{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YMXHO7ZCA32XXMYWZKXYGVNSOC","short_pith_number":"pith:YMXHO7ZC","canonical_record":{"source":{"id":"1310.3746","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-14T16:50:56Z","cross_cats_sorted":["hep-ph","math.MP"],"title_canon_sha256":"fb022ac2ac48c8194a68fcaedb7142167b185337bcbe4e473ea82ea6f90199bd","abstract_canon_sha256":"6fc75ba5606a785b8c55586e9063ef6cfe6b1bfdda951d4a8292b5cfd71c39ab"},"schema_version":"1.0"},"canonical_sha256":"c32e777f2206f57bb316caaf8355b270a5631567089aed5abcc18774db755090","source":{"kind":"arxiv","id":"1310.3746","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3746","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3746v4","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3746","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"pith_short_12","alias_value":"YMXHO7ZCA32X","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YMXHO7ZCA32XXMYW","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YMXHO7ZC","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YMXHO7ZCA32XXMYWZKXYGVNSOC","target":"record","payload":{"canonical_record":{"source":{"id":"1310.3746","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-14T16:50:56Z","cross_cats_sorted":["hep-ph","math.MP"],"title_canon_sha256":"fb022ac2ac48c8194a68fcaedb7142167b185337bcbe4e473ea82ea6f90199bd","abstract_canon_sha256":"6fc75ba5606a785b8c55586e9063ef6cfe6b1bfdda951d4a8292b5cfd71c39ab"},"schema_version":"1.0"},"canonical_sha256":"c32e777f2206f57bb316caaf8355b270a5631567089aed5abcc18774db755090","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:39.576642Z","signature_b64":"zAsz/ZXH24htOtFZ9oDDDxKbKHbYeEZVCsMcw/qFTCjWMD9CU5Wwcyk5KbolpyknecZW3ayMJ6AGcUawQQayBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c32e777f2206f57bb316caaf8355b270a5631567089aed5abcc18774db755090","last_reissued_at":"2026-05-18T02:45:39.576103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:39.576103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.3746","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lbxAgpmGJm0HNoIbjDZWW5OQKnW2/bVJE2Q5/8ePXjcACmgyDA6VO7a+2VjL9I2jw9o1FjsOpkWCHPCNaRNrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:32:55.630241Z"},"content_sha256":"2ca3c0c6ba176f781ebe551e08c86f1e3439baffb60d2d86f036c1522f8e7230","schema_version":"1.0","event_id":"sha256:2ca3c0c6ba176f781ebe551e08c86f1e3439baffb60d2d86f036c1522f8e7230"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YMXHO7ZCA32XXMYWZKXYGVNSOC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the characterization of the SU(3)-subgroups of type C and D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math.MP"],"primary_cat":"math-ph","authors_text":"Patrick Otto Ludl, Walter Grimus","submitted_at":"2013-10-14T16:50:56Z","abstract_excerpt":"We investigate the two classes of finite subgroups of SU(3) that are called type C and D in the book of Miller, Blichfeldt and Dickson. We present two theorems which fully determine the form of the generators in a suitable basis. After exploring further properties of these groups, we are able to construct a complete list of infinite series in which these groups are arranged. For type C there are infinitely many series whereas for type D there are only two. Explicit examples of these series are presented which illustrate the general results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3746","kind":"arxiv","version":4},"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":"2026-05-18T02:45:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ozw0MP+jvTy4cBzI/d8iIVwnvzgyhVEVB65csfRFhBF4DE+bWzaUNVK4xdWbkeB4t86EKYzjR3v+Ad8tXnwrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:32:55.630901Z"},"content_sha256":"21e2d60948b6cf83bd731cb363a88c9a5fc4ad824da9e0a54571b4228d9f92db","schema_version":"1.0","event_id":"sha256:21e2d60948b6cf83bd731cb363a88c9a5fc4ad824da9e0a54571b4228d9f92db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YMXHO7ZCA32XXMYWZKXYGVNSOC/bundle.json","state_url":"https://pith.science/pith/YMXHO7ZCA32XXMYWZKXYGVNSOC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YMXHO7ZCA32XXMYWZKXYGVNSOC/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":"2026-05-31T01:32:55Z","links":{"resolver":"https://pith.science/pith/YMXHO7ZCA32XXMYWZKXYGVNSOC","bundle":"https://pith.science/pith/YMXHO7ZCA32XXMYWZKXYGVNSOC/bundle.json","state":"https://pith.science/pith/YMXHO7ZCA32XXMYWZKXYGVNSOC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YMXHO7ZCA32XXMYWZKXYGVNSOC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YMXHO7ZCA32XXMYWZKXYGVNSOC","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":"6fc75ba5606a785b8c55586e9063ef6cfe6b1bfdda951d4a8292b5cfd71c39ab","cross_cats_sorted":["hep-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-14T16:50:56Z","title_canon_sha256":"fb022ac2ac48c8194a68fcaedb7142167b185337bcbe4e473ea82ea6f90199bd"},"schema_version":"1.0","source":{"id":"1310.3746","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3746","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3746v4","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3746","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"pith_short_12","alias_value":"YMXHO7ZCA32X","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YMXHO7ZCA32XXMYW","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YMXHO7ZC","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:21e2d60948b6cf83bd731cb363a88c9a5fc4ad824da9e0a54571b4228d9f92db","target":"graph","created_at":"2026-05-18T02:45:39Z","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 investigate the two classes of finite subgroups of SU(3) that are called type C and D in the book of Miller, Blichfeldt and Dickson. We present two theorems which fully determine the form of the generators in a suitable basis. After exploring further properties of these groups, we are able to construct a complete list of infinite series in which these groups are arranged. For type C there are infinitely many series whereas for type D there are only two. Explicit examples of these series are presented which illustrate the general results.","authors_text":"Patrick Otto Ludl, Walter Grimus","cross_cats":["hep-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-14T16:50:56Z","title":"On the characterization of the SU(3)-subgroups of type C and D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3746","kind":"arxiv","version":4},"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":"sha256:2ca3c0c6ba176f781ebe551e08c86f1e3439baffb60d2d86f036c1522f8e7230","target":"record","created_at":"2026-05-18T02:45:39Z","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":"6fc75ba5606a785b8c55586e9063ef6cfe6b1bfdda951d4a8292b5cfd71c39ab","cross_cats_sorted":["hep-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-14T16:50:56Z","title_canon_sha256":"fb022ac2ac48c8194a68fcaedb7142167b185337bcbe4e473ea82ea6f90199bd"},"schema_version":"1.0","source":{"id":"1310.3746","kind":"arxiv","version":4}},"canonical_sha256":"c32e777f2206f57bb316caaf8355b270a5631567089aed5abcc18774db755090","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c32e777f2206f57bb316caaf8355b270a5631567089aed5abcc18774db755090","first_computed_at":"2026-05-18T02:45:39.576103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:39.576103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zAsz/ZXH24htOtFZ9oDDDxKbKHbYeEZVCsMcw/qFTCjWMD9CU5Wwcyk5KbolpyknecZW3ayMJ6AGcUawQQayBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:39.576642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3746","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ca3c0c6ba176f781ebe551e08c86f1e3439baffb60d2d86f036c1522f8e7230","sha256:21e2d60948b6cf83bd731cb363a88c9a5fc4ad824da9e0a54571b4228d9f92db"],"state_sha256":"3b5511f5184671f41d473344e28dfbf0c10877ed61e6f9d7aae272a406776b1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QetI/ANtX0JwMsuur6i53ZvFFLoQ2+Otvnr7e84rS6xpC31em+iY8q+49/XINyoiZZgpJnrlfTR+gjQWJ95TAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:32:55.634172Z","bundle_sha256":"7a9f90ff08a45c2fed0bcc12a00b38f5dbe975e01f667f3e661fec7a1c0ca149"}}