{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ZWEFDVKDYVEBGW4QN66NXFK3F7","short_pith_number":"pith:ZWEFDVKD","canonical_record":{"source":{"id":"2410.00167","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2024-09-30T19:16:33Z","cross_cats_sorted":[],"title_canon_sha256":"71b7aa0427db40aba194d4c887b7ce41828f8acf5b455245b5655d651c031ef5","abstract_canon_sha256":"22b5c3f916b1fc0f1718126d67adbc6a16521ff70b9ffe03ea4c04459e8d1536"},"schema_version":"1.0"},"canonical_sha256":"cd8851d543c548135b906fbcdb955b2fc1df6b25f35bd43c3e7b435e6dc42e3d","source":{"kind":"arxiv","id":"2410.00167","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.00167","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"arxiv_version","alias_value":"2410.00167v1","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.00167","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZWEFDVKDYVEB","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"pith_short_16","alias_value":"ZWEFDVKDYVEBGW4Q","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"pith_short_8","alias_value":"ZWEFDVKD","created_at":"2026-07-05T09:14:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ZWEFDVKDYVEBGW4QN66NXFK3F7","target":"record","payload":{"canonical_record":{"source":{"id":"2410.00167","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2024-09-30T19:16:33Z","cross_cats_sorted":[],"title_canon_sha256":"71b7aa0427db40aba194d4c887b7ce41828f8acf5b455245b5655d651c031ef5","abstract_canon_sha256":"22b5c3f916b1fc0f1718126d67adbc6a16521ff70b9ffe03ea4c04459e8d1536"},"schema_version":"1.0"},"canonical_sha256":"cd8851d543c548135b906fbcdb955b2fc1df6b25f35bd43c3e7b435e6dc42e3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:14:00.400769Z","signature_b64":"eF1yKJaFwfNzU37p5M+wVTR2JWjLbfGCaGR8Qs/IvJCm/3b8sum9cED8RvLDKbwdL24vztgFECiaZXrsUxW9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd8851d543c548135b906fbcdb955b2fc1df6b25f35bd43c3e7b435e6dc42e3d","last_reissued_at":"2026-07-05T09:14:00.400341Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:14:00.400341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.00167","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:14:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iuy73/ImzsIIzK89KCH9IiYrWNcTphWLguy8iEglc4pCruGCAyHdpncaylAhzhAiENe8NbpktEijnQQMqgNjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:08:00.850698Z"},"content_sha256":"5fc59c360c7adae804ed7ad1ee83d28d2acd3621843f2a4f5c88dd6182b41bec","schema_version":"1.0","event_id":"sha256:5fc59c360c7adae804ed7ad1ee83d28d2acd3621843f2a4f5c88dd6182b41bec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ZWEFDVKDYVEBGW4QN66NXFK3F7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"S-FP-injective modules","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ayoub Bouziri, Driss Bennis","submitted_at":"2024-09-30T19:16:33Z","abstract_excerpt":"Let R be a commutative ring, and let S be a multiplicative subset of R. In this paper, we introduce and investigate the notion of S-FP-injective modules. Among other results, we show that, under certain conditions, a ring R is S-Noetherian if and only if every S-FP-injective R-module is S-injective. Moreover, we establish, under certain conditions, counterparts of Matlis, Stenstr\\\"om and Cheatham-Stone's characterizations of S-coherent rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00167","kind":"arxiv","version":1},"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/2410.00167/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":"2026-07-05T09:14:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jbw0eOicNur5nppAJa+7KdJuJPVm97UYSsAeNay6AqcTPPoFfwnDuEI14Vk2Dd5Dba2bDh85iKC799QT6FO8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:08:00.851354Z"},"content_sha256":"482ecca702dc932e000f980dd533d3c9cfa9114ee87933dfd412cbbe25de7e61","schema_version":"1.0","event_id":"sha256:482ecca702dc932e000f980dd533d3c9cfa9114ee87933dfd412cbbe25de7e61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZWEFDVKDYVEBGW4QN66NXFK3F7/bundle.json","state_url":"https://pith.science