{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BDFYEGHCVCJ7Z4LISMKHLXO3EU","short_pith_number":"pith:BDFYEGHC","canonical_record":{"source":{"id":"1606.02431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-08T07:32:26Z","cross_cats_sorted":[],"title_canon_sha256":"ff5e80fdf9b3d277f86dc5fe3d0bb4317bacc1cdf2cf54d7b21a301f7fb1036a","abstract_canon_sha256":"3aba0626da331e5f32cd35671a5278fae3ead2ee0d2d42185556414f07334dde"},"schema_version":"1.0"},"canonical_sha256":"08cb8218e2a893fcf168931475dddb2526e4b08944f127f21cd05f0dfa3a8583","source":{"kind":"arxiv","id":"1606.02431","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02431","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02431v1","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02431","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"BDFYEGHCVCJ7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BDFYEGHCVCJ7Z4LI","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BDFYEGHC","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BDFYEGHCVCJ7Z4LISMKHLXO3EU","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-08T07:32:26Z","cross_cats_sorted":[],"title_canon_sha256":"ff5e80fdf9b3d277f86dc5fe3d0bb4317bacc1cdf2cf54d7b21a301f7fb1036a","abstract_canon_sha256":"3aba0626da331e5f32cd35671a5278fae3ead2ee0d2d42185556414f07334dde"},"schema_version":"1.0"},"canonical_sha256":"08cb8218e2a893fcf168931475dddb2526e4b08944f127f21cd05f0dfa3a8583","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:41.382705Z","signature_b64":"vxZ6nYr1Q2UNM2fCqt1f45Pv7dpsrCLoXuAFft+QIyCARCYm5ClNTtXyeUMjKATM/kw5qdn3dMNyamyQiJRtBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08cb8218e2a893fcf168931475dddb2526e4b08944f127f21cd05f0dfa3a8583","last_reissued_at":"2026-05-18T01:12:41.382373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:41.382373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02431","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":"2026-05-18T01:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Sz89+BGBf1k5OLhgOGAGWjKFz1zEEwhGHlYicY5t8G8MdozQzZnAQfdq+01oEXj59vA8HeNKaFh86L38Tb6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:03:40.005476Z"},"content_sha256":"f4f712db7d2e826959b6cef84b5a9290ae31c2dae7bc80f60a2797af42a1cc61","schema_version":"1.0","event_id":"sha256:f4f712db7d2e826959b6cef84b5a9290ae31c2dae7bc80f60a2797af42a1cc61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BDFYEGHCVCJ7Z4LISMKHLXO3EU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite groups with small number of cyclic subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Wei Zhou","submitted_at":"2016-06-08T07:32:26Z","abstract_excerpt":"In this note, we study the finite groups with the number of cylic subgroups no greater than 6."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02431","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":"2026-05-18T01:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GkOUaXzRNM8NVCskBWm+saGx3NcC/V69xazN6j3UpjKG3j5sDcAZRMkRJxEPOwc5ubyoldmDyfe2sPR7eo6sDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:03:40.006117Z"},"content_sha256":"4c1dced89f497d1ffa86988b86ad0b69600b43765605b619e6a3b7ccfc24764a","schema_version":"1.0","event_id":"sha256:4c1dced89f497d1ffa86988b86ad0b69600b43765605b619e6a3b7ccfc24764a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDFYEGHCVCJ7Z4LISMKHLXO3EU/bundle.json","state_url":"https://pith.science/pith/BDFYEGHCVCJ7Z4LISMKHLXO3EU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDFYEGHCVCJ7Z4LISMKHLXO3EU/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":"2026-05-27T14:03:40Z","links":{"resolver":"https://pith.science/pith/BDFYEGHCVCJ7Z4LISMKHLXO3EU","bundle":"https://pith.science/pith/BDFYEGHCVCJ7Z4LISMKHLXO3EU/bundle.json","state":"https://pith.science/pith/BDFYEGHCVCJ7Z4LISMKHLXO3EU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDFYEGHCVCJ7Z4LISMKHLXO3EU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BDFYEGHCVCJ7Z4LISMKHLXO3EU","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":"3aba0626da331e5f32cd35671a5278fae3ead2ee0d2d42185556414f07334dde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-08T07:32:26Z","title_canon_sha256":"ff5e80fdf9b3d277f86dc5fe3d0bb4317bacc1cdf2cf54d7b21a301f7fb1036a"},"schema_version":"1.0","source":{"id":"1606.02431","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02431","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02431v1","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02431","created_at":"2026-05-18T01:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"BDFYEGHCVCJ7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BDFYEGHCVCJ7Z4LI","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BDFYEGHC","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:4c1dced89f497d1ffa86988b86ad0b69600b43765605b619e6a3b7ccfc24764a","target":"graph","created_at":"2026-05-18T01:12:41Z","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":"In this note, we study the finite groups with the number of cylic subgroups no greater than 6.","authors_text":"Wei Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-08T07:32:26Z","title":"Finite groups with small number of cyclic subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02431","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:f4f712db7d2e826959b6cef84b5a9290ae31c2dae7bc80f60a2797af42a1cc61","target":"record","created_at":"2026-05-18T01:12:41Z","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":"3aba0626da331e5f32cd35671a5278fae3ead2ee0d2d42185556414f07334dde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-06-08T07:32:26Z","title_canon_sha256":"ff5e80fdf9b3d277f86dc5fe3d0bb4317bacc1cdf2cf54d7b21a301f7fb1036a"},"schema_version":"1.0","source":{"id":"1606.02431","kind":"arxiv","version":1}},"canonical_sha256":"08cb8218e2a893fcf168931475dddb2526e4b08944f127f21cd05f0dfa3a8583","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08cb8218e2a893fcf168931475dddb2526e4b08944f127f21cd05f0dfa3a8583","first_computed_at":"2026-05-18T01:12:41.382373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:41.382373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vxZ6nYr1Q2UNM2fCqt1f45Pv7dpsrCLoXuAFft+QIyCARCYm5ClNTtXyeUMjKATM/kw5qdn3dMNyamyQiJRtBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:41.382705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02431","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4f712db7d2e826959b6cef84b5a9290ae31c2dae7bc80f60a2797af42a1cc61","sha256:4c1dced89f497d1ffa86988b86ad0b69600b43765605b619e6a3b7ccfc24764a"],"state_sha256":"dc4daf281512947059e0f1fe57e9c1619265edf81e0ee620d9516b74066731ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3a9GcliqApc5Kg53J1l343DyREgVJKDh8pUsWjwJy4rj4hrZ5PqYakllsIU3r7FM3EBmU08ETNKjgwFDr15AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:03:40.009573Z","bundle_sha256":"29ab277631950cb0536652be060a796713e1c10957fc686eeeea3b5aac2f27f8"}}