{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GXRVCPPMLHK7WOZ5PQF32CRQH5","short_pith_number":"pith:GXRVCPPM","canonical_record":{"source":{"id":"1401.1883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-09T02:34:51Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"30d4509d9100d24f98a5ff5e04ab206e089381f6a7ad7bcf0ca7f97705a55654","abstract_canon_sha256":"422569d272171da1a23577e42173e57505e3bbede24ba3fb64e82cf3e6be046a"},"schema_version":"1.0"},"canonical_sha256":"35e3513dec59d5fb3b3d7c0bbd0a303f62531c6b3e13b294ef91d9ad4b2536c8","source":{"kind":"arxiv","id":"1401.1883","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1883","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1883v1","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1883","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"GXRVCPPMLHK7","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GXRVCPPMLHK7WOZ5","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GXRVCPPM","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GXRVCPPMLHK7WOZ5PQF32CRQH5","target":"record","payload":{"canonical_record":{"source":{"id":"1401.1883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-09T02:34:51Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"30d4509d9100d24f98a5ff5e04ab206e089381f6a7ad7bcf0ca7f97705a55654","abstract_canon_sha256":"422569d272171da1a23577e42173e57505e3bbede24ba3fb64e82cf3e6be046a"},"schema_version":"1.0"},"canonical_sha256":"35e3513dec59d5fb3b3d7c0bbd0a303f62531c6b3e13b294ef91d9ad4b2536c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:56.389882Z","signature_b64":"zdHi2f4uzUPKl16I2q2OqfZkFhvSKfI8MnYeM+texB1cB6sZh3fWc5wrKFLOF6Qcw/ujKDm2Anr3DA9WOQRPBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35e3513dec59d5fb3b3d7c0bbd0a303f62531c6b3e13b294ef91d9ad4b2536c8","last_reissued_at":"2026-05-18T03:02:56.389353Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:56.389353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.1883","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":"2026-05-18T03:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V7x9jsII1Eb8LXOeimYxJ9R1LzEAMCJvSpQ6541jqRR6BNeTouvcno6edmSMCHiBGPKq21+vW5Vso/Gt/wkcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:48:50.421732Z"},"content_sha256":"0ba37ba688358ad5c6c0165e7b44d129b3aac650f42a04e6ed02d786cc5839e7","schema_version":"1.0","event_id":"sha256:0ba37ba688358ad5c6c0165e7b44d129b3aac650f42a04e6ed02d786cc5839e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GXRVCPPMLHK7WOZ5PQF32CRQH5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Normal Edge-Transitive Cayley Graphs of Frobenius Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Brian P. Corr, Cheryl E. Praeger","submitted_at":"2014-01-09T02:34:51Z","abstract_excerpt":"A Cayley Graph for a group $G$ is called normal edge-transitive if it admits an edge-transitive action of some subgroup of the Holomorph of $G$ (the normaliser of a regular copy of $G$ in $\\operatorname{Sym}(G)$). We complete the classification of normal edge-transitive Cayley graphs of order a product of two primes by dealing with Cayley graphs for Frobenius groups of such orders. We determine the automorphism groups of these graphs, proving in particular that there is a unique vertex-primitive example, namely the flag graph of the Fano plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1883","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":"2026-05-18T03:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LD+MKZ6SB9XiXqNS7Ba8KBZvI5K3HTxsZ1RUTTY3paRLDXdCgdy0HLEMKUoeBtNgLAOVMgoF0fPs/gXl+OHuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:48:50.422069Z"},"content_sha256":"0055a867319e2ebb2ca5022f8abf637d32317c7769a4ff8c53eeb4abaa604485","schema_version":"1.0","event_id":"sha256:0055a867319e2ebb2ca5022f8abf637d32317c7769a4ff8c53eeb4abaa604485"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GXRVCPPMLHK7WOZ5PQF32CRQH5/bundle.json","state_url":"https://