{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:GUIEVAWCS75I2DDY3KFCWFC5DT","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":"017fcb7cc8e3deea2d32da41c7f334ad3201f7130a6e183cb801c06ca3dc64ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-09-24T16:44:25Z","title_canon_sha256":"2d265f03a6795b35cfa3d1b566683ca742aed0bc18c47e03640c44e566acc850"},"schema_version":"1.0","source":{"id":"2009.11800","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.11800","created_at":"2026-07-05T02:39:57Z"},{"alias_kind":"arxiv_version","alias_value":"2009.11800v3","created_at":"2026-07-05T02:39:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.11800","created_at":"2026-07-05T02:39:57Z"},{"alias_kind":"pith_short_12","alias_value":"GUIEVAWCS75I","created_at":"2026-07-05T02:39:57Z"},{"alias_kind":"pith_short_16","alias_value":"GUIEVAWCS75I2DDY","created_at":"2026-07-05T02:39:57Z"},{"alias_kind":"pith_short_8","alias_value":"GUIEVAWC","created_at":"2026-07-05T02:39:57Z"}],"graph_snapshots":[{"event_id":"sha256:51fc1ec12d8760d0568afb3b6ed59282c2f78799e61eae760767803e221f7b48","target":"graph","created_at":"2026-07-05T02:39:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2009.11800/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A local ring $R$ is regular if and only if every finitely generated $R$-module has finite projective dimension. Moreover, the residue field $k$ is a test module: $R$ is regular if and only if $k$ has finite projective dimension. This characterization can be extended to the bounded derived category $\\mathsf{D}^f(R)$, which contains only small objects if and only if $R$ is regular.\n  Recent results of Pollitz, completing work initiated by Dwyer-Greenlees-Iyengar, yield an analogous characterization for complete intersections: $R$ is a complete intersection if and only if every object in $\\mathsf","authors_text":"Benjamin Briggs, Elo\\'isa Grifo, Josh Pollitz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-09-24T16:44:25Z","title":"Constructing non-proxy small test modules for the complete intersection property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11800","kind":"arxiv","version":3},"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":"sha256:2c5b5cc605214ede3510bb519593b9cab0748c582ce7de17570c9c24d0d50c73","target":"record","created_at":"2026-07-05T02:39:57Z","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":"017fcb7cc8e3deea2d32da41c7f334ad3201f7130a6e183cb801c06ca3dc64ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-09-24T16:44:25Z","title_canon_sha256":"2d265f03a6795b35cfa3d1b566683ca742aed0bc18c47e03640c44e566acc850"},"schema_version":"1.0","source":{"id":"2009.11800","kind":"arxiv","version":3}},"canonical_sha256":"35104a82c297fa8d0c78da8a2b145d1cebe99e6144b984015333e039c8f8c682","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35104a82c297fa8d0c78da8a2b145d1cebe99e6144b984015333e039c8f8c682","first_computed_at":"2026-07-05T02:39:57.265338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:39:57.265338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5wDqhap0z5moE8A34QK4vgQ4MiPlkJW41ppJx4wybf+oIN/XfDfQ/4EyVIDUboE7M7EVB/gjQFdKsx9McyPMBg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:39:57.265929Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.11800","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c5b5cc605214ede3510bb519593b9cab0748c582ce7de17570c9c24d0d50c73","sha256:51fc1ec12d8760d0568afb3b6ed59282c2f78799e61eae760767803e221f7b48"],"state_sha256":"88df64cbcb120f06cc247be1e74544d26617d67f10d720ebb26c67c458615e6e"}