{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2FP77WMRICXHRSSVC6WVPZMNMH","short_pith_number":"pith:2FP77WMR","canonical_record":{"source":{"id":"1310.6275","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-23T16:16:04Z","cross_cats_sorted":[],"title_canon_sha256":"26681cf7cd0a2961bd23b8e774d5fd7c65d5812ce48c14dd61dbb6e56ed13dcd","abstract_canon_sha256":"28c5fca8cbf08d0aea9c129013217c094667f77aacedce5524e668a006f1f3d0"},"schema_version":"1.0"},"canonical_sha256":"d15fffd99140ae78ca5517ad57e58d61f1db1036aa0e5bfc4cfaa999cd3d0dc3","source":{"kind":"arxiv","id":"1310.6275","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6275","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6275v5","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6275","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"pith_short_12","alias_value":"2FP77WMRICXH","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2FP77WMRICXHRSSV","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2FP77WMR","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2FP77WMRICXHRSSVC6WVPZMNMH","target":"record","payload":{"canonical_record":{"source":{"id":"1310.6275","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-23T16:16:04Z","cross_cats_sorted":[],"title_canon_sha256":"26681cf7cd0a2961bd23b8e774d5fd7c65d5812ce48c14dd61dbb6e56ed13dcd","abstract_canon_sha256":"28c5fca8cbf08d0aea9c129013217c094667f77aacedce5524e668a006f1f3d0"},"schema_version":"1.0"},"canonical_sha256":"d15fffd99140ae78ca5517ad57e58d61f1db1036aa0e5bfc4cfaa999cd3d0dc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:27.670053Z","signature_b64":"Asnt2Vt9qqRb2h/DWnLeN9H5I9GbZNmmtNYO0wylJ2dRF8YQzUzkGTlQpA5R3F0yYnVa+0yDS7NxA63rm9hfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d15fffd99140ae78ca5517ad57e58d61f1db1036aa0e5bfc4cfaa999cd3d0dc3","last_reissued_at":"2026-05-18T01:11:27.669476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:27.669476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.6275","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXcz7gwskUS3LeoU8TZHc0v+y/hCQ1UmLVu814s65QLPnoV3FGz7EjtQ+5aJNOPfRmS01IQGsiUi1aMozpbsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:56:36.341453Z"},"content_sha256":"469eed2ab98acc03b934f2c866941f2007ac2fd08dd060aa40f2fec71fda7886","schema_version":"1.0","event_id":"sha256:469eed2ab98acc03b934f2c866941f2007ac2fd08dd060aa40f2fec71fda7886"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2FP77WMRICXHRSSVC6WVPZMNMH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The right angle to look at orthogonal sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Frank Olaf Wagner","submitted_at":"2013-10-23T16:16:04Z","abstract_excerpt":"If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in (X,Y) has a normal hyperdefinable X-internal subgroup N such that G/N is Y-internal; N is unique up to commensurability. In order to make sense of this statement, local simplicity theory for hyperdefinable sets is developped. Moreover, a version of Schlichting's Theorem for hyperdefinable families of commensurable subgroups is shown."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6275","kind":"arxiv","version":5},"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":"2026-05-18T01:11:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FREsGPTWQesptGbLrgFOs3uRKFmihIvZziPW8q50JDhWlwvT11DCUiQLtcuXa34xwvY7OV7QPzIHOq8ZSoj4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:56:36.341788Z"},"content_sha256":"50d51d9978b3d6ca092b5d1e9ca0ff8073718ae26ad4004a1fae0c85242f2add","schema_version":"1.0","event_id":"sha256:50d51d9978b3d6ca092b5d1e9ca0ff8073718ae26ad4004a1fae0c85242f2add"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2FP77WMRICXHRSSVC6WVPZMNMH/bundle.json","state_url":"https://pith.science/pith/2FP77WMRICXHRSSVC6WVPZMNMH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2FP77WMRICXHRSSVC6WVPZMNMH/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":"2026-06-01T16:56:36Z","links":{"resolver":"https://pith.science/pith/2FP77WMRICXHRSSVC6WVPZMNMH","bundle":"https://pith.science/pith/2FP77WMRICXHRSSVC6WVPZMNMH/bundle.json","state":"https://pith.science/pith/2FP77WMRICXHRSSVC6WVPZMNMH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2FP77WMRICXHRSSVC6WVPZMNMH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2FP77WMRICXHRSSVC6WVPZMNMH","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":"28c5fca8cbf08d0aea9c129013217c094667f77aacedce5524e668a006f1f3d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-23T16:16:04Z","title_canon_sha256":"26681cf7cd0a2961bd23b8e774d5fd7c65d5812ce48c14dd61dbb6e56ed13dcd"},"schema_version":"1.0","source":{"id":"1310.6275","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6275","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6275v5","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6275","created_at":"2026-05-18T01:11:27Z"},{"alias_kind":"pith_short_12","alias_value":"2FP77WMRICXH","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2FP77WMRICXHRSSV","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2FP77WMR","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:50d51d9978b3d6ca092b5d1e9ca0ff8073718ae26ad4004a1fae0c85242f2add","target":"graph","created_at":"2026-05-18T01:11:27Z","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":"If X and Y are orthogonal hyperdefinable sets such that X is simple, then any group G interpretable in (X,Y) has a normal hyperdefinable X-internal subgroup N such that G/N is Y-internal; N is unique up to commensurability. In order to make sense of this statement, local simplicity theory for hyperdefinable sets is developped. Moreover, a version of Schlichting's Theorem for hyperdefinable families of commensurable subgroups is shown.","authors_text":"Frank Olaf Wagner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-23T16:16:04Z","title":"The right angle to look at orthogonal sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6275","kind":"arxiv","version":5},"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":"sha256:469eed2ab98acc03b934f2c866941f2007ac2fd08dd060aa40f2fec71fda7886","target":"record","created_at":"2026-05-18T01:11:27Z","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":"28c5fca8cbf08d0aea9c129013217c094667f77aacedce5524e668a006f1f3d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-23T16:16:04Z","title_canon_sha256":"26681cf7cd0a2961bd23b8e774d5fd7c65d5812ce48c14dd61dbb6e56ed13dcd"},"schema_version":"1.0","source":{"id":"1310.6275","kind":"arxiv","version":5}},"canonical_sha256":"d15fffd99140ae78ca5517ad57e58d61f1db1036aa0e5bfc4cfaa999cd3d0dc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d15fffd99140ae78ca5517ad57e58d61f1db1036aa0e5bfc4cfaa999cd3d0dc3","first_computed_at":"2026-05-18T01:11:27.669476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:27.669476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Asnt2Vt9qqRb2h/DWnLeN9H5I9GbZNmmtNYO0wylJ2dRF8YQzUzkGTlQpA5R3F0yYnVa+0yDS7NxA63rm9hfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:27.670053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6275","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:469eed2ab98acc03b934f2c866941f2007ac2fd08dd060aa40f2fec71fda7886","sha256:50d51d9978b3d6ca092b5d1e9ca0ff8073718ae26ad4004a1fae0c85242f2add"],"state_sha256":"a19df4517189b168d24d13f5f6ea323fdfc6e70835c2d61fb0a515b489c6216a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eDY41RLKYVXLUpRMfT1CQIKXsPvFN7lezWreH8A3wbwfMhBDu9nwyo6duOH11YrFZy8ZA2XEZfa4ClxfcCTEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:56:36.343850Z","bundle_sha256":"31441dc2fb597f8831c6f7f3f4daf31aa63875fa23c151dbdf26f6edbde74d9e"}}