{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:Z4Q7SAJZTRILPK5TWYFP26BX57","short_pith_number":"pith:Z4Q7SAJZ","canonical_record":{"source":{"id":"1010.0083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-01T06:47:50Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"51e2fd5650a91bbb7237802c892eb4c7a80adda03627c50f18a30fb0b3682632","abstract_canon_sha256":"092a8814be856090c26d03b8052bacd593332ff0b596648f82f58c2ef675d5b5"},"schema_version":"1.0"},"canonical_sha256":"cf21f901399c50b7abb3b60afd7837effe33c1bd9106a2daf254284337a45430","source":{"kind":"arxiv","id":"1010.0083","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0083","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0083v1","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0083","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"pith_short_12","alias_value":"Z4Q7SAJZTRIL","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Z4Q7SAJZTRILPK5T","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Z4Q7SAJZ","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:Z4Q7SAJZTRILPK5TWYFP26BX57","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-01T06:47:50Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"51e2fd5650a91bbb7237802c892eb4c7a80adda03627c50f18a30fb0b3682632","abstract_canon_sha256":"092a8814be856090c26d03b8052bacd593332ff0b596648f82f58c2ef675d5b5"},"schema_version":"1.0"},"canonical_sha256":"cf21f901399c50b7abb3b60afd7837effe33c1bd9106a2daf254284337a45430","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:00.301585Z","signature_b64":"ImH9qjxX0T4vyu9IFnTFJe7NORooAIVhol3HMFgJ5yMENBPV1VUJf0so1yxZQWCN4lqmxmgucMzsq6LSBCEcDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf21f901399c50b7abb3b60afd7837effe33c1bd9106a2daf254284337a45430","last_reissued_at":"2026-05-18T04:40:00.301123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:00.301123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0083","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":"2026-05-18T04:40:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5oJhkVIV95A4K7iMhWMQztXXuAa5KbYy4GCb7/SecAz9cdtrfa+nKHUzkx5ZRdycO04NiE8/rnsO3YBcyBWcAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:38:09.552063Z"},"content_sha256":"7473f9998535cf10a1c9cc20c7ee670bd2303f6a9541f0ea6cb9e8a7d34e35ee","schema_version":"1.0","event_id":"sha256:7473f9998535cf10a1c9cc20c7ee670bd2303f6a9541f0ea6cb9e8a7d34e35ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:Z4Q7SAJZTRILPK5TWYFP26BX57","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on completely reducible subcomplexes of spherical buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.MG","authors_text":"Linus Kramer","submitted_at":"2010-10-01T06:47:50Z","abstract_excerpt":"A completely reducible subcomplex of a spherical building is a spherical building."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0083","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":"2026-05-18T04:40:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o38sNGshuetopDUH93ysZCixwkni6xT+NCzXRzoOV7aHqzLhDa63w311FrSLU+2+ZY9AvecIBu+PSSmOfPO8Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:38:09.552808Z"},"content_sha256":"139f3608f069ba0d7a22fbe5f9d2f7651a6c92ebf62968d1f31a050ccc853d4b","schema_version":"1.0","event_id":"sha256:139f3608f069ba0d7a22fbe5f9d2f7651a6c92ebf62968d1f31a050ccc853d4b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4Q7SAJZTRILPK5TWYFP26BX57/bundle.json","state_url":"https://pith.science/pith/Z4Q7SAJZTRILPK5TWYFP26BX57/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4Q7SAJZTRILPK5TWYFP26BX57/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":"2026-05-27T01:38:09Z","links":{"resolver":"https://pith.science/pith/Z4Q7SAJZTRILPK5TWYFP26BX57","bundle":"https://pith.science/pith/Z4Q7SAJZTRILPK5TWYFP26BX57/bundle.json","state":"https://pith.science/pith/Z4Q7SAJZTRILPK5TWYFP26BX57/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4Q7SAJZTRILPK5TWYFP26BX57/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:Z4Q7SAJZTRILPK5TWYFP26BX57","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":"092a8814be856090c26d03b8052bacd593332ff0b596648f82f58c2ef675d5b5","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-01T06:47:50Z","title_canon_sha256":"51e2fd5650a91bbb7237802c892eb4c7a80adda03627c50f18a30fb0b3682632"},"schema_version":"1.0","source":{"id":"1010.0083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0083","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0083v1","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0083","created_at":"2026-05-18T04:40:00Z"},{"alias_kind":"pith_short_12","alias_value":"Z4Q7SAJZTRIL","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"Z4Q7SAJZTRILPK5T","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"Z4Q7SAJZ","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:139f3608f069ba0d7a22fbe5f9d2f7651a6c92ebf62968d1f31a050ccc853d4b","target":"graph","created_at":"2026-05-18T04:40:00Z","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 completely reducible subcomplex of a spherical building is a spherical building.","authors_text":"Linus Kramer","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-01T06:47:50Z","title":"Notes on completely reducible subcomplexes of spherical buildings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0083","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":"sha256:7473f9998535cf10a1c9cc20c7ee670bd2303f6a9541f0ea6cb9e8a7d34e35ee","target":"record","created_at":"2026-05-18T04:40:00Z","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":"092a8814be856090c26d03b8052bacd593332ff0b596648f82f58c2ef675d5b5","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-10-01T06:47:50Z","title_canon_sha256":"51e2fd5650a91bbb7237802c892eb4c7a80adda03627c50f18a30fb0b3682632"},"schema_version":"1.0","source":{"id":"1010.0083","kind":"arxiv","version":1}},"canonical_sha256":"cf21f901399c50b7abb3b60afd7837effe33c1bd9106a2daf254284337a45430","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf21f901399c50b7abb3b60afd7837effe33c1bd9106a2daf254284337a45430","first_computed_at":"2026-05-18T04:40:00.301123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:00.301123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ImH9qjxX0T4vyu9IFnTFJe7NORooAIVhol3HMFgJ5yMENBPV1VUJf0so1yxZQWCN4lqmxmgucMzsq6LSBCEcDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:00.301585Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7473f9998535cf10a1c9cc20c7ee670bd2303f6a9541f0ea6cb9e8a7d34e35ee","sha256:139f3608f069ba0d7a22fbe5f9d2f7651a6c92ebf62968d1f31a050ccc853d4b"],"state_sha256":"7c474c0c3a008e795f140126a20ce39ca3c6fe8a593ca010bc50d572e1191a1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l2oY+4SGmVtpxzrOI/TCjV023jWzvDf28gdTqHI0ZAzb+eBxHO1XARvpvYdeC9+/kQ3eq4Uc7MCO1912tmAECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:38:09.557254Z","bundle_sha256":"4187f56b62664b1f81b1773caf2ebf6f7f8faee2106e1f9b9c7da89a46989fca"}}