{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WFODYOIKARUV4NNF4IBHMRKY5L","short_pith_number":"pith:WFODYOIK","canonical_record":{"source":{"id":"1101.2308","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-12T09:45:26Z","cross_cats_sorted":["hep-ph","hep-th","math.MP"],"title_canon_sha256":"4b01b98115d792d0a3b0efe718b06eade32957b95210249b186ac75580b71e70","abstract_canon_sha256":"f2941be3006d5f4a4771ad299b857a63af32a23d04831cfd10ac1d665536c18d"},"schema_version":"1.0"},"canonical_sha256":"b15c3c390a04695e35a5e202764558ead5a9b36099a289976e7bacd93376f757","source":{"kind":"arxiv","id":"1101.2308","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2308","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2308v3","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2308","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"WFODYOIKARUV","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WFODYOIKARUV4NNF","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WFODYOIK","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WFODYOIKARUV4NNF4IBHMRKY5L","target":"record","payload":{"canonical_record":{"source":{"id":"1101.2308","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-12T09:45:26Z","cross_cats_sorted":["hep-ph","hep-th","math.MP"],"title_canon_sha256":"4b01b98115d792d0a3b0efe718b06eade32957b95210249b186ac75580b71e70","abstract_canon_sha256":"f2941be3006d5f4a4771ad299b857a63af32a23d04831cfd10ac1d665536c18d"},"schema_version":"1.0"},"canonical_sha256":"b15c3c390a04695e35a5e202764558ead5a9b36099a289976e7bacd93376f757","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:08.011255Z","signature_b64":"VftiTk3yWxKHWODqo3RuhbhUtCUrssr9fhCQ2s/WSWHaZtXRKsxm1yJ+uY9pcU/s0uHflIMNI5xenb2JDBV6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b15c3c390a04695e35a5e202764558ead5a9b36099a289976e7bacd93376f757","last_reissued_at":"2026-05-18T04:06:08.010615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:08.010615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.2308","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pbJfp66gkX3PgD+aZIVsaoRUbenzu6XED08BZBa7ixQMGpcuJ1xWUG2Cqf0lmfLWI6YImkc0DUIDHmZZgiXoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:02:18.276504Z"},"content_sha256":"d1bef6b868005d96c6312902f14c297795d7764845fab77673e9fced399ddf94","schema_version":"1.0","event_id":"sha256:d1bef6b868005d96c6312902f14c297795d7764845fab77673e9fced399ddf94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WFODYOIKARUV4NNF4IBHMRKY5L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comments on the classification of the finite subgroups of SU(3)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Patrick Otto Ludl","submitted_at":"2011-01-12T09:45:26Z","abstract_excerpt":"Many finite subgroups of SU(3) are commonly used in particle physics. The classification of the finite subgroups of SU(3) began with the work of H.F. Blichfeldt at the beginning of the 20th century. In Blichfeldt's work the two series (C) and (D) of finite subgroups of SU(3) are defined. While the group series Delta(3n^2) and Delta(6n^2) (which are subseries of (C) and (D), respectively) have been intensively studied, there is not much knowledge about the group series (C) and (D). In this work we will show that (C) and (D) have the structures (C) \\cong (Z_m x Z_m') \\rtimes Z_3 and (D) \\cong (Z"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2308","kind":"arxiv","version":3},"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":"2026-05-18T04:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7iGWrE/SoljZvjf7Qxn7i5ofr+ePpwgGsdQ0d04x8rl3VNF8zHf5ysBxzsvRd76Xt5S82yXA/DtRZx0t0oe/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:02:18.276850Z"},"content_sha256":"5f3c8c217854cfb496b16b15d1af4522b4082d58243e3e4637a5a729db65ca21","schema_version":"1.0","event_id":"sha256:5f3c8c217854cfb496b16b15d1af4522b4082d58243e3e4637a5a729db65ca21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFODYOIKARUV4NNF4IBHMRKY5L/bundle.json","state_url":"https://pith.science/pith/WFODYOIKARUV4NNF4IBHMRKY5L