pith.science/pith/GXRVCPPMLHK7WOZ5PQF32CRQH5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GXRVCPPMLHK7WOZ5PQF32CRQH5/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":"2026-06-22T22:48:50Z","links":{"resolver":"https://pith.science/pith/GXRVCPPMLHK7WOZ5PQF32CRQH5","bundle":"https://pith.science/pith/GXRVCPPMLHK7WOZ5PQF32CRQH5/bundle.json","state":"https://pith.science/pith/GXRVCPPMLHK7WOZ5PQF32CRQH5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GXRVCPPMLHK7WOZ5PQF32CRQH5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GXRVCPPMLHK7WOZ5PQF32CRQH5","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":"422569d272171da1a23577e42173e57505e3bbede24ba3fb64e82cf3e6be046a","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-09T02:34:51Z","title_canon_sha256":"30d4509d9100d24f98a5ff5e04ab206e089381f6a7ad7bcf0ca7f97705a55654"},"schema_version":"1.0","source":{"id":"1401.1883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1883","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1883v1","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1883","created_at":"2026-05-18T03:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"GXRVCPPMLHK7","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GXRVCPPMLHK7WOZ5","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GXRVCPPM","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:0055a867319e2ebb2ca5022f8abf637d32317c7769a4ff8c53eeb4abaa604485","target":"graph","created_at":"2026-05-18T03:02:56Z","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":"A Cayley Graph for a group $G$ is called normal edge-transitive if it admits an edge-transitive action of some subgroup of the Holomorph of $G$ (the normaliser of a regular copy of $G$ in $\\operatorname{Sym}(G)$). We complete the classification of normal edge-transitive Cayley graphs of order a product of two primes by dealing with Cayley graphs for Frobenius groups of such orders. We determine the automorphism groups of these graphs, proving in particular that there is a unique vertex-primitive example, namely the flag graph of the Fano plane.","authors_text":"Brian P. Corr, Cheryl E. Praeger","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-09T02:34:51Z","title":"Normal Edge-Transitive Cayley Graphs of Frobenius Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1883","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":"sha256:0ba37ba688358ad5c6c0165e7b44d129b3aac650f42a04e6ed02d786cc5839e7","target":"record","created_at":"2026-05-18T03:02:56Z","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":"422569d272171da1a23577e42173e57505e3bbede24ba3fb64e82cf3e6be046a","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-09T02:34:51Z","title_canon_sha256":"30d4509d9100d24f98a5ff5e04ab206e089381f6a7ad7bcf0ca7f97705a55654"},"schema_version":"1.0","source":{"id":"1401.1883","kind":"arxiv","version":1}},"canonical_sha256":"35e3513dec59d5fb3b3d7c0bbd0a303f62531c6b3e13b294ef91d9ad4b2536c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35e3513dec59d5fb3b3d7c0bbd0a303f62531c6b3e13b294ef91d9ad4b2536c8","first_computed_at":"2026-05-18T03:02:56.389353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:56.389353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zdHi2f4uzUPKl16I2q2OqfZkFhvSKfI8MnYeM+texB1cB6sZh3fWc5wrKFLOF6Qcw/ujKDm2Anr3DA9WOQRPBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:56.389882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ba37ba688358ad5c6c0165e7b44d129b3aac650f42a04e6ed02d786cc5839e7","sha256:0055a867319e2ebb2ca5022f8abf637d32317c7769a4ff8c53eeb4abaa604485"],"state_sha256":"8b8a0d7065c84c7a298fad1afe04f40d60604d2fdb0386b3a6d2f99038161cc4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rriVIzW1pMY7/qHA5Wu8JvlFOr5qmk6zuU6xahxwI8Z42tbQWFuLVCvcQQUBXGvoACsvT9/uxuwy66iaF8upBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:48:50.423997Z","bundle_sha256":"81ca3e0e44300f917eea18b7b7be498638df392cc082dd6090951b3ea8ceea8d"}}