{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:ZKBPIAMQBEK4QCDMAPPHR7LZO2","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":"fa84c29d6b28e1aa70ae012d3bebd120e02bbba805c300dbe752865050c950fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2022-03-25T16:20:23Z","title_canon_sha256":"5a36de6ff1cd07ce5d7f1ebcb1e9d709d4390a5efd2088c1e0e3fddd4e10f50d"},"schema_version":"1.0","source":{"id":"2203.13743","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.13743","created_at":"2026-07-05T04:08:35Z"},{"alias_kind":"arxiv_version","alias_value":"2203.13743v1","created_at":"2026-07-05T04:08:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.13743","created_at":"2026-07-05T04:08:35Z"},{"alias_kind":"pith_short_12","alias_value":"ZKBPIAMQBEK4","created_at":"2026-07-05T04:08:35Z"},{"alias_kind":"pith_short_16","alias_value":"ZKBPIAMQBEK4QCDM","created_at":"2026-07-05T04:08:35Z"},{"alias_kind":"pith_short_8","alias_value":"ZKBPIAMQ","created_at":"2026-07-05T04:08:35Z"}],"graph_snapshots":[{"event_id":"sha256:5cd9ac8a2257e7277869285d09c64ca9a6b5f784f5f9d1b76210aa72198d9742","target":"graph","created_at":"2026-07-05T04:08:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.13743/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a height $\\leq 2$ Landweber exact $\\mathbb{E}_\\infty$-ring $E$ whose homotopy is concentrated in even degrees, we show that any complex orientation of $E$ which satisfies the Ando criterion admits a unique lift to an $\\mathbb{E}_\\infty$-complex orientation $\\mathrm{MU} \\to E$. As a consequence, we give a short proof that the level $n$ elliptic genus lifts uniquely to an $\\mathbb{E}_\\infty$-complex orientation $\\mathrm{MU} \\to \\mathrm{tmf}_1 (n)$ for all $n \\geq 2$.","authors_text":"Andrew Senger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2022-03-25T16:20:23Z","title":"Obstruction theory and the level $n$ elliptic genus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.13743","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":"sha256:995f9bb2f26d400c96a74d81625f99e4fda2d572e7c8a996f79ffc5aa7bbfd29","target":"record","created_at":"2026-07-05T04:08:35Z","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":"fa84c29d6b28e1aa70ae012d3bebd120e02bbba805c300dbe752865050c950fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2022-03-25T16:20:23Z","title_canon_sha256":"5a36de6ff1cd07ce5d7f1ebcb1e9d709d4390a5efd2088c1e0e3fddd4e10f50d"},"schema_version":"1.0","source":{"id":"2203.13743","kind":"arxiv","version":1}},"canonical_sha256":"ca82f401900915c8086c03de78fd79768de5ab1b022eaf9401f1174f1b79e42e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca82f401900915c8086c03de78fd79768de5ab1b022eaf9401f1174f1b79e42e","first_computed_at":"2026-07-05T04:08:35.608095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:08:35.608095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"flTXiGQmNES5Wy3nGiwcLTxe9vwskgkG98O/oxlwQ/ttwshECfPOCGDE1foqyp6iJGM3aCqiNV3HoyJhFMexDg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:08:35.608502Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.13743","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:995f9bb2f26d400c96a74d81625f99e4fda2d572e7c8a996f79ffc5aa7bbfd29","sha256:5cd9ac8a2257e7277869285d09c64ca9a6b5f784f5f9d1b76210aa72198d9742"],"state_sha256":"e80bd083b9b04949f4413d6900982623a51bc96815df79d19a0fbba9e6968bc5"}