{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TPMUMFN3SPSX3K5EPEXPMCXVSW","short_pith_number":"pith:TPMUMFN3","canonical_record":{"source":{"id":"1904.00425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-31T14:44:06Z","cross_cats_sorted":[],"title_canon_sha256":"6f8f3d3efa812f7e3bee006f206f014ab9ba273107b0ed4e0a3ef4c5cc3093b1","abstract_canon_sha256":"1374aaa0c06d0d29225b22157bd66b200670f25d4563e9dbc98d628ff5c01c42"},"schema_version":"1.0"},"canonical_sha256":"9bd94615bb93e57daba4792ef60af595b5323dcdaf84b98fc2c363fd02575183","source":{"kind":"arxiv","id":"1904.00425","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00425","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00425v1","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00425","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"TPMUMFN3SPSX","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TPMUMFN3SPSX3K5E","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TPMUMFN3","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TPMUMFN3SPSX3K5EPEXPMCXVSW","target":"record","payload":{"canonical_record":{"source":{"id":"1904.00425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-31T14:44:06Z","cross_cats_sorted":[],"title_canon_sha256":"6f8f3d3efa812f7e3bee006f206f014ab9ba273107b0ed4e0a3ef4c5cc3093b1","abstract_canon_sha256":"1374aaa0c06d0d29225b22157bd66b200670f25d4563e9dbc98d628ff5c01c42"},"schema_version":"1.0"},"canonical_sha256":"9bd94615bb93e57daba4792ef60af595b5323dcdaf84b98fc2c363fd02575183","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:48.432128Z","signature_b64":"+GLUkKGF1dzko8SEmmAFjy2xB2o0r05A0oBmJYlvqaYgJD/kRd/6RQksiMCuDlojU0ZZq0ALFq7+wm7HAm/uDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bd94615bb93e57daba4792ef60af595b5323dcdaf84b98fc2c363fd02575183","last_reissued_at":"2026-05-17T23:49:48.431492Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:48.431492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.00425","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":"2026-05-17T23:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ylmGSB+xzfuKwTbEz2vwv47iufDF0IctOPd61OHA6+m+Vm6cEQlDlRvPWrT3vFFEoTONzMvu2HobJ46Fj6JfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:48:46.165141Z"},"content_sha256":"eddf849c2fe89ff83e9db843fde44d177db58b5ce4140b934adf1a7b5f3fdcf2","schema_version":"1.0","event_id":"sha256:eddf849c2fe89ff83e9db843fde44d177db58b5ce4140b934adf1a7b5f3fdcf2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TPMUMFN3SPSX3K5EPEXPMCXVSW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A result on the sum of element orders of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Afsaneh Bahri, Behrooz Khosravi, Zeinab Akhlaghi","submitted_at":"2019-03-31T14:44:06Z","abstract_excerpt":"Let $G$ be a finite group and $\\psi(G)=\\sum_{g\\in{G}}{o(g)}$. There are some results about the relation between $\\psi(G)$ and the structure of $G$. For instance, it is proved that if $G$ is a group of order $n$ and $\\psi(G)>\\dfrac{211}{1617}\\psi(C_n)$, then $G$ is solvable. Herzog {\\it{et al.}} in [Herzog {\\it{et al.}}, Two new criteria for solvability of finite groups, J. Algebra, 2018] put forward the following conjecture:\n  \\noindent{\\bf Conjecture.} {\\it {If $G$ is a non-solvable group of order $n$, then $${\\psi(G)}\\,{\\leq}\\,{{\\dfrac{211}{1617}}{\\psi(C_n)}}$$ with equality if and only if $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00425","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":"2026-05-17T23:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q2glpwb0x9NINKbwiabh5VwXsDji9AMH7oZmrHQL8JELnhduPez0jgMTkgpQ8gFLH6DN6IRL4JpL+/giu1WsCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:48:46.165509Z"},"content_sha256":"64ef35b60ad5e71cbecf3efc1ae18e8cc6cdeeaedacddb213feee80bc95a9806","schema_version":"1.0","event_id":"sha256:64ef35b60ad5e71cbecf3efc1ae18e8cc6cdeeaedacddb213feee80bc95a9806"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TPMUMFN3SPSX3K5EPEXPMCXVSW/bundle.json","state_url":"https://pith.science/pith/TPMUMFN3SPSX3K5EPEXPMCXVSW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TPMUMFN3SPSX3K5EPEXPMCXVSW/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":"2026-06-22T13:48:46Z","links":{"resolver":"https://pith.science/pith/TPMUMFN3SPSX3K5EPEXPMCXVSW","bundle":"https://pith.science/pith/TPMUMFN3SPSX3K5EPEXPMCXVSW/bundle.json","state":"https://pith.science/pith/TPMUMFN3SPSX3K5EPEXPMCXVSW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TPMUMFN3SPSX3K5EPEXPMCXVSW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TPMUMFN3SPSX3K5EPEXPMCXVSW","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":"1374aaa0c06d0d29225b22157bd66b200670f25d4563e9dbc98d628ff5c01c42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-31T14:44:06Z","title_canon_sha256":"6f8f3d3efa812f7e3bee006f206f014ab9ba273107b0ed4e0a3ef4c5cc3093b1"},"schema_version":"1.0","source":{"id":"1904.00425","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00425","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00425v1","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00425","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"TPMUMFN3SPSX","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TPMUMFN3SPSX3K5E","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TPMUMFN3","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:64ef35b60ad5e71cbecf3efc1ae18e8cc6cdeeaedacddb213feee80bc95a9806","target":"graph","created_at":"2026-05-17T23:49:48Z","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 $G$ be a finite group and $\\psi(G)=\\sum_{g\\in{G}}{o(g)}$. There are some results about the relation between $\\psi(G)$ and the structure of $G$. For instance, it is proved that if $G$ is a group of order $n$ and $\\psi(G)>\\dfrac{211}{1617}\\psi(C_n)$, then $G$ is solvable. Herzog {\\it{et al.}} in [Herzog {\\it{et al.}}, Two new criteria for solvability of finite groups, J. Algebra, 2018] put forward the following conjecture:\n  \\noindent{\\bf Conjecture.} {\\it {If $G$ is a non-solvable group of order $n$, then $${\\psi(G)}\\,{\\leq}\\,{{\\dfrac{211}{1617}}{\\psi(C_n)}}$$ with equality if and only if $","authors_text":"Afsaneh Bahri, Behrooz Khosravi, Zeinab Akhlaghi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-31T14:44:06Z","title":"A result on the sum of element orders of a finite group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00425","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:eddf849c2fe89ff83e9db843fde44d177db58b5ce4140b934adf1a7b5f3fdcf2","target":"record","created_at":"2026-05-17T23:49:48Z","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":"1374aaa0c06d0d29225b22157bd66b200670f25d4563e9dbc98d628ff5c01c42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-03-31T14:44:06Z","title_canon_sha256":"6f8f3d3efa812f7e3bee006f206f014ab9ba273107b0ed4e0a3ef4c5cc3093b1"},"schema_version":"1.0","source":{"id":"1904.00425","kind":"arxiv","version":1}},"canonical_sha256":"9bd94615bb93e57daba4792ef60af595b5323dcdaf84b98fc2c363fd02575183","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bd94615bb93e57daba4792ef60af595b5323dcdaf84b98fc2c363fd02575183","first_computed_at":"2026-05-17T23:49:48.431492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:48.431492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+GLUkKGF1dzko8SEmmAFjy2xB2o0r05A0oBmJYlvqaYgJD/kRd/6RQksiMCuDlojU0ZZq0ALFq7+wm7HAm/uDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:48.432128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.00425","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eddf849c2fe89ff83e9db843fde44d177db58b5ce4140b934adf1a7b5f3fdcf2","sha256:64ef35b60ad5e71cbecf3efc1ae18e8cc6cdeeaedacddb213feee80bc95a9806"],"state_sha256":"1e9fac893ef364d088a976f575f2c60c8aaeaec58155fd525b1348cff861cdb8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jn9Bo5W/TRM/oYVn/j2CFzLzzMYNjjiSqN03Lz8kXRYkzDYQ1TG7HA+3OmHQd//VuujoOKbagUNepqS7zb/qBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:48:46.167493Z","bundle_sha256":"dc9447f0fb9d71cf7627f7d414d6f6336d31a53c5614f6d18ca869c98822abab"}}