{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HUF632TNGPAHU7ZM42JNTTKE6T","short_pith_number":"pith:HUF632TN","canonical_record":{"source":{"id":"1803.02683","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-03-05T16:12:47Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"8f718d10321d306e6619cabb65079bc2497704dc78ccca1fdf74c7e18435e841","abstract_canon_sha256":"e35fd64589b845fbf12625bcffdb8918f42d881359c80116bbfc8ad1c05f5e71"},"schema_version":"1.0"},"canonical_sha256":"3d0bedea6d33c07a7f2ce692d9cd44f4ca8a86ea6ce60e42071199fb68dfab23","source":{"kind":"arxiv","id":"1803.02683","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02683","created_at":"2026-05-18T00:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02683v1","created_at":"2026-05-18T00:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02683","created_at":"2026-05-18T00:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"HUF632TNGPAH","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HUF632TNGPAHU7ZM","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HUF632TN","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HUF632TNGPAHU7ZM42JNTTKE6T","target":"record","payload":{"canonical_record":{"source":{"id":"1803.02683","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-03-05T16:12:47Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"8f718d10321d306e6619cabb65079bc2497704dc78ccca1fdf74c7e18435e841","abstract_canon_sha256":"e35fd64589b845fbf12625bcffdb8918f42d881359c80116bbfc8ad1c05f5e71"},"schema_version":"1.0"},"canonical_sha256":"3d0bedea6d33c07a7f2ce692d9cd44f4ca8a86ea6ce60e42071199fb68dfab23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:49.517147Z","signature_b64":"jrLSztdnMRQejX2XyM7ZHAB3GVoDSsCOWQdDZVdDZ6zl4dmkQhfrTS5pDhKu/RwL/i1dLNzLg0Y7G07vp3ICDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d0bedea6d33c07a7f2ce692d9cd44f4ca8a86ea6ce60e42071199fb68dfab23","last_reissued_at":"2026-05-18T00:21:49.516575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:49.516575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.02683","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":"2026-05-18T00:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bc6k5CGZI43vxLSqtuioQ7JIeMjyWQpeuPdZ0dx8oBFSQhNXByWyuoeeP0+nBvvNJwa7XMXKuzIXXtw7T8XYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:42:54.580025Z"},"content_sha256":"97bc0cd9488f08928b28c238dc6d45cc13f283977c391fbdf7778dae08bb37b8","schema_version":"1.0","event_id":"sha256:97bc0cd9488f08928b28c238dc6d45cc13f283977c391fbdf7778dae08bb37b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HUF632TNGPAHU7ZM42JNTTKE6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strongly Rickart objects in abelian categories: Applications to strongly regular and strongly Baer objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CT","authors_text":"Gabriela Olteanu, Septimiu Crivei","submitted_at":"2018-03-05T16:12:47Z","abstract_excerpt":"We show how the theory of (dual) strongly relative Rickart objects may be employed in order to study strongly relative regular objects and (dual) strongly relative Baer objects in abelian categories. For each of them, we prove general properties, we analyze the behaviour with respect to (co)products, and we study the transfer via functors. We also give applications to Grothendieck categories, (graded) module categories and comodule categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02683","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":""},"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":"2026-05-18T00:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QKNaKW+eqfAkNr261jPpzcm11NuOspCPnUJ19RstWBaP0CpUwK2a9yxemuPKx9AGXZKdpsUUVAwde2g2CoPUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:42:54.580373Z"},"content_sha256":"0f4bcae1f558f55faf0f147f9ad1a56d5b2ab4f55f20c1fd0deff0cef2f78675","schema_version":"1.0","event_id":"sha256:0f4bcae1f558f55faf0f147f9ad1a56d5b2ab4f55f20c1fd0deff0cef2f78675"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HUF632TNGPAHU7ZM42JNTTKE6T/bundle.json","state_url":"https://pith.science/pith/HUF632TNGPAHU7ZM42JNTTKE6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HUF632TNGPAHU7ZM42JNTTKE6T/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":"2026-06-26T17:42:54Z","links":{"resolver":"https://pith.science/pith/HUF632TNGPAHU7ZM42JNTTKE6T","bundle":"https://pith.science/pith/HUF632TNGPAHU7ZM42JNTTKE6T/bundle.json","state":"https://pith.science/pith/HUF632TNGPAHU7ZM42JNTTKE6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HUF632TNGPAHU7ZM42JNTTKE6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HUF632TNGPAHU7ZM42JNTTKE6T","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":"e35fd64589b845fbf12625bcffdb8918f42d881359c80116bbfc8ad1c05f5e71","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-03-05T16:12:47Z","title_canon_sha256":"8f718d10321d306e6619cabb65079bc2497704dc78ccca1fdf74c7e18435e841"},"schema_version":"1.0","source":{"id":"1803.02683","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02683","created_at":"2026-05-18T00:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02683v1","created_at":"2026-05-18T00:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02683","created_at":"2026-05-18T00:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"HUF632TNGPAH","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HUF632TNGPAHU7ZM","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HUF632TN","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:0f4bcae1f558f55faf0f147f9ad1a56d5b2ab4f55f20c1fd0deff0cef2f78675","target":"graph","created_at":"2026-05-18T00:21:49Z","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":"We show how the theory of (dual) strongly relative Rickart objects may be employed in order to study strongly relative regular objects and (dual) strongly relative Baer objects in abelian categories. For each of them, we prove general properties, we analyze the behaviour with respect to (co)products, and we study the transfer via functors. We also give applications to Grothendieck categories, (graded) module categories and comodule categories.","authors_text":"Gabriela Olteanu, Septimiu Crivei","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-03-05T16:12:47Z","title":"Strongly Rickart objects in abelian categories: Applications to strongly regular and strongly Baer objects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02683","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":"sha256:97bc0cd9488f08928b28c238dc6d45cc13f283977c391fbdf7778dae08bb37b8","target":"record","created_at":"2026-05-18T00:21:49Z","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":"e35fd64589b845fbf12625bcffdb8918f42d881359c80116bbfc8ad1c05f5e71","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-03-05T16:12:47Z","title_canon_sha256":"8f718d10321d306e6619cabb65079bc2497704dc78ccca1fdf74c7e18435e841"},"schema_version":"1.0","source":{"id":"1803.02683","kind":"arxiv","version":1}},"canonical_sha256":"3d0bedea6d33c07a7f2ce692d9cd44f4ca8a86ea6ce60e42071199fb68dfab23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d0bedea6d33c07a7f2ce692d9cd44f4ca8a86ea6ce60e42071199fb68dfab23","first_computed_at":"2026-05-18T00:21:49.516575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:49.516575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jrLSztdnMRQejX2XyM7ZHAB3GVoDSsCOWQdDZVdDZ6zl4dmkQhfrTS5pDhKu/RwL/i1dLNzLg0Y7G07vp3ICDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:49.517147Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02683","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97bc0cd9488f08928b28c238dc6d45cc13f283977c391fbdf7778dae08bb37b8","sha256:0f4bcae1f558f55faf0f147f9ad1a56d5b2ab4f55f20c1fd0deff0cef2f78675"],"state_sha256":"22029f3cf716c001442cedee319ee7c052767362c8eb6ab24d91413f7d593273"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AIuyeKykVEPgOn4QIthEt8YXU2DtvNYcNsTZ0a1UJgClzL+Z/LWRhnZV05TsL61r1cOWPhNJA1AfDByFj9/wAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T17:42:54.582219Z","bundle_sha256":"539e6795cc916e3e0e7a2763f4ed8910571aeca32d20a535d0f71a939e7dabe8"}}