{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RLTYGTHI5WIIHJO6E7EXAEYIOF","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":"a1f91f9f34fac798cc3fc383ecf736dfc5a33a15c2c76f79f7ff9a867d787af6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-01-31T00:22:25Z","title_canon_sha256":"a0fcdce72c719d1f2dfd707c3b6043f128ef534081659bb252f558799f3f8939"},"schema_version":"1.0","source":{"id":"1401.8034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.8034","created_at":"2026-05-18T03:00:36Z"},{"alias_kind":"arxiv_version","alias_value":"1401.8034v1","created_at":"2026-05-18T03:00:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.8034","created_at":"2026-05-18T03:00:36Z"},{"alias_kind":"pith_short_12","alias_value":"RLTYGTHI5WII","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RLTYGTHI5WIIHJO6","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RLTYGTHI","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:c5e90d2a43ee1cb69acfcb18056e70768bffdb59aa2e13bfb5b80a00c39b46c9","target":"graph","created_at":"2026-05-18T03:00:36Z","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":"Let R be a subring of the rationals with least non-invertible prime p. Let X = X^{n} \\cup_{\\alpha} (\\bigcup_{j \\in J} e^{q}) be a cell attachment with J finite and q small with respect to p. Let E(X_R) denote the group of homotopy self-equivalences of the R-localization X_R. We use DG Lie models to construct a short exact sequence 0 \\to \\bigoplus_{j \\in J}\\pi_q(X^n)_R \\to E(X_R) \\to C^q \\to 0 where C^q is a subgroup of GL_{|J|}(R) \\times E(X^n_R). We obtain a related result for the R-localization of the nilpotent group E_*(X) of classes inducing the identity on homology. We deduce some explici","authors_text":"Mahmoud Benkhalifa, Samuel Bruce Smith","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-01-31T00:22:25Z","title":"The effect of cell-attachment on the group of self-equivalences of an R-localized space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.8034","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":"sha256:0563d83e1eb9fcb98a49244eb95a7c517154ce587962b0f95d6b0d540bff05af","target":"record","created_at":"2026-05-18T03:00:36Z","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":"a1f91f9f34fac798cc3fc383ecf736dfc5a33a15c2c76f79f7ff9a867d787af6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-01-31T00:22:25Z","title_canon_sha256":"a0fcdce72c719d1f2dfd707c3b6043f128ef534081659bb252f558799f3f8939"},"schema_version":"1.0","source":{"id":"1401.8034","kind":"arxiv","version":1}},"canonical_sha256":"8ae7834ce8ed9083a5de27c9701308717a4918f5b79acf6c7ee45a55f955081e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ae7834ce8ed9083a5de27c9701308717a4918f5b79acf6c7ee45a55f955081e","first_computed_at":"2026-05-18T03:00:36.405183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:36.405183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QBIHckVL+xHksAuxD7aovkzSUes4xRt5Xlhf5e3M7xDCDvjZnRf4gRvHsvC/dn8Ba5qF3qmrr/bReQ0OMT79DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:36.406050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.8034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0563d83e1eb9fcb98a49244eb95a7c517154ce587962b0f95d6b0d540bff05af","sha256:c5e90d2a43ee1cb69acfcb18056e70768bffdb59aa2e13bfb5b80a00c39b46c9"],"state_sha256":"58eb84874d044901cf9977ee36797a641b8bed24057182c605df4860ec2ebdaa"}