{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BNTME6S7FDE4UUVWRBXRLBKTCT","short_pith_number":"pith:BNTME6S7","canonical_record":{"source":{"id":"1602.07132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-23T12:11:39Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"d81d5b7a295455bba104a91e1eadd291b70516ea4502ccc6c364a1555412275c","abstract_canon_sha256":"67031a9bf4393ba8ed24584b20233cfb0598a61fcca9166bed343e47970b6d9f"},"schema_version":"1.0"},"canonical_sha256":"0b66c27a5f28c9ca52b6886f15855314d43df93a95c3e618f236596f0a5815e8","source":{"kind":"arxiv","id":"1602.07132","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07132","created_at":"2026-05-17T23:55:05Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07132v1","created_at":"2026-05-17T23:55:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07132","created_at":"2026-05-17T23:55:05Z"},{"alias_kind":"pith_short_12","alias_value":"BNTME6S7FDE4","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BNTME6S7FDE4UUVW","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BNTME6S7","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BNTME6S7FDE4UUVWRBXRLBKTCT","target":"record","payload":{"canonical_record":{"source":{"id":"1602.07132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-23T12:11:39Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"d81d5b7a295455bba104a91e1eadd291b70516ea4502ccc6c364a1555412275c","abstract_canon_sha256":"67031a9bf4393ba8ed24584b20233cfb0598a61fcca9166bed343e47970b6d9f"},"schema_version":"1.0"},"canonical_sha256":"0b66c27a5f28c9ca52b6886f15855314d43df93a95c3e618f236596f0a5815e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:05.497339Z","signature_b64":"o7RKuMBFmddExeVag23Dqxs5YcLRe1qL0pulsP341itzbY80QFjkh4VeejgEXq7SXJ9reODG0gk7nVjo4yjLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b66c27a5f28c9ca52b6886f15855314d43df93a95c3e618f236596f0a5815e8","last_reissued_at":"2026-05-17T23:55:05.496891Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:05.496891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.07132","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":"2026-05-17T23:55:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hAZ6pVfDB3ZkAl3oFYpb+yZa6i9ZczsNoePdvVC5ApdFvXxaXpIXN5zcQER7DCfv87oyHhop8+84+q3syhgaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:09:24.858346Z"},"content_sha256":"ef457d5e5a183538b9311a91307a4616b5b0b2960b62ab0d972b673b62d9c2cf","schema_version":"1.0","event_id":"sha256:ef457d5e5a183538b9311a91307a4616b5b0b2960b62ab0d972b673b62d9c2cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BNTME6S7FDE4UUVWRBXRLBKTCT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cartan coherent configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Andrey Vasil'ev, Ilia Ponomarenko","submitted_at":"2016-02-23T12:11:39Z","abstract_excerpt":"The Cartan scheme $\\cal X$ of a finite group $G$ with a $(B,N)$-pair is defined to be the coherent configuration associated with the action of $G$ on the right cosets of the Cartan subgroup $B\\cap N$ by the right multiplications. It is proved that if $G$ is a simple group of Lie type, then asymptotically, the coherent configuration $\\cal X$ is 2-separable, i.e., the array of 2-dimensional intersection numbers determines $\\cal X$ up to isomorphism. It is also proved that in this case, the base number of $\\cal X$ equals 2. This enables us to construct a polynomial-time algorithm for recognizing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07132","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":"2026-05-17T23:55:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"28G4rpbTK5Y02+FsO34wt/vtr8gx+TFpjWUxHz8te4+nrAtgJdx8FtphEMuDjhO8Zd+2eoori4WBIRZWfI2IDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:09:24.858699Z"},"content_sha256":"9d0b9c70fa9740a3ac602fd00c2bc529255c5a307b417ab228cbe4e58248a882","schema_version":"1.0","event_id":"sha256:9d0b9c70fa9740a3ac602fd00c2bc529255c5a307b417ab228cbe4e58248a882"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNTME6S7FDE4UUVWRBXRLBKTCT/bundle.json","