{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O6432BWHKGVS4JWU4B5JKHTXPK","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":"2ceb123e65e69375447c45ba14b6bda7b6592833b3ebc9ade0708d8e672b8c10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-09-13T00:53:20Z","title_canon_sha256":"fd0357a9730d1d9576206a2f2f3e6298bb2f6e3cc9421bfbf91b0c48331789a2"},"schema_version":"1.0","source":{"id":"1809.04723","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04723","created_at":"2026-05-18T00:05:49Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04723v1","created_at":"2026-05-18T00:05:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04723","created_at":"2026-05-18T00:05:49Z"},{"alias_kind":"pith_short_12","alias_value":"O6432BWHKGVS","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"O6432BWHKGVS4JWU","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"O6432BWH","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:d0e367932e8a19c92d80740fdcaf483bb18d24a8921117875b2c7cc66d76ee6e","target":"graph","created_at":"2026-05-18T00:05:49Z","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 prove that if $R$ is an $\\mathbb{E}_2$-ring with homotopy concentrated in even degrees, and $\\{x_j\\}$ is any sequence of elements in $\\pi_{2*}(R)$, then $R/(x_1,x_2,\\cdots)$ admits the structure of an $\\mathbb{E}_1$-$R$-algebra. This removes an assumption, common in the literature, that $\\{x_j\\}$ be a regular sequence.","authors_text":"Dylan Wilson, Jeremy Hahn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-09-13T00:53:20Z","title":"Quotients of even rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04723","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":"sha256:96bb3e6b310bb7a9486b9f2764030d59f9dd97e2fd5c7b40efc5c3fb43796472","target":"record","created_at":"2026-05-18T00:05:49Z","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":"2ceb123e65e69375447c45ba14b6bda7b6592833b3ebc9ade0708d8e672b8c10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-09-13T00:53:20Z","title_canon_sha256":"fd0357a9730d1d9576206a2f2f3e6298bb2f6e3cc9421bfbf91b0c48331789a2"},"schema_version":"1.0","source":{"id":"1809.04723","kind":"arxiv","version":1}},"canonical_sha256":"77b9bd06c751ab2e26d4e07a951e777ab69361459939ded10c41362c1cd07a92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77b9bd06c751ab2e26d4e07a951e777ab69361459939ded10c41362c1cd07a92","first_computed_at":"2026-05-18T00:05:49.828386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:49.828386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v8aa16ak2BHnJTDCBC2ZFemz0AOfLC56+AfhENztBANSW+s3c9lzDO01yzvylyJBAo1nFUbnRFgwDycih7lRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:49.829045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.04723","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96bb3e6b310bb7a9486b9f2764030d59f9dd97e2fd5c7b40efc5c3fb43796472","sha256:d0e367932e8a19c92d80740fdcaf483bb18d24a8921117875b2c7cc66d76ee6e"],"state_sha256":"b258eb4255886037ac52f71852c1346b4f91690cc65601778d07ff6cdba7357f"}