{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:ZBZACSHPEK3ZYDPKYZN3KJIICZ","short_pith_number":"pith:ZBZACSHP","schema_version":"1.0","canonical_sha256":"c8720148ef22b79c0deac65bb5250816432daf8efc47f83aac36374da23db898","source":{"kind":"arxiv","id":"math/0001008","version":1},"attestation_state":"computed","paper":{"title":"Hyper-K{\\\"a}hler Hierarchies and their twistor theory","license":"","headline":"","cross_cats":["gr-qc","nlin.SI"],"primary_cat":"math.DG","authors_text":"Lionel J. Mason, Maciej Dunajski","submitted_at":"2000-01-03T19:19:51Z","abstract_excerpt":"A twistor construction of the hierarchy associated with the hyper-K\\\"ahler equations on a metric (the anti-self-dual Einstein vacuum equations, ASDVE, in four dimensions) is given. The recursion operator R is constructed and used to build an infinite-dimensional symmetry algebra and in particular higher flows for the hyper-K\\\"ahler equations. It is shown that R acts on the twistor data by multiplication with a rational function. The structures are illustrated by the example of the Sparling-Tod (Eguchi-Hansen) solution. An extended space-time ${\\cal N}$ is constructed whose extra dimensions cor"},"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":"math/0001008","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2000-01-03T19:19:51Z","cross_cats_sorted":["gr-qc","nlin.SI"],"title_canon_sha256":"c72c6663774a7781857a81148b7f30da050cd53fc6d02417dad2351c344a7843","abstract_canon_sha256":"b5711b919dab2c4e3af6dfa6c4654a56889400f6a812f8ee1758a75262864249"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:21:12.021971Z","signature_b64":"9ufjqXpIGE967fGtk37ks3sfoIIcE7LKIpPjcc4ApF+OFPZnjSrIgs0ApO3nIyFc9Ln+Vqyq9JAPyJCm99sjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8720148ef22b79c0deac65bb5250816432daf8efc47f83aac36374da23db898","last_reissued_at":"2026-07-04T16:21:12.021541Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:21:12.021541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hyper-K{\\\"a}hler Hierarchies and their twistor theory","license":"","headline":"","cross_cats":["gr-qc","nlin.SI"],"primary_cat":"math.DG","authors_text":"Lionel J. Mason, Maciej Dunajski","submitted_at":"2000-01-03T19:19:51Z","abstract_excerpt":"A twistor construction of the hierarchy associated with the hyper-K\\\"ahler equations on a metric (the anti-self-dual Einstein vacuum equations, ASDVE, in four dimensions) is given. The recursion operator R is constructed and used to build an infinite-dimensional symmetry algebra and in particular higher flows for the hyper-K\\\"ahler equations. It is shown that R acts on the twistor data by multiplication with a rational function. The structures are illustrated by the example of the Sparling-Tod (Eguchi-Hansen) solution. An extended space-time ${\\cal N}$ is constructed whose extra dimensions cor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0001008","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/math/0001008/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":"math/0001008","created_at":"2026-07-04T16:21:12.021604+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0001008v1","created_at":"2026-07-04T16:21:12.021604+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0001008","created_at":"2026-07-04T16:21:12.021604+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZBZACSHPEK3Z","created_at":"2026-07-04T16:21:12.021604+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZBZACSHPEK3ZYDPK","created_at":"2026-07-04T16:21:12.021604+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZBZACSHP","created_at":"2026-07-04T16:21:12.021604+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2604.11602","citing_title":"Celestial 1-form symmetries","ref_index":32,"is_internal_anchor":true},{"citing_arxiv_id":"2604.13362","citing_title":"Quasi-Local Celestial Charges and Multipoles","ref_index":64,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZBZACSHPEK3ZYDPKYZN3KJIICZ","json":"https://pith.science/pith/ZBZACSHPEK3ZYDPKYZN3KJIICZ.json","graph_json":"https://pith.science/api/pith-number/ZBZACSHPEK3ZYDPKYZN3KJIICZ/graph.json","events_json":"https://pith.science/api/pith-number/ZBZACSHPEK3ZYDPKYZN3KJIICZ/events.json","paper":"https://pith.science/paper/ZBZACSHP"},"agent_actions":{"view_html":"https://pith.science/pith/ZBZACSHPEK3ZYDPKYZN3KJIICZ","download_json":"https://pith.science/pith/ZBZACSHPEK3ZYDPKYZN3KJIICZ.json","view_paper":"https://pith.science/paper/ZBZACSHP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0001008&json=true","fetch_graph":"https://pith.science/api/pith-number/ZBZACSHPEK3ZYDPKYZN3KJIICZ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZBZACSHPEK3ZYDPKYZN3KJIICZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZBZACSHPEK3ZYDPKYZN3KJIICZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZBZACSHPEK3ZYDPKYZN3KJIICZ/action/storage_attestation","attest_author":"https://pith.science/pith/ZBZACSHPEK3ZYDPKYZN3KJIICZ/action/author_attestation","sign_citation":"https://pith.science/pith/ZBZACSHPEK3ZYDPKYZN3KJIICZ/action/citation_signature","submit_replication":"https://pith.science/pith/ZBZACSHPEK3ZYDPKYZN3KJIICZ/action/replication_record"}},"created_at":"2026-07-04T16:21:12.021604+00:00","updated_at":"2026-07-04T16:21:12.021604+00:00"}