{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:N6HQP46O6QMUKAM6OBPWWB3FK6","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":"d759b298be1b050c84e2824d3803dd007474e21a7b9327881e35e28536de834d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-03T10:02:31Z","title_canon_sha256":"cf06c6aed7554fa246f0dc255392f8c65da98853bc7b2f5c03a540b589f18482"},"schema_version":"1.0","source":{"id":"1903.00874","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00874","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00874v2","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00874","created_at":"2026-05-17T23:51:51Z"},{"alias_kind":"pith_short_12","alias_value":"N6HQP46O6QMU","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N6HQP46O6QMUKAM6","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N6HQP46O","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:86ff389ea15578a37b243b97e05a902c630a05a1ffabaaf42c798cd7e43639f0","target":"graph","created_at":"2026-05-17T23:51:51Z","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":"It is a well-known result that, in projective space over a field, every set-theoretical complete intersection of positive dimension in connected in codimension one (Hartshorne [H1,3.4.6] or [H2, Theorem 1.3]). Another important connectedness result is that a local ring with disconnected punctured sprectrum has depth at most $1$ ([H1, Proposition 2.1]). The two results are related, Hartshorne calls the latter \"the keystone to the proof\" of the former (loc. cit).\n  In this short note we show that the latter result generalizes smoothly from set-theoretical to cohomologically complete intersection","authors_text":"Michael Hellus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-03T10:02:31Z","title":"Generalization of a connectedness result to cohomologically complete intersections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00874","kind":"arxiv","version":2},"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:a8a8d7dd3f2969cb095f7d69c063c202beb8ee1df0ff0422de9c0145d51a3dde","target":"record","created_at":"2026-05-17T23:51:51Z","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":"d759b298be1b050c84e2824d3803dd007474e21a7b9327881e35e28536de834d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-03-03T10:02:31Z","title_canon_sha256":"cf06c6aed7554fa246f0dc255392f8c65da98853bc7b2f5c03a540b589f18482"},"schema_version":"1.0","source":{"id":"1903.00874","kind":"arxiv","version":2}},"canonical_sha256":"6f8f07f3cef41945019e705f6b0765578bca7e28f2439b2cd91bede8e2c28e31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f8f07f3cef41945019e705f6b0765578bca7e28f2439b2cd91bede8e2c28e31","first_computed_at":"2026-05-17T23:51:51.911812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:51.911812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ui2CtHILvLixH9Rvr0wUzWBZ54WUYJj9wynzT5PUo45NXJ9+3LiYy3ieE554KcbnYIoIoCsIztIIVS2CaqdiAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:51.912537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00874","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8a8d7dd3f2969cb095f7d69c063c202beb8ee1df0ff0422de9c0145d51a3dde","sha256:86ff389ea15578a37b243b97e05a902c630a05a1ffabaaf42c798cd7e43639f0"],"state_sha256":"000ba9f2637bdd793ce80e25ff387d83f74eeaa4fdc25c404a891d2f85180d17"}