state_url":"https://pith.science/pith/BNTME6S7FDE4UUVWRBXRLBKTCT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNTME6S7FDE4UUVWRBXRLBKTCT/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":"2026-05-28T20:09:24Z","links":{"resolver":"https://pith.science/pith/BNTME6S7FDE4UUVWRBXRLBKTCT","bundle":"https://pith.science/pith/BNTME6S7FDE4UUVWRBXRLBKTCT/bundle.json","state":"https://pith.science/pith/BNTME6S7FDE4UUVWRBXRLBKTCT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNTME6S7FDE4UUVWRBXRLBKTCT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BNTME6S7FDE4UUVWRBXRLBKTCT","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":"67031a9bf4393ba8ed24584b20233cfb0598a61fcca9166bed343e47970b6d9f","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-23T12:11:39Z","title_canon_sha256":"d81d5b7a295455bba104a91e1eadd291b70516ea4502ccc6c364a1555412275c"},"schema_version":"1.0","source":{"id":"1602.07132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07132","created_at":"2026-05-17T23:55:05Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07132v1","created_at":"2026-05-17T23:55:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07132","created_at":"2026-05-17T23:55:05Z"},{"alias_kind":"pith_short_12","alias_value":"BNTME6S7FDE4","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BNTME6S7FDE4UUVW","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BNTME6S7","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:9d0b9c70fa9740a3ac602fd00c2bc529255c5a307b417ab228cbe4e58248a882","target":"graph","created_at":"2026-05-17T23:55:05Z","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":"The Cartan scheme $\\cal X$ of a finite group $G$ with a $(B,N)$-pair is defined to be the coherent configuration associated with the action of $G$ on the right cosets of the Cartan subgroup $B\\cap N$ by the right multiplications. It is proved that if $G$ is a simple group of Lie type, then asymptotically, the coherent configuration $\\cal X$ is 2-separable, i.e., the array of 2-dimensional intersection numbers determines $\\cal X$ up to isomorphism. It is also proved that in this case, the base number of $\\cal X$ equals 2. This enables us to construct a polynomial-time algorithm for recognizing ","authors_text":"Andrey Vasil'ev, Ilia Ponomarenko","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-23T12:11:39Z","title":"Cartan coherent configurations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07132","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:ef457d5e5a183538b9311a91307a4616b5b0b2960b62ab0d972b673b62d9c2cf","target":"record","created_at":"2026-05-17T23:55:05Z","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":"67031a9bf4393ba8ed24584b20233cfb0598a61fcca9166bed343e47970b6d9f","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-23T12:11:39Z","title_canon_sha256":"d81d5b7a295455bba104a91e1eadd291b70516ea4502ccc6c364a1555412275c"},"schema_version":"1.0","source":{"id":"1602.07132","kind":"arxiv","version":1}},"canonical_sha256":"0b66c27a5f28c9ca52b6886f15855314d43df93a95c3e618f236596f0a5815e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b66c27a5f28c9ca52b6886f15855314d43df93a95c3e618f236596f0a5815e8","first_computed_at":"2026-05-17T23:55:05.496891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:05.496891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o7RKuMBFmddExeVag23Dqxs5YcLRe1qL0pulsP341itzbY80QFjkh4VeejgEXq7SXJ9reODG0gk7nVjo4yjLCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:05.497339Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef457d5e5a183538b9311a91307a4616b5b0b2960b62ab0d972b673b62d9c2cf","sha256:9d0b9c70fa9740a3ac602fd00c2bc529255c5a307b417ab228cbe4e58248a882"],"state_sha256":"b83a53354df07dc2c5785645a4397060a195e436d5d69240e036f982659b4146"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FZ3B9qA6gnx6zst8/KiQ4G0uD/8cHPG5KyQupQdCIt9JoS4uri6/ic3Q2Py/vWsz9H9x1r/zJcgVmcCbcoVtAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:09:24.860869Z","bundle_sha256":"c7a0d76df41810392b7ba9f1f81ca1e2c40b24f49a2a959ccdbe859ddac4f5e1"}}