{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IJ62QMBXPNMDAJETIOGC6IVYEN","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":"10974dab33cd0ee8e859d943bb402d25cfdeefeb40505ea86980a93971cce982","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-13T19:23:53Z","title_canon_sha256":"6e552aff2531106f3c10adc644a974ab3605f1af561ba1f578ed924e8168d407"},"schema_version":"1.0","source":{"id":"1711.04806","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04806","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04806v3","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04806","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"IJ62QMBXPNMD","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IJ62QMBXPNMDAJET","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IJ62QMBX","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:b1b8bcff83453e683c2e83c6f1c13c95447804e2b61623d5f181873c4b944c48","target":"graph","created_at":"2026-05-18T00:10:47Z","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":"Morava $E$-theory $E$ is an $E_\\infty$-ring with an action of the Morava stabilizer group $\\Gamma$. We study the derived stack $\\operatorname{Spf} E/\\Gamma$. Descent-theoretic techniques allow us to deduce a theorem of Hopkins-Mahowald-Sadofsky on the $K(n)$-local Picard group, as well as a recent result of Barthel-Beaudry-Stojanoska on the Anderson duals of higher real $K$-theories.","authors_text":"Sanath K. Devalapurkar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-13T19:23:53Z","title":"The Lubin-Tate stack and Gross-Hopkins duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04806","kind":"arxiv","version":3},"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":"sha256:5ee93e0bf751f807d100abd12f414f645e73c13e4e9db213e8ddbe295ba83a5b","target":"record","created_at":"2026-05-18T00:10:47Z","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":"10974dab33cd0ee8e859d943bb402d25cfdeefeb40505ea86980a93971cce982","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-13T19:23:53Z","title_canon_sha256":"6e552aff2531106f3c10adc644a974ab3605f1af561ba1f578ed924e8168d407"},"schema_version":"1.0","source":{"id":"1711.04806","kind":"arxiv","version":3}},"canonical_sha256":"427da830377b58302493438c2f22b8235d1d51b060535be097b698f919f62ba4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"427da830377b58302493438c2f22b8235d1d51b060535be097b698f919f62ba4","first_computed_at":"2026-05-18T00:10:47.232925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:47.232925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p6S85Joe9T+mESgwXTqXFd/SxSCVz1cQff/EyJn62Hx3TJy3lmF9+WuPwM0XFI5xkh4uU4QylkCp1LOlShdiDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:47.233566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04806","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ee93e0bf751f807d100abd12f414f645e73c13e4e9db213e8ddbe295ba83a5b","sha256:b1b8bcff83453e683c2e83c6f1c13c95447804e2b61623d5f181873c4b944c48"],"state_sha256":"32d12e374499bff8b0df2c4f924526e1e78370185236a99cd51d4962f873b81e"}