{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2ZED5QYSNM2VLFCZRHU3GYMJLX","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":"22f5fe04f375da02984c206b7a306370586cb361bc5ac81b1f1693632ff87cb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-15T22:22:48Z","title_canon_sha256":"c8f5b8fd301e48ce8c31b3279864ebf749ab830808e71eeb51495563fe4561dd"},"schema_version":"1.0","source":{"id":"1708.04707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04707","created_at":"2026-05-18T00:37:58Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04707v1","created_at":"2026-05-18T00:37:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04707","created_at":"2026-05-18T00:37:58Z"},{"alias_kind":"pith_short_12","alias_value":"2ZED5QYSNM2V","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2ZED5QYSNM2VLFCZ","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2ZED5QYS","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:6cf6f80a74b9b92072555143ea98dae8f6528844750da5312ddca4f9e6028892","target":"graph","created_at":"2026-05-18T00:37:58Z","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 extend the Oprea's result $G_1(\\mathbb{S}^{2n+1}/H)=\\mathcal{Z}H$ to the 1st generalized Gottlieb group $G_1^f(\\mathbb{S}^{2n+1}/H)$ for a map $f\\colon A\\to \\mathbb{S}^{2n+1}/H$. Then, we compute or estimate the groups $G_m^f(\\mathbb{S}^{2n+1}/H)$ and $P_m^f(\\mathbb{S}^{2n+1}/H)$ for some $m>1$ and finite groups $H$.","authors_text":"Marek Golasi\\'nski, Thiago de Melo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-15T22:22:48Z","title":"Generalized Gottlieb and Whitehead center groups of space forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04707","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":"sha256:0b83f34fbfe949d09d72b325c2d877b013fdfb0463a7099959c6dc8ad3216e5a","target":"record","created_at":"2026-05-18T00:37:58Z","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":"22f5fe04f375da02984c206b7a306370586cb361bc5ac81b1f1693632ff87cb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-08-15T22:22:48Z","title_canon_sha256":"c8f5b8fd301e48ce8c31b3279864ebf749ab830808e71eeb51495563fe4561dd"},"schema_version":"1.0","source":{"id":"1708.04707","kind":"arxiv","version":1}},"canonical_sha256":"d6483ec3126b3555945989e9b361895dd92ad8e48ed149ee61702db1bc4ed089","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6483ec3126b3555945989e9b361895dd92ad8e48ed149ee61702db1bc4ed089","first_computed_at":"2026-05-18T00:37:58.136080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:58.136080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BAsKNZtPjY1J7K3P7OzCxtvfQLPwKLkBI1z7g6OdTGl7Nl+Jax7cG96jxk/TDbKrcfyiBKXKZtrKHE23joxEAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:58.136736Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b83f34fbfe949d09d72b325c2d877b013fdfb0463a7099959c6dc8ad3216e5a","sha256:6cf6f80a74b9b92072555143ea98dae8f6528844750da5312ddca4f9e6028892"],"state_sha256":"de167ce873437d8dc17cd5008752bf42b808ba561dabca395ff02d47a3846fa2"}