7AFHTBFWLLSC7SADSD27ZT.json","view_paper":"https://pith.science/paper/KY6O7AFH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.2219&json=true","fetch_graph":"https://pith.science/api/pith-number/KY6O7AFHTBFWLLSC7SADSD27ZT/graph.json","fetch_events":"https://pith.science/api/pith-number/KY6O7AFHTBFWLLSC7SADSD27ZT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KY6O7AFHTBFWLLSC7SADSD27ZT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KY6O7AFHTBFWLLSC7SADSD27ZT/action/storage_attestation","attest_author":"https://pith.science/pith/KY6O7AFHTBFWLLSC7SADSD27ZT/action/author_attestation","sign_citation":"https://pith.science/pith/KY6O7AFHTBFWLLSC7SADSD27ZT/action/citation_signature","submit_replication":"https://pith.science/pith/KY6O7AFHTBFWLLSC7SADSD27ZT/action/replication_record"}},"created_at":"2026-07-04T15:42:34.594693+00:00","updated_at":"2026-07-04T15:42:34.594693+00:00"}