{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CZON7MH3SKVS4MXUV6V2TCMSWH","short_pith_number":"pith:CZON7MH3","canonical_record":{"source":{"id":"1512.08073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-26T04:47:08Z","cross_cats_sorted":[],"title_canon_sha256":"cba67298078e373741d659ed78086e921ccbdc92b688736e3cca9972beb09993","abstract_canon_sha256":"92e5bedb03c7de25045d0625777c9ce9e66d4f24523c93b694785f7e8e4fc32e"},"schema_version":"1.0"},"canonical_sha256":"165cdfb0fb92ab2e32f4afaba98992b1cd7db85a423e9300da434b84c58e6409","source":{"kind":"arxiv","id":"1512.08073","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08073","created_at":"2026-05-18T01:23:43Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08073v1","created_at":"2026-05-18T01:23:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08073","created_at":"2026-05-18T01:23:43Z"},{"alias_kind":"pith_short_12","alias_value":"CZON7MH3SKVS","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CZON7MH3SKVS4MXU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CZON7MH3","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CZON7MH3SKVS4MXUV6V2TCMSWH","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-26T04:47:08Z","cross_cats_sorted":[],"title_canon_sha256":"cba67298078e373741d659ed78086e921ccbdc92b688736e3cca9972beb09993","abstract_canon_sha256":"92e5bedb03c7de25045d0625777c9ce9e66d4f24523c93b694785f7e8e4fc32e"},"schema_version":"1.0"},"canonical_sha256":"165cdfb0fb92ab2e32f4afaba98992b1cd7db85a423e9300da434b84c58e6409","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:43.357715Z","signature_b64":"mR4l2duthPyCoK3vpfsXqHzpOPLJpL6bpmMjCgrVIby+O9y32aEEcBKzEQsALEiNY506H97sEOjQkR1rZlF2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"165cdfb0fb92ab2e32f4afaba98992b1cd7db85a423e9300da434b84c58e6409","last_reissued_at":"2026-05-18T01:23:43.356916Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:43.356916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08073","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":"2026-05-18T01:23:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"reaAM7AG9OmXZUp1Sqtva759SXSL7xNU/o4Sws9p9v5aPPQvs0mQM6K68rIBJBUv7IC25INBz2yrjGTqUotDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:17:42.160441Z"},"content_sha256":"e9fe087c8bce45b5af2210fc351f65af6beddda12a3e327ed16377bcd168a3a7","schema_version":"1.0","event_id":"sha256:e9fe087c8bce45b5af2210fc351f65af6beddda12a3e327ed16377bcd168a3a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CZON7MH3SKVS4MXUV6V2TCMSWH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New characterizations for core inverses in rings with involution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jianlong Chen, Sanzhang Xu, Xiaoxiang Zhang","submitted_at":"2015-12-26T04:47:08Z","abstract_excerpt":"The core inverse for a complex matrix was introduced by Baksalary and Trenkler. Raki\\'c, Din\\v{c}i\\'c and Djordjevi\\'c generalized the core inverse of a complex matrix to the case of an element in a ring. They also proved that the core inverse of an element in a ring can be characterized by five equations and every core invertible element is group invertible. It is natural to ask when a group invertible element is core invertible, in this paper, we will answer this question. We will use three equations to characterize the core inverse of an element. That is, let $a, b\\in R$, then $a\\in R^{\\tin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08073","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":"2026-05-18T01:23:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lw419w++Nsq1Yoo6opYhUbkXrft0GqduGjGrlwEqj04v3gSY0Et26ytH1M8tvdFjOH1vpwn0bgCCU4ymle+EDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:17:42.161216Z"},"content_sha256":"5c914f17941c4c683089246b89537775b5559a82b97df99a8bfde42f2d5a2195","schema_version":"1.0","event_id":"sha256:5c914f17941c4c683089246b89537775b5559a82b97df99a8bfde42f2d5a2195"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CZON7MH3SKVS4MXUV6V2TCMSWH/bundle.json","state_url":"https://pith.science/pith/CZON7MH3SKVS4MXUV6V2TCMSWH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CZON7MH3SKVS4MXUV6V2TCMSWH/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":"2026-05-31T01:17:42Z","links":{"resolver":"https://pith.science/pith/CZON7MH3SKVS4MXUV6V2TCMSWH","bundle":"https://pith.science/pith/CZON7MH3SKVS4MXUV6V2TCMSWH/bundle.json","state":"https://pith.science/pith/CZON7MH3SKVS4MXUV6V2TCMSWH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CZON7MH3SKVS4MXUV6V2TCMSWH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CZON7MH3SKVS4MXUV6V2TCMSWH","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":"92e5bedb03c7de25045d0625777c9ce9e66d4f24523c93b694785f7e8e4fc32e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-26T04:47:08Z","title_canon_sha256":"cba67298078e373741d659ed78086e921ccbdc92b688736e3cca9972beb09993"},"schema_version":"1.0","source":{"id":"1512.08073","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08073","created_at":"2026-05-18T01:23:43Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08073v1","created_at":"2026-05-18T01:23:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08073","created_at":"2026-05-18T01:23:43Z"},{"alias_kind":"pith_short_12","alias_value":"CZON7MH3SKVS","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CZON7MH3SKVS4MXU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CZON7MH3","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:5c914f17941c4c683089246b89537775b5559a82b97df99a8bfde42f2d5a2195","target":"graph","created_at":"2026-05-18T01:23:43Z","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":"The core inverse for a complex matrix was introduced by Baksalary and Trenkler. Raki\\'c, Din\\v{c}i\\'c and Djordjevi\\'c generalized the core inverse of a complex matrix to the case of an element in a ring. They also proved that the core inverse of an element in a ring can be characterized by five equations and every core invertible element is group invertible. It is natural to ask when a group invertible element is core invertible, in this paper, we will answer this question. We will use three equations to characterize the core inverse of an element. That is, let $a, b\\in R$, then $a\\in R^{\\tin","authors_text":"Jianlong Chen, Sanzhang Xu, Xiaoxiang Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-26T04:47:08Z","title":"New characterizations for core inverses in rings with involution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08073","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:e9fe087c8bce45b5af2210fc351f65af6beddda12a3e327ed16377bcd168a3a7","target":"record","created_at":"2026-05-18T01:23:43Z","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":"92e5bedb03c7de25045d0625777c9ce9e66d4f24523c93b694785f7e8e4fc32e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-26T04:47:08Z","title_canon_sha256":"cba67298078e373741d659ed78086e921ccbdc92b688736e3cca9972beb09993"},"schema_version":"1.0","source":{"id":"1512.08073","kind":"arxiv","version":1}},"canonical_sha256":"165cdfb0fb92ab2e32f4afaba98992b1cd7db85a423e9300da434b84c58e6409","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"165cdfb0fb92ab2e32f4afaba98992b1cd7db85a423e9300da434b84c58e6409","first_computed_at":"2026-05-18T01:23:43.356916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:43.356916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mR4l2duthPyCoK3vpfsXqHzpOPLJpL6bpmMjCgrVIby+O9y32aEEcBKzEQsALEiNY506H97sEOjQkR1rZlF2Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:43.357715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08073","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9fe087c8bce45b5af2210fc351f65af6beddda12a3e327ed16377bcd168a3a7","sha256:5c914f17941c4c683089246b89537775b5559a82b97df99a8bfde42f2d5a2195"],"state_sha256":"f12b18f0cd64f9bb2a513b4ddf9bdb967474809bee82c6e334bed4dd3fdcf6cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SEBk4+99ya8LIlZgToINPIbEZ6zawHWFEjZ3Whcsb8Mdt3SViV+ufLX+Dn3iW7Tdwbo1QqS0XlHOXPViOdk9DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:17:42.165012Z","bundle_sha256":"9e94b64c85a844533f7607a15802e72f0c32e076d3ec4f2b38c8ceaf04b55710"}}