{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DHGCGODZLKIDDNO7IT66XALRXH","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":"960582f3b46b9c37e96a07a1ee8a54dc2068d2a37bf7f33776655a30e763f647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-16T09:07:46Z","title_canon_sha256":"295bb1907b75f48a4ee92830177e55567d99888625dcb309930c501884862bdb"},"schema_version":"1.0","source":{"id":"1705.05604","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05604","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05604v2","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05604","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"DHGCGODZLKID","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DHGCGODZLKIDDNO7","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DHGCGODZ","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:8c1b6846a1f52b453e96eb98a400ebdb516e6a1e8b21927e9a64d3e836691261","target":"graph","created_at":"2026-05-18T00:34:15Z","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":"In this work, the set of quasi-primary ideals of a commutative ring with identity is equipped with a topology and is called quasi-primary spectrum. Some topological properties of this space are examined. Further, a sheaf of rings on the quasi-primary spectrum is constructed and it is shown that this sheaf is the direct image sheaf with respect to the inclusion map from the prime spectrum of a ring to the quasi-primary spectrum of the same ring.","authors_text":"Neslihan Ay\\c{s}en \\\"Ozkiri\\c{s}\\c{c}i, Zehra Bilgin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-16T09:07:46Z","title":"Quasi-Primary Spectrum of a Commutative Ring and a Sheaf of Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05604","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:f1ea83a5e1f332098eeb3e096229da01590048a3e0cd563bcdf6f55fd5848867","target":"record","created_at":"2026-05-18T00:34:15Z","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":"960582f3b46b9c37e96a07a1ee8a54dc2068d2a37bf7f33776655a30e763f647","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-16T09:07:46Z","title_canon_sha256":"295bb1907b75f48a4ee92830177e55567d99888625dcb309930c501884862bdb"},"schema_version":"1.0","source":{"id":"1705.05604","kind":"arxiv","version":2}},"canonical_sha256":"19cc2338795a9031b5df44fdeb8171b9e797dd423f5ded4cae5117010bd77b4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19cc2338795a9031b5df44fdeb8171b9e797dd423f5ded4cae5117010bd77b4a","first_computed_at":"2026-05-18T00:34:15.209761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:15.209761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H0riNnpFCKk8FeL4fn3mmdC7yMG8b1xyGIUDx/k3jfOf37Z4jIGX3faweMpnkgfxKsy64Xk9HVa7/0QyC6IaCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:15.210461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05604","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1ea83a5e1f332098eeb3e096229da01590048a3e0cd563bcdf6f55fd5848867","sha256:8c1b6846a1f52b453e96eb98a400ebdb516e6a1e8b21927e9a64d3e836691261"],"state_sha256":"16dcabe28bd719a3f690aa93a333c48640b92db56e55eaabdf8dcd93bd4597a2"}