{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FVEOCMDUT4MXTZQKC35A5GWK2H","short_pith_number":"pith:FVEOCMDU","canonical_record":{"source":{"id":"1709.03857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-12T14:21:53Z","cross_cats_sorted":[],"title_canon_sha256":"2b9e17111dbf62fe7694efaa1f1bb9892db78885333211afb6adce73e9f66b87","abstract_canon_sha256":"29c7790a09160d6a0234f5c32fd2787261826c3ccdbde1d74cdc1144bf7a47e7"},"schema_version":"1.0"},"canonical_sha256":"2d48e130749f1979e60a16fa0e9acad1d6036c51bced91518184ef77f9877b61","source":{"kind":"arxiv","id":"1709.03857","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03857","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03857v1","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03857","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"pith_short_12","alias_value":"FVEOCMDUT4MX","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FVEOCMDUT4MXTZQK","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FVEOCMDU","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FVEOCMDUT4MXTZQKC35A5GWK2H","target":"record","payload":{"canonical_record":{"source":{"id":"1709.03857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-12T14:21:53Z","cross_cats_sorted":[],"title_canon_sha256":"2b9e17111dbf62fe7694efaa1f1bb9892db78885333211afb6adce73e9f66b87","abstract_canon_sha256":"29c7790a09160d6a0234f5c32fd2787261826c3ccdbde1d74cdc1144bf7a47e7"},"schema_version":"1.0"},"canonical_sha256":"2d48e130749f1979e60a16fa0e9acad1d6036c51bced91518184ef77f9877b61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:29.207242Z","signature_b64":"GisW+OiIYqGewLzNHl5CYPvAgYpAOTSpGWIC04KZ10H7FsZ5SyPvrq+TLCNtgS1pWFl6AtNo3rJ4Z6zRj9OtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d48e130749f1979e60a16fa0e9acad1d6036c51bced91518184ef77f9877b61","last_reissued_at":"2026-05-18T00:35:29.206627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:29.206627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.03857","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":"2026-05-18T00:35:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"249w4bxe+sNQouavSyGXLZda47ENRCvZph9UWZef1e6j35JAFQsqr0I4lK9TO0idxBMZ/0qsa0yzt2Y7eUplDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:09:07.179632Z"},"content_sha256":"ec4b5a635b1c9ba9de67ec001d7a2513097a89309e781debdc3c9883f36dcf53","schema_version":"1.0","event_id":"sha256:ec4b5a635b1c9ba9de67ec001d7a2513097a89309e781debdc3c9883f36dcf53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FVEOCMDUT4MXTZQKC35A5GWK2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semi-extraspecial Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark L. Lewis","submitted_at":"2017-09-12T14:21:53Z","abstract_excerpt":"We survey the results regarding semi-extraspecial $p$-groups. Semi-extraspecial groups can be viewed as generalizations of extraspecial groups. We present the connections between semi-extraspecial groups and Camina groups and VZ-groups, and give upper bounds on the order of the center and the orders of abelian normal subgroups. We define ultraspecial groups to be semi-extraspecial groups where the center is as large as possible, and demonstrate a connection between ultraspecial groups that have at least two abelian subgroups whose order is the maximum and semifields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03857","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":"2026-05-18T00:35:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hu0ebzfNuMd7frNEA2474lP3jrEddC2UaNrDwIIFzHF0GEbUkX8Twbbo3g9f4CwveOiWhECyyx8sxc0M8WXOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:09:07.179978Z"},"content_sha256":"d640bd5aa3bd334f76454b3e5704f3f88dbc70b89e80f2d72ce01a5deb730265","schema_version":"1.0","event_id":"sha256:d640bd5aa3bd334f76454b3e5704f3f88dbc70b89e80f2d72ce01a5deb730265"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FVEOCMDUT4MXTZQKC35A5GWK2H/bundle.json","state_url":"https://pith.science/pith/FVEOCMDUT4MXTZQKC35A5GWK2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FVEOCMDUT4MXTZQKC35A5GWK2H/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":"2026-06-20T04:09:07Z","links":{"resolver":"https://pith.science/pith/FVEOCMDUT4MXTZQKC35A5GWK2H","bundle":"https://pith.science/pith/FVEOCMDUT4MXTZQKC35A5GWK2H/bundle.json","state":"https://pith.science/pith/FVEOCMDUT4MXTZQKC35A5GWK2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FVEOCMDUT4MXTZQKC35A5GWK2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FVEOCMDUT4MXTZQKC35A5GWK2H","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":"29c7790a09160d6a0234f5c32fd2787261826c3ccdbde1d74cdc1144bf7a47e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-12T14:21:53Z","title_canon_sha256":"2b9e17111dbf62fe7694efaa1f1bb9892db78885333211afb6adce73e9f66b87"},"schema_version":"1.0","source":{"id":"1709.03857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03857","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03857v1","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03857","created_at":"2026-05-18T00:35:29Z"},{"alias_kind":"pith_short_12","alias_value":"FVEOCMDUT4MX","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FVEOCMDUT4MXTZQK","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FVEOCMDU","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:d640bd5aa3bd334f76454b3e5704f3f88dbc70b89e80f2d72ce01a5deb730265","target":"graph","created_at":"2026-05-18T00:35:29Z","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 survey the results regarding semi-extraspecial $p$-groups. Semi-extraspecial groups can be viewed as generalizations of extraspecial groups. We present the connections between semi-extraspecial groups and Camina groups and VZ-groups, and give upper bounds on the order of the center and the orders of abelian normal subgroups. We define ultraspecial groups to be semi-extraspecial groups where the center is as large as possible, and demonstrate a connection between ultraspecial groups that have at least two abelian subgroups whose order is the maximum and semifields.","authors_text":"Mark L. Lewis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-12T14:21:53Z","title":"Semi-extraspecial Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03857","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:ec4b5a635b1c9ba9de67ec001d7a2513097a89309e781debdc3c9883f36dcf53","target":"record","created_at":"2026-05-18T00:35:29Z","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":"29c7790a09160d6a0234f5c32fd2787261826c3ccdbde1d74cdc1144bf7a47e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-09-12T14:21:53Z","title_canon_sha256":"2b9e17111dbf62fe7694efaa1f1bb9892db78885333211afb6adce73e9f66b87"},"schema_version":"1.0","source":{"id":"1709.03857","kind":"arxiv","version":1}},"canonical_sha256":"2d48e130749f1979e60a16fa0e9acad1d6036c51bced91518184ef77f9877b61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d48e130749f1979e60a16fa0e9acad1d6036c51bced91518184ef77f9877b61","first_computed_at":"2026-05-18T00:35:29.206627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:29.206627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GisW+OiIYqGewLzNHl5CYPvAgYpAOTSpGWIC04KZ10H7FsZ5SyPvrq+TLCNtgS1pWFl6AtNo3rJ4Z6zRj9OtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:29.207242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec4b5a635b1c9ba9de67ec001d7a2513097a89309e781debdc3c9883f36dcf53","sha256:d640bd5aa3bd334f76454b3e5704f3f88dbc70b89e80f2d72ce01a5deb730265"],"state_sha256":"c4f51eb98cb09c01a1d83275e2ac2949df7a7bcc5442b0c79bc535ed4f897d01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rdjtvUlCTYn2QckrlNxtbAht7o31BjpwbtKe+LmxawdpIlpHjcoCqGayPPbO4d6vEzxQihCxmzB9d4YjQznEAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T04:09:07.181956Z","bundle_sha256":"e7a2b088770fcc813396ad7be27e605517a285fb090160791ae51e0ac480d39f"}}