{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YMVAX5YWV2KP4D4C5CHRGYA5LT","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":"6112dc2e99a9b704d043b95725f2e78704356023c9e71e6d014a9b690b93f287","cross_cats_sorted":["math.OA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-24T12:19:48Z","title_canon_sha256":"dcae7fe4cb81462b047e290552f5ef97adec43896d4984430dc6ceda89f4b286"},"schema_version":"1.0","source":{"id":"1212.5901","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5901","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5901v3","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5901","created_at":"2026-05-18T02:57:06Z"},{"alias_kind":"pith_short_12","alias_value":"YMVAX5YWV2KP","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YMVAX5YWV2KP4D4C","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YMVAX5YW","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:4d1ba3e522c8f71450859eb398fc58e56f9fa1d3f30bf8e7e678c15a5a677436","target":"graph","created_at":"2026-05-18T02:57:06Z","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":"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^","authors_text":"Beatriz Abadie, Guillermo Corti\\~nas","cross_cats":["math.OA","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-24T12:19:48Z","title":"Homotopy invariance through small stabilizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5901","kind":"arxiv","version":3},"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":"sha256:0641cdd42f645674661e6c1d1f2dc2ed76b4a3a226ee5658fa0d95ba82863899","target":"record","created_at":"2026-05-18T02:57:06Z","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":"6112dc2e99a9b704d043b95725f2e78704356023c9e71e6d014a9b690b93f287","cross_cats_sorted":["math.OA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-12-24T12:19:48Z","title_canon_sha256":"dcae7fe4cb81462b047e290552f5ef97adec43896d4984430dc6ceda89f4b286"},"schema_version":"1.0","source":{"id":"1212.5901","kind":"arxiv","version":3}},"canonical_sha256":"c32a0bf716ae94fe0f82e88f13601d5ceb0929360e30368a7baf2759531d1460","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c32a0bf716ae94fe0f82e88f13601d5ceb0929360e30368a7baf2759531d1460","first_computed_at":"2026-05-18T02:57:06.824989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:06.824989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PZ1nhoCsBxP8e0qUsf1tIpUc/toDDlHSe9SbJu6TZEoESbiqnAExoSM67NYSrzz4IoW8P6d7xmnnytEHpFiKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:06.825624Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5901","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0641cdd42f645674661e6c1d1f2dc2ed76b4a3a226ee5658fa0d95ba82863899","sha256:4d1ba3e522c8f71450859eb398fc58e56f9fa1d3f30bf8e7e678c15a5a677436"],"state_sha256":"fb3005712909fc92b93ed754db7c8d33e29f8ed7795b2011b382646631ed14fc"}