{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:YMVAX5YWV2KP4D4C5CHRGYA5LT","short_pith_number":"pith:YMVAX5YW","schema_version":"1.0","canonical_sha256":"c32a0bf716ae94fe0f82e88f13601d5ceb0929360e30368a7baf2759531d1460","source":{"kind":"arxiv","id":"1212.5901","version":3},"attestation_state":"computed","paper":{"title":"Homotopy invariance through small stabilizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.RA"],"primary_cat":"math.KT","authors_text":"Beatriz Abadie, Guillermo Corti\\~nas","submitted_at":"2012-12-24T12:19:48Z","abstract_excerpt":"We associate an algebra $\\Gami(\\fA)$ to each bornological algebra $\\fA$. The algebra $\\Gami(\\fA)$ contains a two-sided ideal $I_{S(\\fA)}$ for each symmetric ideal $S\\triqui\\elli$ of bounded sequences of complex numbers. In the case of $\\Gami=\\Gami(\\C)$, these are all the two-sided ideals, and $I_S\\mapsto J_S=\\cB I_S\\cB$ gives a bijection between the two-sided ideals of $\\Gami$ and those of $\\cB=\\cB(\\ell^2)$. We prove that Weibel's $K$-theory groups $KH_*(I_{S(\\fA)})$ are homotopy invariant for certain ideals $S$ including $c_0$ and $\\ell^p$. Moreover, if either $S=c_0$ and $\\fA$ is a local $C^"},"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":"1212.5901","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-24T12:19:48Z","cross_cats_sorted":["math.OA","math.RA"],"title_canon_sha256":"dcae7fe4cb81462b047e290552f5ef97adec43896d4984430dc6ceda89f4b286","abstract_canon_sha256":"6112dc2e99a9b704d043b95725f2e78704356023c9e71e6d014a9b690b93f287"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:06.825624Z","signature_b64":"PZ1nhoCsBxP8e0qUsf1tIpUc/toDDlHSe9SbJu6TZEoESbiqnAExoSM67NYSrzz4IoW8P6d7xmnnytEHpFiKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c32a0bf716ae94fe0f82e88f13601d5ceb0929360e30368a7baf2759531d1460","last_reissued_at":"2026-05-18T02:57:06.824989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:06.824989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homotopy invariance through small stabilizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.RA"],"primary_cat":"math.KT","authors_text":"Beatriz Abadie, Guillermo Corti\\~nas","submitted_at":"2012-12-24T12:19:48Z","abstract_excerpt":"We associate an algebra $\\Gami(\\fA)$ to each bornological algebra $\\fA$. The algebra $\\Gami(\\fA)$ contains a two-sided ideal $I_{S(\\fA)}$ for each symmetric ideal $S\\triqui\\elli$ of bounded sequences of complex numbers. In the case of $\\Gami=\\Gami(\\C)$, these are all the two-sided ideals, and $I_S\\mapsto J_S=\\cB I_S\\cB$ gives a bijection between the two-sided ideals of $\\Gami$ and those of $\\cB=\\cB(\\ell^2)$. We prove that Weibel's $K$-theory groups $KH_*(I_{S(\\fA)})$ are homotopy invariant for certain ideals $S$ including $c_0$ and $\\ell^p$. Moreover, if either $S=c_0$ and $\\fA$ is a local $C^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5901","kind":"arxiv","version":3},"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":"1212.5901","created_at":"2026-05-18T02:57:06.825083+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.5901v3","created_at":"2026-05-18T02:57:06.825083+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5901","created_at":"2026-05-18T02:57:06.825083+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMVAX5YWV2KP","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMVAX5YWV2KP4D4C","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMVAX5YW","created_at":"2026-05-18T12:27:27.928770+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/YMVAX5YWV2KP4D4C5CHRGYA5LT","json":"https://pith.science/pith/YMVAX5YWV2KP4D4C5CHRGYA5LT.json","graph_json":"https://pith.science/api/pith-number/YMVAX5YWV2KP4D4C5CHRGYA5LT/graph.json","events_json":"https://pith.science/api/pith-number/YMVAX5YWV2KP4D4C5CHRGYA5LT/events.json","paper":"https://pith.science/paper/YMVAX5YW"},"agent_actions":{"view_html":"https://pith.science/pith/YMVAX5YWV2KP4D4C5CHRGYA5LT","download_json":"https://pith.science/pith/YMVAX5YWV2KP4D4C5CHRGYA5LT.json","view_paper":"https://pith.science/paper/YMVAX5YW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.5901&json=true","fetch_graph":"https://pith.science/api/pith-number/YMVAX5YWV2KP4D4C5CHRGYA5LT/graph.json","fetch_events":"https://pith.science/api/pith-number/YMVAX5YWV2KP4D4C5CHRGYA5LT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMVAX5YWV2KP4D4C5CHRGYA5LT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMVAX5YWV2KP4D4C5CHRGYA5LT/action/storage_attestation","attest_author":"https://pith.science/pith/YMVAX5YWV2KP4D4C5CHRGYA5LT/action/author_attestation","sign_citation":"https://pith.science/pith/YMVAX5YWV2KP4D4C5CHRGYA5LT/action/citation_signature","submit_replication":"https://pith.science/pith/YMVAX5YWV2KP4D4C5CHRGYA5LT/action/replication_record"}},"created_at":"2026-05-18T02:57:06.825083+00:00","updated_at":"2026-05-18T02:57:06.825083+00:00"}