{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SRYI5LTMNZ5IQYPRFK6LNSHBBZ","short_pith_number":"pith:SRYI5LTM","canonical_record":{"source":{"id":"1205.5985","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2012-05-27T17:05:04Z","cross_cats_sorted":[],"title_canon_sha256":"6059dec523c14ce72362bae14eb972c9dadc3aa25240a0f41fd99353977ed951","abstract_canon_sha256":"dc1f428920405960cd414436266c1c3417bdc22ac1751ccd2fe9d8325175384b"},"schema_version":"1.0"},"canonical_sha256":"94708eae6c6e7a8861f12abcb6c8e10e43b9715d8adbd42057e13bb65507a274","source":{"kind":"arxiv","id":"1205.5985","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5985","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5985v2","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5985","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"SRYI5LTMNZ5I","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SRYI5LTMNZ5IQYPR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SRYI5LTM","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SRYI5LTMNZ5IQYPRFK6LNSHBBZ","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5985","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2012-05-27T17:05:04Z","cross_cats_sorted":[],"title_canon_sha256":"6059dec523c14ce72362bae14eb972c9dadc3aa25240a0f41fd99353977ed951","abstract_canon_sha256":"dc1f428920405960cd414436266c1c3417bdc22ac1751ccd2fe9d8325175384b"},"schema_version":"1.0"},"canonical_sha256":"94708eae6c6e7a8861f12abcb6c8e10e43b9715d8adbd42057e13bb65507a274","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:31.772338Z","signature_b64":"5H9JKr6FNtJv8ijl5AMG11zrDpEqbrfIIJ7pwDgWeZCGsysfoax+Z8jN0F4unAzfObjc5PLcZE8C8PZAVB0NCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94708eae6c6e7a8861f12abcb6c8e10e43b9715d8adbd42057e13bb65507a274","last_reissued_at":"2026-05-18T03:32:31.771487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:31.771487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5985","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iH5b5Qpau6HSpDe6lYb/2gxf6I9wm4Clt59L46bgTMfWFI65Q9MSexN8Mz6aJ9L93FeKbJO6H2AuugUfDD25Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:59:19.330205Z"},"content_sha256":"9def87912e8f1741cd15dffd9f10d31ac9778a6778f562e2977ecb47c75ac4a0","schema_version":"1.0","event_id":"sha256:9def87912e8f1741cd15dffd9f10d31ac9778a6778f562e2977ecb47c75ac4a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SRYI5LTMNZ5IQYPRFK6LNSHBBZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local cohomology modules and Gorenstein injectivity with respect to a semidualizing module","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Majid Rahro Zargar","submitted_at":"2012-05-27T17:05:04Z","abstract_excerpt":"Let $(R,\\fm)$ be a local ring and let $C$ be a semidualizing $R$--module. In this paper, we are concerned in $C$--injective and $G_{C}$--injective dimensions of certain local cohomology modules of $R$. Firstly, the injective dimension of $C$ and the above quantities of dimensions is compared. Then, as an application of the above comparisons, a characterization of a dualizing module of $R$ is given. Finally, it is shown that if $R$ is Cohen-Macaulay of dimension $d$ such that $\\H_{\\fm}^{d}(C)$ is $C$--injective, then $R$ is Gorernstein. This is an answer to the question which was recently prese"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5985","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AmPBDIu6ivuOb/0ZEU4r9vO/TGDRnxG4wtGVzp+BbdX6C3WSZLXUldK3/v5ZSYKbVY45c4EVMPyEvabhK8CmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:59:19.330586Z"},"content_sha256":"1720d06cb7c53383ac54b4e8813d63b891e0bc208568470d43ac1fbd6f4c7062","schema_version":"1.0","event_id":"sha256:1720d06cb7c53383ac54b4e8813d63b891e0bc208568470d43ac1fbd6f4c7062"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SRYI5LTMNZ5IQYPRFK6LNSHBBZ/bundle.json","state_url":"https://pith.science/pith/SRYI5LTMNZ5IQYPRFK6LNSHBBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SRYI5LTMNZ5IQYPRFK6LNSHBBZ/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":"2026-06-25T06:59:19Z","links":{"resolver":"https://pith.science/pith/SRYI5LTMNZ5IQYPRFK6LNSHBBZ","bundle":"https://pith.science/pith/SRYI5LTMNZ5IQYPRFK6LNSHBBZ/bundle.json","state":"https://pith.science/pith/SRYI5LTMNZ5IQYPRFK6LNSHBBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SRYI5LTMNZ5IQYPRFK6LNSHBBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SRYI5LTMNZ5IQYPRFK6LNSHBBZ","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":"dc1f428920405960cd414436266c1c3417bdc22ac1751ccd2fe9d8325175384b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2012-05-27T17:05:04Z","title_canon_sha256":"6059dec523c14ce72362bae14eb972c9dadc3aa25240a0f41fd99353977ed951"},"schema_version":"1.0","source":{"id":"1205.5985","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5985","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5985v2","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5985","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"SRYI5LTMNZ5I","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SRYI5LTMNZ5IQYPR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SRYI5LTM","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:1720d06cb7c53383ac54b4e8813d63b891e0bc208568470d43ac1fbd6f4c7062","target":"graph","created_at":"2026-05-18T03:32:31Z","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 $(R,\\fm)$ be a local ring and let $C$ be a semidualizing $R$--module. In this paper, we are concerned in $C$--injective and $G_{C}$--injective dimensions of certain local cohomology modules of $R$. Firstly, the injective dimension of $C$ and the above quantities of dimensions is compared. Then, as an application of the above comparisons, a characterization of a dualizing module of $R$ is given. Finally, it is shown that if $R$ is Cohen-Macaulay of dimension $d$ such that $\\H_{\\fm}^{d}(C)$ is $C$--injective, then $R$ is Gorernstein. This is an answer to the question which was recently prese","authors_text":"Majid Rahro Zargar","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2012-05-27T17:05:04Z","title":"Local cohomology modules and Gorenstein injectivity with respect to a semidualizing module"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5985","kind":"arxiv","version":2},"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":"sha256:9def87912e8f1741cd15dffd9f10d31ac9778a6778f562e2977ecb47c75ac4a0","target":"record","created_at":"2026-05-18T03:32:31Z","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":"dc1f428920405960cd414436266c1c3417bdc22ac1751ccd2fe9d8325175384b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AC","submitted_at":"2012-05-27T17:05:04Z","title_canon_sha256":"6059dec523c14ce72362bae14eb972c9dadc3aa25240a0f41fd99353977ed951"},"schema_version":"1.0","source":{"id":"1205.5985","kind":"arxiv","version":2}},"canonical_sha256":"94708eae6c6e7a8861f12abcb6c8e10e43b9715d8adbd42057e13bb65507a274","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94708eae6c6e7a8861f12abcb6c8e10e43b9715d8adbd42057e13bb65507a274","first_computed_at":"2026-05-18T03:32:31.771487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:31.771487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5H9JKr6FNtJv8ijl5AMG11zrDpEqbrfIIJ7pwDgWeZCGsysfoax+Z8jN0F4unAzfObjc5PLcZE8C8PZAVB0NCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:31.772338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5985","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9def87912e8f1741cd15dffd9f10d31ac9778a6778f562e2977ecb47c75ac4a0","sha256:1720d06cb7c53383ac54b4e8813d63b891e0bc208568470d43ac1fbd6f4c7062"],"state_sha256":"903336ede81c4fc01725e2be49be20d9686f8c4aec340b318cff87d66eda5929"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HqB2sDpGkVrotsVkU1RFwkFUF8QPg6ot5N9qtgBwP5rWrPJTGq6kDm2Yg74y15nm1hUhd9gmO8IGZ8kw8WynCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T06:59:19.332698Z","bundle_sha256":"ad4add288c09769c1a8daacfd292cdf44b2351d4f3df3c2c2455bfc94d94e109"}}