{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:UPN27BNLWPBFKUX4M4XQC3LHLH","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":"60fe904db5504f84f4709e41bdd4dd64d09b68176d25f19486cccd3aa825a35d","cross_cats_sorted":["math.KT"],"license":"","primary_cat":"math.OA","submitted_at":"2001-01-23T01:20:29Z","title_canon_sha256":"81ce65e67b24d6e3b0fcc7f7acceebef58068e43035b13ea99f24af44d000c54"},"schema_version":"1.0","source":{"id":"math/0101184","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0101184","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0101184v2","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0101184","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"UPN27BNLWPBF","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"UPN27BNLWPBFKUX4","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"UPN27BNL","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:a655a0e89a01126d64f92258c58a8918dd90de5e0db3b1b6a38674ef805d9652","target":"graph","created_at":"2026-05-18T01:05:37Z","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":"Motivated by the search for new examples of \"noncommutative manifolds\", we study the noncommutative geometry of the group C*-algebras of various discrete groups. The examples we consier are the infinite dihedral group\n ${\\bf Z} \\times_{\\sigma} {\\bf Z}_2$ and the semidirect product ${\\bf Z} \\times_{\\sigma} {\\bf Z}$. We present a unified treatment of the K-homology and cyclic cohomology of these algebras.","authors_text":"Tom Hadfield","cross_cats":["math.KT"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2001-01-23T01:20:29Z","title":"Fredholm modules over certain group C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101184","kind":"arxiv","version":2},"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":"sha256:319700e24b8388d6c1b3127b83ab6c15eb5a6ae076207a667f93e80e3a36d941","target":"record","created_at":"2026-05-18T01:05:37Z","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":"60fe904db5504f84f4709e41bdd4dd64d09b68176d25f19486cccd3aa825a35d","cross_cats_sorted":["math.KT"],"license":"","primary_cat":"math.OA","submitted_at":"2001-01-23T01:20:29Z","title_canon_sha256":"81ce65e67b24d6e3b0fcc7f7acceebef58068e43035b13ea99f24af44d000c54"},"schema_version":"1.0","source":{"id":"math/0101184","kind":"arxiv","version":2}},"canonical_sha256":"a3dbaf85abb3c25552fc672f016d6759f97f6313626057657f8d0c0ee03dbcfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3dbaf85abb3c25552fc672f016d6759f97f6313626057657f8d0c0ee03dbcfd","first_computed_at":"2026-05-18T01:05:37.968484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:37.968484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+JiAE/xrjEd/PPuuYK2aNdti4FC35agDoWHihPye1POD34WKhMOVeAazY/b8U7ruMD/Ix7xPogB+jMKShuI+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:37.969008Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0101184","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:319700e24b8388d6c1b3127b83ab6c15eb5a6ae076207a667f93e80e3a36d941","sha256:a655a0e89a01126d64f92258c58a8918dd90de5e0db3b1b6a38674ef805d9652"],"state_sha256":"1607fe2935cec706ab4140919389609c95677816d1620f7b4a208ab57f895222"}