{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:GUIEVAWCS75I2DDY3KFCWFC5DT","short_pith_number":"pith:GUIEVAWC","canonical_record":{"source":{"id":"2009.11800","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-09-24T16:44:25Z","cross_cats_sorted":[],"title_canon_sha256":"2d265f03a6795b35cfa3d1b566683ca742aed0bc18c47e03640c44e566acc850","abstract_canon_sha256":"017fcb7cc8e3deea2d32da41c7f334ad3201f7130a6e183cb801c06ca3dc64ef"},"schema_version":"1.0"},"canonical_sha256":"35104a82c297fa8d0c78da8a2b145d1cebe99e6144b984015333e039c8f8c682","source":{"kind":"arxiv","id":"2009.11800","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:GUIEVAWCS75I2DDY3KFCWFC5DT","target":"record","payload":{"canonical_record":{"source":{"id":"2009.11800","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-09-24T16:44:25Z","cross_cats_sorted":[],"title_canon_sha256":"2d265f03a6795b35cfa3d1b566683ca742aed0bc18c47e03640c44e566acc850","abstract_canon_sha256":"017fcb7cc8e3deea2d32da41c7f334ad3201f7130a6e183cb801c06ca3dc64ef"},"schema_version":"1.0"},"canonical_sha256":"35104a82c297fa8d0c78da8a2b145d1cebe99e6144b984015333e039c8f8c682","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:39:57.265929Z","signature_b64":"5wDqhap0z5moE8A34QK4vgQ4MiPlkJW41ppJx4wybf+oIN/XfDfQ/4EyVIDUboE7M7EVB/gjQFdKsx9McyPMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35104a82c297fa8d0c78da8a2b145d1cebe99e6144b984015333e039c8f8c682","last_reissued_at":"2026-07-05T02:39:57.265338Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:39:57.265338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.11800","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:39:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YrG2YXDNZpI6JC//wof1hdk7YwbJvm86eEozS0pjF918euZM+jBQkRSOCm4gq/U11xQU0KrBnViS0cnTHDDZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T22:38:19.981558Z"},"content_sha256":"2c5b5cc605214ede3510bb519593b9cab0748c582ce7de17570c9c24d0d50c73","schema_version":"1.0","event_id":"sha256:2c5b5cc605214ede3510bb519593b9cab0748c582ce7de17570c9c24d0d50c73"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:GUIEVAWCS75I2DDY3KFCWFC5DT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constructing non-proxy small test modules for the complete intersection property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Benjamin Briggs, Elo\\'isa Grifo, Josh Pollitz","submitted_at":"2020-09-24T16:44:25Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11800","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.11800/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:39:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GT+4KoI16rtDT0JRALGbmTIFWsrbxRji8ABVw03ZvY+BJFacS4r/EhY9NaaVUW0ocjaOmkw0MSip8OKb6YA1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T22:38:19.982142Z"},"content_sha256":"51fc1ec12d8760d0568afb3b6ed59282c2f78799e61eae760767803e221f7b48","schema_version":"1.0","event_id":"sha256:51fc1ec12d8760d0568afb3b6ed59282c2f78799e61eae760767803e221f7b48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GUIEVAWCS75I2DDY3KFCWFC5DT/bundle.json","state_url":"https://pith.science/pith/GUIEVAWCS75I2DDY3KFCWFC5DT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GUIEVAWCS75I2DDY3KFCWFC5DT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T22:38:19Z","links":{"resolver":"https://pith.science/pith/GUIEVAWCS75I2DDY3KFCWFC5DT","bundle":"https://pith.science/pith/GUIEVAWCS75I2DDY3KFCWFC5DT/bundle.json","state":"https://pith.science/pith/GUIEVAWCS75I2DDY3KFCWFC5DT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GUIEVAWCS75I2DDY3KFCWFC5DT/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1lGSMdUrD+zgYCmrdtsE5g52uYWE02zzzX45ojZD0LtAXyXYCP/dIXYi6PpcmrYtgco2VfNhr23na7Ke5C7lCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T22:38:19.987388Z","bundle_sha256":"75ff3425f560f1b866d0c1eb31209cbebc4a1a09a49376ecd107bdb34e464656"}}