{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:T76JBDOCJMJEBRQSKOUXBAUHBV","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":"a1e84f1437164dc64dcc25b1da7a00f7faa65f01405029ff631ec8f428a5e9e5","cross_cats_sorted":["math.AG","math.CT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-03-08T03:00:57Z","title_canon_sha256":"e5ce29e857c3f4cec7f119b5ba5f3ecc40bdaf011270d0d844e3bc6db758c018"},"schema_version":"1.0","source":{"id":"1203.1683","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1683","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1683v1","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1683","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"T76JBDOCJMJE","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"T76JBDOCJMJEBRQS","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"T76JBDOC","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:b753a4caaefba830bce0523743aeea876e9cf5eb95b95ea336fb58a5bae820b3","target":"graph","created_at":"2026-05-18T04:00:37Z","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":"This paper gives upper bounds for the dimension of the singularity category of a Cohen-Macaulay local ring with an isolated singularity. One of them recovers an upper bound given by Ballard, Favero and Katzarkov in the case of a hypersurface.","authors_text":"Hailong Dao, Ryo Takahashi","cross_cats":["math.AG","math.CT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-03-08T03:00:57Z","title":"Upper bounds for dimensions of singularity categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1683","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:d7f8bb1de0f3cf8c87ca22b2bedf37b7f685730fe7959fe9438ec0356b0c0645","target":"record","created_at":"2026-05-18T04:00:37Z","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":"a1e84f1437164dc64dcc25b1da7a00f7faa65f01405029ff631ec8f428a5e9e5","cross_cats_sorted":["math.AG","math.CT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-03-08T03:00:57Z","title_canon_sha256":"e5ce29e857c3f4cec7f119b5ba5f3ecc40bdaf011270d0d844e3bc6db758c018"},"schema_version":"1.0","source":{"id":"1203.1683","kind":"arxiv","version":1}},"canonical_sha256":"9ffc908dc24b1240c61253a97082870d64dceabcc1fbca076cf7a578ead00496","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ffc908dc24b1240c61253a97082870d64dceabcc1fbca076cf7a578ead00496","first_computed_at":"2026-05-18T04:00:37.276871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:37.276871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L9HiB0cQXQZn2KWy/EbYU1JFHTRHCTEJQd+05BGRrbe1n/wcch/G2jtu+SBDYTJQj0qEPnV3QuBRbpoX3+YOCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:37.277489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1683","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7f8bb1de0f3cf8c87ca22b2bedf37b7f685730fe7959fe9438ec0356b0c0645","sha256:b753a4caaefba830bce0523743aeea876e9cf5eb95b95ea336fb58a5bae820b3"],"state_sha256":"59724b7819c0d42092faf1b41ca604f7f8cdf7f6567c29199664c21cb8af7d9b"}