{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ALD3PFRZKVF6E5RZLKZ2RXS4US","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":"5105554ee490c9134528058b5aedd4d754640952f4320701ef7ca504c410e159","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-08-22T13:09:20Z","title_canon_sha256":"75249770725da23a5dece1857b320c0204d8c061200a845554217eddd23c2092"},"schema_version":"1.0","source":{"id":"1808.07342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07342","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07342v1","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07342","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"ALD3PFRZKVF6","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"ALD3PFRZKVF6E5RZ","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"ALD3PFRZ","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:73a93cc11bd1d3fb5d0857d49f9e4280055bc7b515c773e12c074ea6e6de39e4","target":"graph","created_at":"2026-05-18T00:07:29Z","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":"For a compact Lie group G we show that if the representing spectrum for Borel cohomology generates its category of modules if G is connected. For a closed subgroup H of G we consider the map C^*(BG)--->C^*(BH) and establish the sense in which it is relatively Gorenstein. Throughout, we pay careful attention to the importance of connectedness of the groups.","authors_text":"J.P.C.Greenlees","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-08-22T13:09:20Z","title":"Borel cohomology and the relative Gorenstein condition for classifying spaces of compact Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07342","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:ddc6dc4f272210a1b29639bbd95320e40c0b9d314167bd8adac3493fb2202973","target":"record","created_at":"2026-05-18T00:07:29Z","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":"5105554ee490c9134528058b5aedd4d754640952f4320701ef7ca504c410e159","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-08-22T13:09:20Z","title_canon_sha256":"75249770725da23a5dece1857b320c0204d8c061200a845554217eddd23c2092"},"schema_version":"1.0","source":{"id":"1808.07342","kind":"arxiv","version":1}},"canonical_sha256":"02c7b79639554be276395ab3a8de5ca493a30282deab1a99007c6a1574e2229b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02c7b79639554be276395ab3a8de5ca493a30282deab1a99007c6a1574e2229b","first_computed_at":"2026-05-18T00:07:29.118725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:29.118725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eql7hR8E1wx9w/IBDBpYNBGCGcT4BcizRXKmZ1lOyxT7NA14Xrqc1V9gnkWp756HipmQRH8UFWrE4qSx44AoAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:29.119427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.07342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddc6dc4f272210a1b29639bbd95320e40c0b9d314167bd8adac3493fb2202973","sha256:73a93cc11bd1d3fb5d0857d49f9e4280055bc7b515c773e12c074ea6e6de39e4"],"state_sha256":"801cfe8ec2057b73cf1f0d816a793db2234fb3b3b899c406132011017eecd747"}