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFODYOIKARUV4NNF4IBHMRKY5L/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":"2026-06-04T17:02:18Z","links":{"resolver":"https://pith.science/pith/WFODYOIKARUV4NNF4IBHMRKY5L","bundle":"https://pith.science/pith/WFODYOIKARUV4NNF4IBHMRKY5L/bundle.json","state":"https://pith.science/pith/WFODYOIKARUV4NNF4IBHMRKY5L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFODYOIKARUV4NNF4IBHMRKY5L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WFODYOIKARUV4NNF4IBHMRKY5L","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":"f2941be3006d5f4a4771ad299b857a63af32a23d04831cfd10ac1d665536c18d","cross_cats_sorted":["hep-ph","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-12T09:45:26Z","title_canon_sha256":"4b01b98115d792d0a3b0efe718b06eade32957b95210249b186ac75580b71e70"},"schema_version":"1.0","source":{"id":"1101.2308","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2308","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2308v3","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2308","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"WFODYOIKARUV","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WFODYOIKARUV4NNF","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WFODYOIK","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:5f3c8c217854cfb496b16b15d1af4522b4082d58243e3e4637a5a729db65ca21","target":"graph","created_at":"2026-05-18T04:06:08Z","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":"Many finite subgroups of SU(3) are commonly used in particle physics. The classification of the finite subgroups of SU(3) began with the work of H.F. Blichfeldt at the beginning of the 20th century. In Blichfeldt's work the two series (C) and (D) of finite subgroups of SU(3) are defined. While the group series Delta(3n^2) and Delta(6n^2) (which are subseries of (C) and (D), respectively) have been intensively studied, there is not much knowledge about the group series (C) and (D). In this work we will show that (C) and (D) have the structures (C) \\cong (Z_m x Z_m') \\rtimes Z_3 and (D) \\cong (Z","authors_text":"Patrick Otto Ludl","cross_cats":["hep-ph","hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-12T09:45:26Z","title":"Comments on the classification of the finite subgroups of SU(3)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2308","kind":"arxiv","version":3},"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:d1bef6b868005d96c6312902f14c297795d7764845fab77673e9fced399ddf94","target":"record","created_at":"2026-05-18T04:06:08Z","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":"f2941be3006d5f4a4771ad299b857a63af32a23d04831cfd10ac1d665536c18d","cross_cats_sorted":["hep-ph","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-01-12T09:45:26Z","title_canon_sha256":"4b01b98115d792d0a3b0efe718b06eade32957b95210249b186ac75580b71e70"},"schema_version":"1.0","source":{"id":"1101.2308","kind":"arxiv","version":3}},"canonical_sha256":"b15c3c390a04695e35a5e202764558ead5a9b36099a289976e7bacd93376f757","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b15c3c390a04695e35a5e202764558ead5a9b36099a289976e7bacd93376f757","first_computed_at":"2026-05-18T04:06:08.010615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:08.010615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VftiTk3yWxKHWODqo3RuhbhUtCUrssr9fhCQ2s/WSWHaZtXRKsxm1yJ+uY9pcU/s0uHflIMNI5xenb2JDBV6CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:08.011255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2308","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1bef6b868005d96c6312902f14c297795d7764845fab77673e9fced399ddf94","sha256:5f3c8c217854cfb496b16b15d1af4522b4082d58243e3e4637a5a729db65ca21"],"state_sha256":"aee28f58dab6b06dd7e1227d3505236d2f9f2a1b1c8ad0a97ab44d8c92023e0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5n7BKmcLz2WzlGychBAnqcYsFX5Do70cWfQC6plLHelQ7Nz/QSs74LFgLK2gxjijBfmiGjfgaSfdg5jonlXLCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:02:18.281022Z","bundle_sha256":"c3973c273b3bdeb740df4b95dbb06acb9ed8d0c1a061e5bdec5c5bc0b67fff09"}}