/pith/ZWEFDVKDYVEBGW4QN66NXFK3F7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZWEFDVKDYVEBGW4QN66NXFK3F7/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":"2026-08-13T04:08:00Z","links":{"resolver":"https://pith.science/pith/ZWEFDVKDYVEBGW4QN66NXFK3F7","bundle":"https://pith.science/pith/ZWEFDVKDYVEBGW4QN66NXFK3F7/bundle.json","state":"https://pith.science/pith/ZWEFDVKDYVEBGW4QN66NXFK3F7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZWEFDVKDYVEBGW4QN66NXFK3F7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZWEFDVKDYVEBGW4QN66NXFK3F7","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":"22b5c3f916b1fc0f1718126d67adbc6a16521ff70b9ffe03ea4c04459e8d1536","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2024-09-30T19:16:33Z","title_canon_sha256":"71b7aa0427db40aba194d4c887b7ce41828f8acf5b455245b5655d651c031ef5"},"schema_version":"1.0","source":{"id":"2410.00167","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.00167","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"arxiv_version","alias_value":"2410.00167v1","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.00167","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZWEFDVKDYVEB","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"pith_short_16","alias_value":"ZWEFDVKDYVEBGW4Q","created_at":"2026-07-05T09:14:00Z"},{"alias_kind":"pith_short_8","alias_value":"ZWEFDVKD","created_at":"2026-07-05T09:14:00Z"}],"graph_snapshots":[{"event_id":"sha256:482ecca702dc932e000f980dd533d3c9cfa9114ee87933dfd412cbbe25de7e61","target":"graph","created_at":"2026-07-05T09:14:00Z","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/2410.00167/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let R be a commutative ring, and let S be a multiplicative subset of R. In this paper, we introduce and investigate the notion of S-FP-injective modules. Among other results, we show that, under certain conditions, a ring R is S-Noetherian if and only if every S-FP-injective R-module is S-injective. Moreover, we establish, under certain conditions, counterparts of Matlis, Stenstr\\\"om and Cheatham-Stone's characterizations of S-coherent rings.","authors_text":"Ayoub Bouziri, Driss Bennis","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2024-09-30T19:16:33Z","title":"S-FP-injective modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00167","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":"sha256:5fc59c360c7adae804ed7ad1ee83d28d2acd3621843f2a4f5c88dd6182b41bec","target":"record","created_at":"2026-07-05T09:14:00Z","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":"22b5c3f916b1fc0f1718126d67adbc6a16521ff70b9ffe03ea4c04459e8d1536","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2024-09-30T19:16:33Z","title_canon_sha256":"71b7aa0427db40aba194d4c887b7ce41828f8acf5b455245b5655d651c031ef5"},"schema_version":"1.0","source":{"id":"2410.00167","kind":"arxiv","version":1}},"canonical_sha256":"cd8851d543c548135b906fbcdb955b2fc1df6b25f35bd43c3e7b435e6dc42e3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd8851d543c548135b906fbcdb955b2fc1df6b25f35bd43c3e7b435e6dc42e3d","first_computed_at":"2026-07-05T09:14:00.400341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:14:00.400341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eF1yKJaFwfNzU37p5M+wVTR2JWjLbfGCaGR8Qs/IvJCm/3b8sum9cED8RvLDKbwdL24vztgFECiaZXrsUxW9AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:14:00.400769Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.00167","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fc59c360c7adae804ed7ad1ee83d28d2acd3621843f2a4f5c88dd6182b41bec","sha256:482ecca702dc932e000f980dd533d3c9cfa9114ee87933dfd412cbbe25de7e61"],"state_sha256":"0c83e32530eee29e1f118148fc3cec8e762874676dd801a8929ee1c533a7c709"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c+jrV4v+y+mUT3C/PesTaXM6ytQ6fpZ+jmVFofMUn+wsNSg9Yab0T5eE5LEZB6niD2CzPVEfT5lnTu6Qx3s4Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T04:08:00.857960Z","bundle_sha256":"820361ec9a1b816361d19c067f4d428434273ff3da32fc5ace01c94e2a673462"}}