{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6ZP4YOBVYH56GODRKYZI7Y6XSN","short_pith_number":"pith:6ZP4YOBV","schema_version":"1.0","canonical_sha256":"f65fcc3835c1fbe3387156328fe3d7935bab9ea56ed4f4f6413e45adffc57c5d","source":{"kind":"arxiv","id":"1706.00563","version":1},"attestation_state":"computed","paper":{"title":"Graded C*-algebras, graded K-theory, and twisted P-graph C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Aidan Sims, Alex Kumjian, David Pask","submitted_at":"2017-06-02T06:02:01Z","abstract_excerpt":"We develop methods for computing graded K-theory of C*-algebras as defined in terms of Kasparov theory. We establish graded versions of Pimsner's six-term sequences for graded Hilbert bimodules whose left action is injective and by compacts, and a graded Pimsner-Voiculescu sequence. We introduce the notion of a twisted P-graph C*-algebra and establish connections with graded C*-algebras. Specifically, we show how a functor from a P-graph into the group of order two determines a grading of the associated C*-algebra. We apply our graded version of Pimsner's exact sequence to compute the graded K"},"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":"1706.00563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-02T06:02:01Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"d786141a9754e85297ed04730b434251899b408f2118877284d1a244fcfb3942","abstract_canon_sha256":"209ccdf94668c5cc2bccbe91192eba7a72989ba6f1d3df6c2c86d1e0f8416cc1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:12.720020Z","signature_b64":"eZm3nW+IfaBJ7AxcxosFZOFPdArL8g0LVu/kaopIereNQqre0YDfZtjisuCUOPuhqbEbkJc9PijF4WU/NmKWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f65fcc3835c1fbe3387156328fe3d7935bab9ea56ed4f4f6413e45adffc57c5d","last_reissued_at":"2026-05-18T00:43:12.719471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:12.719471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graded C*-algebras, graded K-theory, and twisted P-graph C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Aidan Sims, Alex Kumjian, David Pask","submitted_at":"2017-06-02T06:02:01Z","abstract_excerpt":"We develop methods for computing graded K-theory of C*-algebras as defined in terms of Kasparov theory. We establish graded versions of Pimsner's six-term sequences for graded Hilbert bimodules whose left action is injective and by compacts, and a graded Pimsner-Voiculescu sequence. We introduce the notion of a twisted P-graph C*-algebra and establish connections with graded C*-algebras. Specifically, we show how a functor from a P-graph into the group of order two determines a grading of the associated C*-algebra. We apply our graded version of Pimsner's exact sequence to compute the graded K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00563","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.00563","created_at":"2026-05-18T00:43:12.719561+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.00563v1","created_at":"2026-05-18T00:43:12.719561+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00563","created_at":"2026-05-18T00:43:12.719561+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ZP4YOBVYH56","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ZP4YOBVYH56GODR","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ZP4YOBV","created_at":"2026-05-18T12:31:03.183658+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/6ZP4YOBVYH56GODRKYZI7Y6XSN","json":"https://pith.science/pith/6ZP4YOBVYH56GODRKYZI7Y6XSN.json","graph_json":"https://pith.science/api/pith-number/6ZP4YOBVYH56GODRKYZI7Y6XSN/graph.json","events_json":"https://pith.science/api/pith-number/6ZP4YOBVYH56GODRKYZI7Y6XSN/events.json","paper":"https://pith.science/paper/6ZP4YOBV"},"agent_actions":{"view_html":"https://pith.science/pith/6ZP4YOBVYH56GODRKYZI7Y6XSN","download_json":"https://pith.science/pith/6ZP4YOBVYH56GODRKYZI7Y6XSN.json","view_paper":"https://pith.science/paper/6ZP4YOBV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.00563&json=true","fetch_graph":"https://pith.science/api/pith-number/6ZP4YOBVYH56GODRKYZI7Y6XSN/graph.json","fetch_events":"https://pith.science/api/pith-number/6ZP4YOBVYH56GODRKYZI7Y6XSN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ZP4YOBVYH56GODRKYZI7Y6XSN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ZP4YOBVYH56GODRKYZI7Y6XSN/action/storage_attestation","attest_author":"https://pith.science/pith/6ZP4YOBVYH56GODRKYZI7Y6XSN/action/author_attestation","sign_citation":"https://pith.science/pith/6ZP4YOBVYH56GODRKYZI7Y6XSN/action/citation_signature","submit_replication":"https://pith.science/pith/6ZP4YOBVYH56GODRKYZI7Y6XSN/action/replication_record"}},"created_at":"2026-05-18T00:43:12.719561+00:00","updated_at":"2026-05-18T00:43:12.719561+00:00"}