{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:IZL6KIBMQH4ZNI7IYDKENCT4SH","short_pith_number":"pith:IZL6KIBM","schema_version":"1.0","canonical_sha256":"4657e5202c81f996a3e8c0d4468a7c91c9f13b86a385ddc525811ec60c8e73a2","source":{"kind":"arxiv","id":"1211.6576","version":5},"attestation_state":"computed","paper":{"title":"Noncommutative stable homotopy and stable infinity categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.OA","authors_text":"Snigdhayan Mahanta","submitted_at":"2012-11-28T11:10:00Z","abstract_excerpt":"The noncommutative stable homotopy category $\\mathtt{NSH}$ is a triangulated category that is the universal receptacle for triangulated homology theories on separable $C^*$-algebras. We show that the triangulated category $\\mathtt{NSH}$ is topological as defined by Schwede using the formalism of (stable) infinity categories. More precisely, we construct a stable presentable infinity category of noncommutative spectra and show that $\\mathtt{NSH}^{op}$ sits inside its homotopy category as a full triangulated subcategory, from which the above result can be deduced. We also introduce a presentable"},"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":"1211.6576","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-28T11:10:00Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"6cae66c52266f93f0e948764b977b4f90b8f07788f2b1fa10003ff67287270c1","abstract_canon_sha256":"4545acf71c9c7b062376d103bb5f672ac16c5e210d706d4a68ecfdf0f84a8c7e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:09.984188Z","signature_b64":"45pAaTaYwQ2FSJIBxblwjPp0sxG+AkJrEicDr6sN7K1wSltO35vR80kVLLsUJUoIAetd9Aj7ssOCsNPUiI5GAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4657e5202c81f996a3e8c0d4468a7c91c9f13b86a385ddc525811ec60c8e73a2","last_reissued_at":"2026-05-18T00:43:09.983570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:09.983570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noncommutative stable homotopy and stable infinity categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.OA","authors_text":"Snigdhayan Mahanta","submitted_at":"2012-11-28T11:10:00Z","abstract_excerpt":"The noncommutative stable homotopy category $\\mathtt{NSH}$ is a triangulated category that is the universal receptacle for triangulated homology theories on separable $C^*$-algebras. We show that the triangulated category $\\mathtt{NSH}$ is topological as defined by Schwede using the formalism of (stable) infinity categories. More precisely, we construct a stable presentable infinity category of noncommutative spectra and show that $\\mathtt{NSH}^{op}$ sits inside its homotopy category as a full triangulated subcategory, from which the above result can be deduced. We also introduce a presentable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6576","kind":"arxiv","version":5},"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":"1211.6576","created_at":"2026-05-18T00:43:09.983663+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.6576v5","created_at":"2026-05-18T00:43:09.983663+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6576","created_at":"2026-05-18T00:43:09.983663+00:00"},{"alias_kind":"pith_short_12","alias_value":"IZL6KIBMQH4Z","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"IZL6KIBMQH4ZNI7I","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"IZL6KIBM","created_at":"2026-05-18T12:27:09.501522+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/IZL6KIBMQH4ZNI7IYDKENCT4SH","json":"https://pith.science/pith/IZL6KIBMQH4ZNI7IYDKENCT4SH.json","graph_json":"https://pith.science/api/pith-number/IZL6KIBMQH4ZNI7IYDKENCT4SH/graph.json","events_json":"https://pith.science/api/pith-number/IZL6KIBMQH4ZNI7IYDKENCT4SH/events.json","paper":"https://pith.science/paper/IZL6KIBM"},"agent_actions":{"view_html":"https://pith.science/pith/IZL6KIBMQH4ZNI7IYDKENCT4SH","download_json":"https://pith.science/pith/IZL6KIBMQH4ZNI7IYDKENCT4SH.json","view_paper":"https://pith.science/paper/IZL6KIBM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.6576&json=true","fetch_graph":"https://pith.science/api/pith-number/IZL6KIBMQH4ZNI7IYDKENCT4SH/graph.json","fetch_events":"https://pith.science/api/pith-number/IZL6KIBMQH4ZNI7IYDKENCT4SH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IZL6KIBMQH4ZNI7IYDKENCT4SH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IZL6KIBMQH4ZNI7IYDKENCT4SH/action/storage_attestation","attest_author":"https://pith.science/pith/IZL6KIBMQH4ZNI7IYDKENCT4SH/action/author_attestation","sign_citation":"https://pith.science/pith/IZL6KIBMQH4ZNI7IYDKENCT4SH/action/citation_signature","submit_replication":"https://pith.science/pith/IZL6KIBMQH4ZNI7IYDKENCT4SH/action/replication_record"}},"created_at":"2026-05-18T00:43:09.983663+00:00","updated_at":"2026-05-18T00:43:09.983663+00:00"}