{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TJ6KVMUEQITGDRVPASRJDC5VA3","short_pith_number":"pith:TJ6KVMUE","canonical_record":{"source":{"id":"1107.0364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-02T09:16:07Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"9a29c0705ed21d9f5af335ec71d35cf86a941d53dd359aced84f45599539f5ee","abstract_canon_sha256":"35956f8846fc6adf44f7d3f1c71e83d0563ce37e481ddedb99e8e271b8b0fa51"},"schema_version":"1.0"},"canonical_sha256":"9a7caab284822661c6af04a2918bb506d2e98a4828546bfd6bfae4ec5a853774","source":{"kind":"arxiv","id":"1107.0364","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0364","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0364v1","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0364","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"TJ6KVMUEQITG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TJ6KVMUEQITGDRVP","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TJ6KVMUE","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TJ6KVMUEQITGDRVPASRJDC5VA3","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-02T09:16:07Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"9a29c0705ed21d9f5af335ec71d35cf86a941d53dd359aced84f45599539f5ee","abstract_canon_sha256":"35956f8846fc6adf44f7d3f1c71e83d0563ce37e481ddedb99e8e271b8b0fa51"},"schema_version":"1.0"},"canonical_sha256":"9a7caab284822661c6af04a2918bb506d2e98a4828546bfd6bfae4ec5a853774","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:54.098062Z","signature_b64":"xcXVdZgcF0cpr0jW+IXulPMxy2+jxcYo9OJcEn8LmSFSjoni9MwJCABGYIm00mfs/z/p7xmSPaBj4B71wmJNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a7caab284822661c6af04a2918bb506d2e98a4828546bfd6bfae4ec5a853774","last_reissued_at":"2026-05-18T04:18:54.097648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:54.097648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0364","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":"2026-05-18T04:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xy2uhEosMkcd4hsHIdbe2dlNIWqgu0kcFF+DgwitX8s5ofO9cMeyRGSCzoolsqMkTA5msv5DRKiveQF/8/97CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:06:19.146659Z"},"content_sha256":"afe63cd54009f286f4899025d31cd7919d12a2e74232b095fe839639d823b38a","schema_version":"1.0","event_id":"sha256:afe63cd54009f286f4899025d31cd7919d12a2e74232b095fe839639d823b38a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TJ6KVMUEQITGDRVPASRJDC5VA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fissioned triangular schemes via sharply 3-transitive groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Jianmin Ma, Kaishun Wang","submitted_at":"2011-07-02T09:16:07Z","abstract_excerpt":"n [D. de Caen, E.R. van Dam. Fissioned triangular schemes via the cross-ratio, {Europ. J. Combin.}, 22 (2001) 297-301], de Caen and van Dam constructed a fission scheme $\\FT(q+1)$ of the triangular scheme on $\\PG(1,q)$. This fission scheme comes from the naturally induced action of $\\PGL(2,q)$ on the 2-element subsets of $\\PG(1,q)$. The group $\\PGL(2,q)$ is one of two infinite families of finite sharply 3-transitive groups. The other such family $\\Mq(q)$ is a \"twisted\" version of $\\PGL(2,q)$, where $q$ is an even power of an odd prime. The group $\\PSL(2,q)$ is the intersection of $\\PGL(2,q)$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0364","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":"2026-05-18T04:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1aDwmT6ipfOqX6pMlTSO0Vla4vbJvY9T5vsZcLocUKu5oLKdw7WqSenfU4+9ic3J426ZJMz1QLzoa94K43pOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:06:19.147018Z"},"content_sha256":"e4588cd003130481d0d1be8eba7e0f00d500a3bfba831e6307c5dda17b8c4e86","schema_version":"1.0","event_id":"sha256:e4588cd003130481d0d1be8eba7e0f00d500a3bfba831e6307c5dda17b8c4e86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TJ6KVMUEQITGDRVPASRJDC5VA3/bundle.json","state_url":"https://pith.science/pith/TJ6KVMUEQITGDRVPASRJDC5VA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TJ6KVMUEQITGDRVPASRJDC5VA3/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":"2026-06-04T05:06:19Z","links":{"resolver":"https://pith.science/pith/TJ6KVMUEQITGDRVPASRJDC5VA3","bundle":"https://pith.science/pith/TJ6KVMUEQITGDRVPASRJDC5VA3/bundle.json","state":"https://pith.science/pith/TJ6KVMUEQITGDRVPASRJDC5VA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TJ6KVMUEQITGDRVPASRJDC5VA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TJ6KVMUEQITGDRVPASRJDC5VA3","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":"35956f8846fc6adf44f7d3f1c71e83d0563ce37e481ddedb99e8e271b8b0fa51","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-02T09:16:07Z","title_canon_sha256":"9a29c0705ed21d9f5af335ec71d35cf86a941d53dd359aced84f45599539f5ee"},"schema_version":"1.0","source":{"id":"1107.0364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0364","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0364v1","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0364","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"TJ6KVMUEQITG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TJ6KVMUEQITGDRVP","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TJ6KVMUE","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:e4588cd003130481d0d1be8eba7e0f00d500a3bfba831e6307c5dda17b8c4e86","target":"graph","created_at":"2026-05-18T04:18:54Z","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":"n [D. de Caen, E.R. van Dam. Fissioned triangular schemes via the cross-ratio, {Europ. J. Combin.}, 22 (2001) 297-301], de Caen and van Dam constructed a fission scheme $\\FT(q+1)$ of the triangular scheme on $\\PG(1,q)$. This fission scheme comes from the naturally induced action of $\\PGL(2,q)$ on the 2-element subsets of $\\PG(1,q)$. The group $\\PGL(2,q)$ is one of two infinite families of finite sharply 3-transitive groups. The other such family $\\Mq(q)$ is a \"twisted\" version of $\\PGL(2,q)$, where $q$ is an even power of an odd prime. The group $\\PSL(2,q)$ is the intersection of $\\PGL(2,q)$ a","authors_text":"Jianmin Ma, Kaishun Wang","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-02T09:16:07Z","title":"Fissioned triangular schemes via sharply 3-transitive groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0364","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:afe63cd54009f286f4899025d31cd7919d12a2e74232b095fe839639d823b38a","target":"record","created_at":"2026-05-18T04:18:54Z","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":"35956f8846fc6adf44f7d3f1c71e83d0563ce37e481ddedb99e8e271b8b0fa51","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-02T09:16:07Z","title_canon_sha256":"9a29c0705ed21d9f5af335ec71d35cf86a941d53dd359aced84f45599539f5ee"},"schema_version":"1.0","source":{"id":"1107.0364","kind":"arxiv","version":1}},"canonical_sha256":"9a7caab284822661c6af04a2918bb506d2e98a4828546bfd6bfae4ec5a853774","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a7caab284822661c6af04a2918bb506d2e98a4828546bfd6bfae4ec5a853774","first_computed_at":"2026-05-18T04:18:54.097648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:54.097648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xcXVdZgcF0cpr0jW+IXulPMxy2+jxcYo9OJcEn8LmSFSjoni9MwJCABGYIm00mfs/z/p7xmSPaBj4B71wmJNAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:54.098062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afe63cd54009f286f4899025d31cd7919d12a2e74232b095fe839639d823b38a","sha256:e4588cd003130481d0d1be8eba7e0f00d500a3bfba831e6307c5dda17b8c4e86"],"state_sha256":"28226ec27ec111fc8317f5e4beb8290f9d5054f5154e5155f135c898eafeedf5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8wkziebFDLV/RWhtXmDogwL224w4Bt2Afp4Bvk6pYoBWxAnYd13n43+VjFCI9L5suTbRfP/bM80e0yxqQ6QMAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T05:06:19.149007Z","bundle_sha256":"3bff9b15fa7e9d361efd06a104f99b16e6f66965b4f103c632e2b9a01cf1fd12"}}