{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7QJMHTJOJE2RZPPS7FIL3XQ4YI","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":"0b47aa6a71658b859d92c5290091c90d36867a1d3918758926fe479fbc7b3794","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-23T13:04:17Z","title_canon_sha256":"f25bd684559e94ece1d1fb7df139cfa695fe951a465239a698b680182ea58d74"},"schema_version":"1.0","source":{"id":"1504.06163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06163","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06163v1","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06163","created_at":"2026-05-18T02:18:02Z"},{"alias_kind":"pith_short_12","alias_value":"7QJMHTJOJE2R","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7QJMHTJOJE2RZPPS","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7QJMHTJO","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:8380582b58a177e6011b26e7f975c5ec2bf52f1aa35cb543616c369b2c8bdcca","target":"graph","created_at":"2026-05-18T02:18:02Z","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":"Let $(R,\\m,k)$ be a commutative noetherian local ring of Krull dimension $d$. We prove that the cohomology annihilator $\\ca(R)$ of $R$ is $\\m$-primary if and only if for some $n\\ge0$ the $n$-th syzygies in $\\mod R$ are constructed from syzygies of $k$ by taking direct sums/summands and a fixed number of extensions. These conditions yield that $R$ is an isolated singularity such that the bounded derived category $\\db(R)$ and the singularity category $\\ds(R)$ have finite dimension, and the converse holds when $R$ is Gorenstein. We also show that the modules locally free on the punctured spectrum","authors_text":"Abdolnaser Bahlekeh, Ehsan Hakimian, Ryo Takahashi, Shokrollah Salarian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-23T13:04:17Z","title":"Annihilation of cohomology, generation of modules and finiteness of derived dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06163","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":"sha256:09b089f30455cd3962442e5fd8e1c3a6953d691ce32af9e3b067889a63430484","target":"record","created_at":"2026-05-18T02:18:02Z","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":"0b47aa6a71658b859d92c5290091c90d36867a1d3918758926fe479fbc7b3794","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-23T13:04:17Z","title_canon_sha256":"f25bd684559e94ece1d1fb7df139cfa695fe951a465239a698b680182ea58d74"},"schema_version":"1.0","source":{"id":"1504.06163","kind":"arxiv","version":1}},"canonical_sha256":"fc12c3cd2e49351cbdf2f950bdde1cc226a225b528322bcadbad49d37290e45b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc12c3cd2e49351cbdf2f950bdde1cc226a225b528322bcadbad49d37290e45b","first_computed_at":"2026-05-18T02:18:02.362757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:02.362757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fzzyCOK2LOVaXAgvbaIuTZW3RHfUqFmoyOqsnsOCzg8kJccAs55LaM96zrakMfBL4EJe/RtnteeN8Zi+ucsIDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:02.363247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09b089f30455cd3962442e5fd8e1c3a6953d691ce32af9e3b067889a63430484","sha256:8380582b58a177e6011b26e7f975c5ec2bf52f1aa35cb543616c369b2c8bdcca"],"state_sha256":"a2bbbb296afca6c6b64c0a72397bed6c019de9b448259014c121f2cca33137bd"}