{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VCSRXYBQXEGOPDZINBMJGHHJCG","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":"7aabde8359f1cb4fb418d440b0d9653ad0cf790a5052c1b46110b12a7627cb44","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-09-03T23:03:00Z","title_canon_sha256":"ea8c2ef66fe7535d51c10c72838fed417598fe6983c61bedf28e8e704807e47d"},"schema_version":"1.0","source":{"id":"1409.1281","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1281","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1281v1","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1281","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"VCSRXYBQXEGO","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VCSRXYBQXEGOPDZI","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VCSRXYBQ","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:5e67002cfe22c7094a75e0f41fa8f2991023c9ee91eded0a6cde11848ae83f33","target":"graph","created_at":"2026-05-18T00:44:28Z","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":"Using the Bockstein spectral sequence developed previously by the authors, we compute the ring ER(n)^*(BO(q)) explicitly. We then use this calculation to show that the ring spectrum MO[2^{n+1}] is ER(n)-orientable (but not ER(n+1)-orientable), where MO[2^{n+1}] is defined as the Thom spectrum for the self map of BO given by multiplication by 2^{n+1}.","authors_text":"Nitu Kitchloo, W. Stephen Wilson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-09-03T23:03:00Z","title":"The ER(n)-cohomology of BO(q), and real Johnson-Wilson orientations for vector bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1281","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":"sha256:6d3b751f6c2dc631f801a66f0617ff2b91ca179f877decf55c465707ea3da14f","target":"record","created_at":"2026-05-18T00:44:28Z","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":"7aabde8359f1cb4fb418d440b0d9653ad0cf790a5052c1b46110b12a7627cb44","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-09-03T23:03:00Z","title_canon_sha256":"ea8c2ef66fe7535d51c10c72838fed417598fe6983c61bedf28e8e704807e47d"},"schema_version":"1.0","source":{"id":"1409.1281","kind":"arxiv","version":1}},"canonical_sha256":"a8a51be030b90ce78f286858931ce911a4f70a793e5c3b779574fa3083096b04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8a51be030b90ce78f286858931ce911a4f70a793e5c3b779574fa3083096b04","first_computed_at":"2026-05-18T00:44:28.836138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:28.836138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/RrMN7oTTXSYscEx34MD5zURj4CbECh5qgVw7dF+QPgeL2+kdQCbbqr5Wgrss4etaxXM6VLo1LE2Ptzbs90eCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:28.836801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1281","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d3b751f6c2dc631f801a66f0617ff2b91ca179f877decf55c465707ea3da14f","sha256:5e67002cfe22c7094a75e0f41fa8f2991023c9ee91eded0a6cde11848ae83f33"],"state_sha256":"5e8e1379bb66c46260cffc8058fb2b7336c0725c6fa6f02e661e67ea23542036"}