{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7RM2DAYBUBXW5PF3SCUQAH4E47","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":"543fe86c31465076546e750c47b59754f69f58f9cd3a95ebcce26ca9780f1ac5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-01-22T10:57:39Z","title_canon_sha256":"b6b8f3152e76f39bdea0091b212587af6e5b32567117b546197c40a4e921978e"},"schema_version":"1.0","source":{"id":"1101.4278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4278","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4278v1","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4278","created_at":"2026-05-18T02:59:45Z"},{"alias_kind":"pith_short_12","alias_value":"7RM2DAYBUBXW","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7RM2DAYBUBXW5PF3","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7RM2DAYB","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:f0d02a0faed99e96c2e7b8c3d0fa927d9ff0bdcd2346098064b7c82e97fea7f6","target":"graph","created_at":"2026-05-18T02:59:45Z","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":"Connected components of $\\Map(S^4,B\\SU(2))$ are the classifying spaces of gauge groups of principal $\\SU(2)$-bundles over $S^4$. Tsukuda [Tsu01] has investigated the homotopy types of connected components of $\\Map(S^4,B\\SU(2))$. But unfortunately, the proof of Lemma 2.4 in [Tsu01] is not correct for $p=2$. In this paper, we give a complete proof. Moreover, we investigate the further divisibility of $\\epsilon_i$ defined in [Tsu01]. In [Tsu], it is shown that divisibility of $\\epsilon_i$ have some information about $A_i$-equivalence types of the gauge groups.","authors_text":"Mitsunobu Tsutaya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-01-22T10:57:39Z","title":"A note on homotopy types of connected components of Map(S^4,BSU(2))"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4278","kind":"arxiv","version":1},"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:e051f4a3273ca3f26f876de63ef129c17dd26a2c0fd30e9ff60dc0cf4b37b684","target":"record","created_at":"2026-05-18T02:59:45Z","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":"543fe86c31465076546e750c47b59754f69f58f9cd3a95ebcce26ca9780f1ac5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-01-22T10:57:39Z","title_canon_sha256":"b6b8f3152e76f39bdea0091b212587af6e5b32567117b546197c40a4e921978e"},"schema_version":"1.0","source":{"id":"1101.4278","kind":"arxiv","version":1}},"canonical_sha256":"fc59a18301a06f6ebcbb90a9001f84e7c0790858b9f3bed623083ff0119e4348","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc59a18301a06f6ebcbb90a9001f84e7c0790858b9f3bed623083ff0119e4348","first_computed_at":"2026-05-18T02:59:45.600674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:45.600674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZWP+DEaQbRxARaV92yhv3V5sHBGyYHxybix1fX1iAJXHxUSp6seYqnKXCWrcPasDDGAnTN8jzjK1Jk0WpQHMBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:45.601556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e051f4a3273ca3f26f876de63ef129c17dd26a2c0fd30e9ff60dc0cf4b37b684","sha256:f0d02a0faed99e96c2e7b8c3d0fa927d9ff0bdcd2346098064b7c82e97fea7f6"],"state_sha256":"65dd9ac89356d169f553b0f6934d82040b7104733a6f1c59019a45237a2a90df"}