{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:ENNG2SUGISZBXKNNVVENC4JSKI","short_pith_number":"pith:ENNG2SUG","schema_version":"1.0","canonical_sha256":"235a6d4a8644b21ba9adad48d1713252195019187a330e3efd06f55a1e635d4a","source":{"kind":"arxiv","id":"0806.3546","version":1},"attestation_state":"computed","paper":{"title":"$C^*$-algebras associated with algebraic correspondences on the Riemann sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Tsuyoshi Kajiwara, Yasuo Watatani","submitted_at":"2008-06-22T07:47:17Z","abstract_excerpt":"Let $p(z,w)$ be a polynomial in two variables. We call the solution of the algebraic equation $p(z,w) = 0$ the algebraic correspondence. We regard it as the graph of the multivalued function $z \\mapsto w$ defined implicitly by $p(z,w) = 0$. Algebraic correspondences on the Riemann sphere $\\hat{\\mathbb C}$ give a generalization of dynamical systems of Klein groups and rational functions. We introduce $C^*$-algebras associated with algebraic correspondences on the Riemann sphere. We show that if an algebraic correspondence is free and expansive on a closed $p$-invariant subset $J$ of $\\hat{\\math"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0806.3546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-06-22T07:47:17Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"1e3ff23bd0220f08df45f6c12cd5a6d046959d71527be6b3550816f3ae11e2de","abstract_canon_sha256":"cb320beaca95fc1c7d8a550503d473c22c2b791166902c1b2988ad851851b3b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:12:22.882147Z","signature_b64":"fERSezsmZjFi0mcJ02hF+MW4Y9dmxCxVGZZuRfYXifwCyhSUcbmm5b4nzt9qVy+eySxU3nMP3AMFwHobWxMWDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"235a6d4a8644b21ba9adad48d1713252195019187a330e3efd06f55a1e635d4a","last_reissued_at":"2026-07-04T15:12:22.881709Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:12:22.881709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$C^*$-algebras associated with algebraic correspondences on the Riemann sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Tsuyoshi Kajiwara, Yasuo Watatani","submitted_at":"2008-06-22T07:47:17Z","abstract_excerpt":"Let $p(z,w)$ be a polynomial in two variables. We call the solution of the algebraic equation $p(z,w) = 0$ the algebraic correspondence. We regard it as the graph of the multivalued function $z \\mapsto w$ defined implicitly by $p(z,w) = 0$. Algebraic correspondences on the Riemann sphere $\\hat{\\mathbb C}$ give a generalization of dynamical systems of Klein groups and rational functions. We introduce $C^*$-algebras associated with algebraic correspondences on the Riemann sphere. We show that if an algebraic correspondence is free and expansive on a closed $p$-invariant subset $J$ of $\\hat{\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.3546","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/0806.3546/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":"0806.3546","created_at":"2026-07-04T15:12:22.881773+00:00"},{"alias_kind":"arxiv_version","alias_value":"0806.3546v1","created_at":"2026-07-04T15:12:22.881773+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.3546","created_at":"2026-07-04T15:12:22.881773+00:00"},{"alias_kind":"pith_short_12","alias_value":"ENNG2SUGISZB","created_at":"2026-07-04T15:12:22.881773+00:00"},{"alias_kind":"pith_short_16","alias_value":"ENNG2SUGISZBXKNN","created_at":"2026-07-04T15:12:22.881773+00:00"},{"alias_kind":"pith_short_8","alias_value":"ENNG2SUG","created_at":"2026-07-04T15:12:22.881773+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/ENNG2SUGISZBXKNNVVENC4JSKI","json":"https://pith.science/pith/ENNG2SUGISZBXKNNVVENC4JSKI.json","graph_json":"https://pith.science/api/pith-number/ENNG2SUGISZBXKNNVVENC4JSKI/graph.json","events_json":"https://pith.science/api/pith-number/ENNG2SUGISZBXKNNVVENC4JSKI/events.json","paper":"https://pith.science/paper/ENNG2SUG"},"agent_actions":{"view_html":"https://pith.science/pith/ENNG2SUGISZBXKNNVVENC4JSKI","download_json":"https://pith.science/pith/ENNG2SUGISZBXKNNVVENC4JSKI.json","view_paper":"https://pith.science/paper/ENNG2SUG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0806.3546&json=true","fetch_graph":"https://pith.science/api/pith-number/ENNG2SUGISZBXKNNVVENC4JSKI/graph.json","fetch_events":"https://pith.science/api/pith-number/ENNG2SUGISZBXKNNVVENC4JSKI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ENNG2SUGISZBXKNNVVENC4JSKI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ENNG2SUGISZBXKNNVVENC4JSKI/action/storage_attestation","attest_author":"https://pith.science/pith/ENNG2SUGISZBXKNNVVENC4JSKI/action/author_attestation","sign_citation":"https://pith.science/pith/ENNG2SUGISZBXKNNVVENC4JSKI/action/citation_signature","submit_replication":"https://pith.science/pith/ENNG2SUGISZBXKNNVVENC4JSKI/action/replication_record"}},"created_at":"2026-07-04T15:12:22.881773+00:00","updated_at":"2026-07-04T15:12:22.881773+00:00"}