{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SGZY2YR3GNFIC3JIQUF35ZJNUG","short_pith_number":"pith:SGZY2YR3","schema_version":"1.0","canonical_sha256":"91b38d623b334a816d28850bbee52da1afe44fdf978b801dd145035b642a0f08","source":{"kind":"arxiv","id":"1708.03258","version":1},"attestation_state":"computed","paper":{"title":"E-theory Spectra for graded C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.OA","authors_text":"Sarah L. Browne","submitted_at":"2017-08-10T15:33:54Z","abstract_excerpt":"This paper brings together C*-algebras and algebraic topology in terms of viewing a C*-algebraic invariant in terms of a topological spectrum. E-theory, E(A,B), is a bivariant functor in the sense that is a cohomology functor in the first variable and a homology functor in the second variable but underlying goes from the category of separable C*-algebras and *-homomorphisms to the category of abelian groups and group homomorphisms. Here we create a generalisation of a orthogonal spectrum to quasi-topological spaces for E-theory. This includes a rich product structure in the context of graded s"},"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":"1708.03258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-08-10T15:33:54Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"fa2ea6038d523287003ec6ddc8a3b97822864b315f068a3f68a9924352782958","abstract_canon_sha256":"7c4d2323e9544f6dfed24c179106cee6d6159d7e5262ad5288c16a57e23ccb7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:14.319816Z","signature_b64":"/NHkPk7IS8r9A3ZoCYaZIuIKRAk+FBOW/9954nXBZ5f38RJixjNpaSSTMkNjuMBrP11ZGt9mwgDA/ry1nn7iCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91b38d623b334a816d28850bbee52da1afe44fdf978b801dd145035b642a0f08","last_reissued_at":"2026-05-18T00:38:14.319137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:14.319137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"E-theory Spectra for graded C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.OA","authors_text":"Sarah L. Browne","submitted_at":"2017-08-10T15:33:54Z","abstract_excerpt":"This paper brings together C*-algebras and algebraic topology in terms of viewing a C*-algebraic invariant in terms of a topological spectrum. E-theory, E(A,B), is a bivariant functor in the sense that is a cohomology functor in the first variable and a homology functor in the second variable but underlying goes from the category of separable C*-algebras and *-homomorphisms to the category of abelian groups and group homomorphisms. Here we create a generalisation of a orthogonal spectrum to quasi-topological spaces for E-theory. This includes a rich product structure in the context of graded s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03258","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":"1708.03258","created_at":"2026-05-18T00:38:14.319248+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.03258v1","created_at":"2026-05-18T00:38:14.319248+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03258","created_at":"2026-05-18T00:38:14.319248+00:00"},{"alias_kind":"pith_short_12","alias_value":"SGZY2YR3GNFI","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SGZY2YR3GNFIC3JI","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SGZY2YR3","created_at":"2026-05-18T12:31:43.269735+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/SGZY2YR3GNFIC3JIQUF35ZJNUG","json":"https://pith.science/pith/SGZY2YR3GNFIC3JIQUF35ZJNUG.json","graph_json":"https://pith.science/api/pith-number/SGZY2YR3GNFIC3JIQUF35ZJNUG/graph.json","events_json":"https://pith.science/api/pith-number/SGZY2YR3GNFIC3JIQUF35ZJNUG/events.json","paper":"https://pith.science/paper/SGZY2YR3"},"agent_actions":{"view_html":"https://pith.science/pith/SGZY2YR3GNFIC3JIQUF35ZJNUG","download_json":"https://pith.science/pith/SGZY2YR3GNFIC3JIQUF35ZJNUG.json","view_paper":"https://pith.science/paper/SGZY2YR3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.03258&json=true","fetch_graph":"https://pith.science/api/pith-number/SGZY2YR3GNFIC3JIQUF35ZJNUG/graph.json","fetch_events":"https://pith.science/api/pith-number/SGZY2YR3GNFIC3JIQUF35ZJNUG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SGZY2YR3GNFIC3JIQUF35ZJNUG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SGZY2YR3GNFIC3JIQUF35ZJNUG/action/storage_attestation","attest_author":"https://pith.science/pith/SGZY2YR3GNFIC3JIQUF35ZJNUG/action/author_attestation","sign_citation":"https://pith.science/pith/SGZY2YR3GNFIC3JIQUF35ZJNUG/action/citation_signature","submit_replication":"https://pith.science/pith/SGZY2YR3GNFIC3JIQUF35ZJNUG/action/replication_record"}},"created_at":"2026-05-18T00:38:14.319248+00:00","updated_at":"2026-05-18T00:38:14.319248+00:00"}