{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PTB3UKM2RZZHQPRCWIG2UVWXDX","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":"f57e5adfe9a7819b9fe77fbf96d606be815ee5c5d20ee7d967bae591a09871df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-18T15:48:27Z","title_canon_sha256":"a969d0c6e28cb450821602a178fead4b535514a9e2863faf48985d3571066978"},"schema_version":"1.0","source":{"id":"1106.3663","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3663","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3663v1","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3663","created_at":"2026-05-18T04:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"PTB3UKM2RZZH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PTB3UKM2RZZHQPRC","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PTB3UKM2","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:a86f5358b625ce5b3cca2840a69bc956867593d94d55ed58911c3fc0fc1761df","target":"graph","created_at":"2026-05-18T04:19:42Z","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 introduce a weak order ideal property that suffices for establishing the Evans-Griffith Syzygy Theorem. We study this weak order ideal property in settings that allow for comparison between homological algebra over a local ring $R$ versus a hypersurface ring $R/(x^n)$. Consequently we solve some relevant cases of the Evans-Griffith syzygy conjecture over local rings of unramified mixed characteristic $p$, with the case of syzygies of prime ideals of Cohen-Macaulay local rings of unramified mixed characteristic being noted. We reduce the remaining considerations to modules annihilated by $p^","authors_text":"Alexandra Seceleanu, Phillip A. Griffith","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-18T15:48:27Z","title":"Syzygy Theorems via Comparison of Order Ideals on a Hypersurface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3663","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":"sha256:71759495ad0af20922df0ced5ed294e1853b845854a9f1e42c064b97be687744","target":"record","created_at":"2026-05-18T04:19:42Z","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":"f57e5adfe9a7819b9fe77fbf96d606be815ee5c5d20ee7d967bae591a09871df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-06-18T15:48:27Z","title_canon_sha256":"a969d0c6e28cb450821602a178fead4b535514a9e2863faf48985d3571066978"},"schema_version":"1.0","source":{"id":"1106.3663","kind":"arxiv","version":1}},"canonical_sha256":"7cc3ba299a8e72783e22b20daa56d71dfefd00cb61fe98af0690ee6bf3da7936","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cc3ba299a8e72783e22b20daa56d71dfefd00cb61fe98af0690ee6bf3da7936","first_computed_at":"2026-05-18T04:19:42.492829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:42.492829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ZNui1tmBxt8hVjGdzSJbd+8w2gF5+dwdnWfRq6sVoPMrEA/5MWfh4WYC1gQEbH8mtUPwL70idOGNrMZNpLaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:42.493366Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3663","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71759495ad0af20922df0ced5ed294e1853b845854a9f1e42c064b97be687744","sha256:a86f5358b625ce5b3cca2840a69bc956867593d94d55ed58911c3fc0fc1761df"],"state_sha256":"f43e9e2274575137652a70e7e0a95b338c543c09cf71dfc01fe6433296b64047"}