{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:CPKCYV6FCLV6CUOXUE2LHFKWW7","short_pith_number":"pith:CPKCYV6F","canonical_record":{"source":{"id":"2304.00527","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-04-02T12:56:16Z","cross_cats_sorted":["math.KT","math.RA"],"title_canon_sha256":"616d1c2c5bcf3b9c07ccaf64373b08f00f1de520013241c0d07926179d395c67","abstract_canon_sha256":"03b6644f06718c4394162a8b399a6d4cc3b41b92320871e82e81349d99686cde"},"schema_version":"1.0"},"canonical_sha256":"13d42c57c512ebe151d7a134b39556b7d0541dabcdf4ecb7027769d0cbfca2dc","source":{"kind":"arxiv","id":"2304.00527","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00527","created_at":"2026-05-27T14:06:33Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00527v3","created_at":"2026-05-27T14:06:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00527","created_at":"2026-05-27T14:06:33Z"},{"alias_kind":"pith_short_12","alias_value":"CPKCYV6FCLV6","created_at":"2026-05-27T14:06:33Z"},{"alias_kind":"pith_short_16","alias_value":"CPKCYV6FCLV6CUOX","created_at":"2026-05-27T14:06:33Z"},{"alias_kind":"pith_short_8","alias_value":"CPKCYV6F","created_at":"2026-05-27T14:06:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:CPKCYV6FCLV6CUOXUE2LHFKWW7","target":"record","payload":{"canonical_record":{"source":{"id":"2304.00527","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-04-02T12:56:16Z","cross_cats_sorted":["math.KT","math.RA"],"title_canon_sha256":"616d1c2c5bcf3b9c07ccaf64373b08f00f1de520013241c0d07926179d395c67","abstract_canon_sha256":"03b6644f06718c4394162a8b399a6d4cc3b41b92320871e82e81349d99686cde"},"schema_version":"1.0"},"canonical_sha256":"13d42c57c512ebe151d7a134b39556b7d0541dabcdf4ecb7027769d0cbfca2dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T14:06:33.411326Z","signature_b64":"0Jt1m+OQ019w6wL/v6qBh4HllZUkEpBE2aECG7qq7FRBoHvGZOpnQPdgcyAzyIx22Zu1UzP0jPXZWOnfvGnoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13d42c57c512ebe151d7a134b39556b7d0541dabcdf4ecb7027769d0cbfca2dc","last_reissued_at":"2026-05-27T14:06:33.410143Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T14:06:33.410143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.00527","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":"2026-05-27T14:06:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LPIVIGiX0j2TYgGpiPettotz/qrSwpGCLjJf5pw3RdDGwzOY4U3rSy07LEtQYZx/6fsiRCLYuMqGh18fCYobAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:07:14.164217Z"},"content_sha256":"4b066656b553e26d4852155a7df502a2d55725071963bc544bc28b446cc90b27","schema_version":"1.0","event_id":"sha256:4b066656b553e26d4852155a7df502a2d55725071963bc544bc28b446cc90b27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:CPKCYV6FCLV6CUOXUE2LHFKWW7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"G-dimensions for DG-modules over commutative DG-rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.KT","math.RA"],"primary_cat":"math.AC","authors_text":"Jiangsheng Hu, Rongmin Zhu, Xiaoyan Yang","submitted_at":"2023-04-02T12:56:16Z","abstract_excerpt":"We define and study a notion of G-dimension for DG-modules over a non-positively graded commutative noetherian DG-ring $A$. Some criteria for the finiteness of the G-dimension of a DG-module are given by applying a DG-version of projective resolution introduced by Minamoto [Israel J. Math. 245 (2021) 409-454]. Moreover, it is proved that the finiteness of G-dimension characterizes the local Gorenstein property of $A$. Applications go in three directions. The first is to establish the connection between G-dimensions and the little finitistic dimensions of &\\mathcal{A}&. The second is to charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00527","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/2304.00527/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":"2026-05-27T14:06:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iPlYqmio4G/WHhW1Ms/qN5ruuC64y24SiNks+Nhwmq0kXWscpUPo3nUYsQAuXzJWC4xaVKXaTtIdBq9k3hOLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:07:14.164613Z"},"content_sha256":"a112c690613b08f5e89fe98956511af1aa94bb7ae65433d0336001fa55105bc9","schema_version":"1.0","event_id":"sha256:a112c690613b08f5e89fe98956511af1aa94bb7ae65433d0336001fa55105bc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CPKCYV6FCLV6CUOXUE2LHFKWW7/bundle.json","state_url":"https://pith.science/pith/CPKCYV6FCLV6CUOXUE2LHFKWW7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CPKCYV6FCLV6CUOXUE2LHFKWW7/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":"2026-06-07T08:07:14Z","links":{"resolver":"https://pith.science/pith/CPKCYV6FCLV6CUOXUE2LHFKWW7","bundle":"https://pith.science/pith/CPKCYV6FCLV6CUOXUE2LHFKWW7/bundle.json","state":"https://pith.science/pith/CPKCYV6FCLV6CUOXUE2LHFKWW7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CPKCYV6FCLV6CUOXUE2LHFKWW7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:CPKCYV6FCLV6CUOXUE2LHFKWW7","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":"03b6644f06718c4394162a8b399a6d4cc3b41b92320871e82e81349d99686cde","cross_cats_sorted":["math.KT","math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-04-02T12:56:16Z","title_canon_sha256":"616d1c2c5bcf3b9c07ccaf64373b08f00f1de520013241c0d07926179d395c67"},"schema_version":"1.0","source":{"id":"2304.00527","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.00527","created_at":"2026-05-27T14:06:33Z"},{"alias_kind":"arxiv_version","alias_value":"2304.00527v3","created_at":"2026-05-27T14:06:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.00527","created_at":"2026-05-27T14:06:33Z"},{"alias_kind":"pith_short_12","alias_value":"CPKCYV6FCLV6","created_at":"2026-05-27T14:06:33Z"},{"alias_kind":"pith_short_16","alias_value":"CPKCYV6FCLV6CUOX","created_at":"2026-05-27T14:06:33Z"},{"alias_kind":"pith_short_8","alias_value":"CPKCYV6F","created_at":"2026-05-27T14:06:33Z"}],"graph_snapshots":[{"event_id":"sha256:a112c690613b08f5e89fe98956511af1aa94bb7ae65433d0336001fa55105bc9","target":"graph","created_at":"2026-05-27T14:06:33Z","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/2304.00527/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define and study a notion of G-dimension for DG-modules over a non-positively graded commutative noetherian DG-ring $A$. Some criteria for the finiteness of the G-dimension of a DG-module are given by applying a DG-version of projective resolution introduced by Minamoto [Israel J. Math. 245 (2021) 409-454]. Moreover, it is proved that the finiteness of G-dimension characterizes the local Gorenstein property of $A$. Applications go in three directions. The first is to establish the connection between G-dimensions and the little finitistic dimensions of &\\mathcal{A}&. The second is to charact","authors_text":"Jiangsheng Hu, Rongmin Zhu, Xiaoyan Yang","cross_cats":["math.KT","math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-04-02T12:56:16Z","title":"G-dimensions for DG-modules over commutative DG-rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.00527","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":"sha256:4b066656b553e26d4852155a7df502a2d55725071963bc544bc28b446cc90b27","target":"record","created_at":"2026-05-27T14:06:33Z","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":"03b6644f06718c4394162a8b399a6d4cc3b41b92320871e82e81349d99686cde","cross_cats_sorted":["math.KT","math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-04-02T12:56:16Z","title_canon_sha256":"616d1c2c5bcf3b9c07ccaf64373b08f00f1de520013241c0d07926179d395c67"},"schema_version":"1.0","source":{"id":"2304.00527","kind":"arxiv","version":3}},"canonical_sha256":"13d42c57c512ebe151d7a134b39556b7d0541dabcdf4ecb7027769d0cbfca2dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13d42c57c512ebe151d7a134b39556b7d0541dabcdf4ecb7027769d0cbfca2dc","first_computed_at":"2026-05-27T14:06:33.410143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T14:06:33.410143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Jt1m+OQ019w6wL/v6qBh4HllZUkEpBE2aECG7qq7FRBoHvGZOpnQPdgcyAzyIx22Zu1UzP0jPXZWOnfvGnoDw==","signature_status":"signed_v1","signed_at":"2026-05-27T14:06:33.411326Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.00527","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b066656b553e26d4852155a7df502a2d55725071963bc544bc28b446cc90b27","sha256:a112c690613b08f5e89fe98956511af1aa94bb7ae65433d0336001fa55105bc9"],"state_sha256":"3d6602e53011698507df7705c94b0a9dc0fd90b553cc58b57f3b2692afa9a179"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UOhN4UlLEK65mf3AIET+LOnpLamedVNUYTioe0+2TUt/55XxG7oioOW+glIAsP2syFInXBCbDwQQKrfceAmdBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T08:07:14.166956Z","bundle_sha256":"b39dd615b88e99aeaf860f6e82ee0a72baf8c9f9b042dc97fe353af9d24c10ed"}}