{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HYV6TO7Y4CQUKPJRYNNCQ2NB6Z","short_pith_number":"pith:HYV6TO7Y","canonical_record":{"source":{"id":"1108.5375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-26T19:24:26Z","cross_cats_sorted":["math.AT","math.GR"],"title_canon_sha256":"afcfe1c2cc8ed952870b1c12934124c21d6974e2a26d3e3036b8ee39de7d5de7","abstract_canon_sha256":"304b6e96c44a96f5c2eb7cf5c9bb73da723d1690948227dea5adca7784e54e49"},"schema_version":"1.0"},"canonical_sha256":"3e2be9bbf8e0a1453d31c35a2869a1f64a5a3a7a08d0556f687995ec4e5aae0e","source":{"kind":"arxiv","id":"1108.5375","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5375","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5375v1","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5375","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"HYV6TO7Y4CQU","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HYV6TO7Y4CQUKPJR","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HYV6TO7Y","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HYV6TO7Y4CQUKPJRYNNCQ2NB6Z","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-26T19:24:26Z","cross_cats_sorted":["math.AT","math.GR"],"title_canon_sha256":"afcfe1c2cc8ed952870b1c12934124c21d6974e2a26d3e3036b8ee39de7d5de7","abstract_canon_sha256":"304b6e96c44a96f5c2eb7cf5c9bb73da723d1690948227dea5adca7784e54e49"},"schema_version":"1.0"},"canonical_sha256":"3e2be9bbf8e0a1453d31c35a2869a1f64a5a3a7a08d0556f687995ec4e5aae0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:38.474851Z","signature_b64":"VeqYqS3SG8CU/zcpOwD+XWeQDwSGpFdVN9vCjXZQrS4h72c26xEIr4mySd2e/ulDbNA+HK2wzI9TYVZjx1FQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e2be9bbf8e0a1453d31c35a2869a1f64a5a3a7a08d0556f687995ec4e5aae0e","last_reissued_at":"2026-05-18T04:14:38.474398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:38.474398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5375","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":"2026-05-18T04:14:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HkH3qAZ+vWok2SS7XnJeWZk57X2o79mok5WZYXaTAkQ779HbJwYPbUMoiPf8w3AWnkwDQEfbl9d+GDLKjvqaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:28:51.522425Z"},"content_sha256":"437033141bd463f93bc14ea90470da7102e652b03b9278c7b7b9ee13ffc99416","schema_version":"1.0","event_id":"sha256:437033141bd463f93bc14ea90470da7102e652b03b9278c7b7b9ee13ffc99416"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HYV6TO7Y4CQUKPJRYNNCQ2NB6Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Commuting categories for blocks and fusion systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR"],"primary_cat":"math.RT","authors_text":"Adam Glesser, Markus Lickelmann","submitted_at":"2011-08-26T19:24:26Z","abstract_excerpt":"We extend the notion of a commuting poset for a finite group to p-blocks and fusion systems, and we generalize a result, due originally to Alperin and proved independently by Aschbacher and Segev, to commuting graphs of blocks, with a very short proof based on the G-equivariant version, due to Thevenaz and Webb, of a result of Quillen."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5375","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":"2026-05-18T04:14:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SToxOhoALFgzoYmX/sPRL8leTAknMoK9TeeF6GH5wiB43q25AUwSEQI31xLQbrTSIBXrU9fiegfoixtpnebeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:28:51.523152Z"},"content_sha256":"a83a6c529430b1085c4dcbf6fa9829b3c7574273272ffb8876edc7171d953ba5","schema_version":"1.0","event_id":"sha256:a83a6c529430b1085c4dcbf6fa9829b3c7574273272ffb8876edc7171d953ba5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYV6TO7Y4CQUKPJRYNNCQ2NB6Z/bundle.json","state_url":"https://pith.science/pith/HYV6TO7Y4CQUKPJRYNNCQ2NB6Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYV6TO7Y4CQUKPJRYNNCQ2NB6Z/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":"2026-06-10T10:28:51Z","links":{"resolver":"https://pith.science/pith/HYV6TO7Y4CQUKPJRYNNCQ2NB6Z","bundle":"https://pith.science/pith/HYV6TO7Y4CQUKPJRYNNCQ2NB6Z/bundle.json","state":"https://pith.science/pith/HYV6TO7Y4CQUKPJRYNNCQ2NB6Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYV6TO7Y4CQUKPJRYNNCQ2NB6Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HYV6TO7Y4CQUKPJRYNNCQ2NB6Z","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":"304b6e96c44a96f5c2eb7cf5c9bb73da723d1690948227dea5adca7784e54e49","cross_cats_sorted":["math.AT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-26T19:24:26Z","title_canon_sha256":"afcfe1c2cc8ed952870b1c12934124c21d6974e2a26d3e3036b8ee39de7d5de7"},"schema_version":"1.0","source":{"id":"1108.5375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5375","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5375v1","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5375","created_at":"2026-05-18T04:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"HYV6TO7Y4CQU","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HYV6TO7Y4CQUKPJR","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HYV6TO7Y","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:a83a6c529430b1085c4dcbf6fa9829b3c7574273272ffb8876edc7171d953ba5","target":"graph","created_at":"2026-05-18T04:14:38Z","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":"We extend the notion of a commuting poset for a finite group to p-blocks and fusion systems, and we generalize a result, due originally to Alperin and proved independently by Aschbacher and Segev, to commuting graphs of blocks, with a very short proof based on the G-equivariant version, due to Thevenaz and Webb, of a result of Quillen.","authors_text":"Adam Glesser, Markus Lickelmann","cross_cats":["math.AT","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-26T19:24:26Z","title":"Commuting categories for blocks and fusion systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5375","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":"sha256:437033141bd463f93bc14ea90470da7102e652b03b9278c7b7b9ee13ffc99416","target":"record","created_at":"2026-05-18T04:14:38Z","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":"304b6e96c44a96f5c2eb7cf5c9bb73da723d1690948227dea5adca7784e54e49","cross_cats_sorted":["math.AT","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-08-26T19:24:26Z","title_canon_sha256":"afcfe1c2cc8ed952870b1c12934124c21d6974e2a26d3e3036b8ee39de7d5de7"},"schema_version":"1.0","source":{"id":"1108.5375","kind":"arxiv","version":1}},"canonical_sha256":"3e2be9bbf8e0a1453d31c35a2869a1f64a5a3a7a08d0556f687995ec4e5aae0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e2be9bbf8e0a1453d31c35a2869a1f64a5a3a7a08d0556f687995ec4e5aae0e","first_computed_at":"2026-05-18T04:14:38.474398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:38.474398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VeqYqS3SG8CU/zcpOwD+XWeQDwSGpFdVN9vCjXZQrS4h72c26xEIr4mySd2e/ulDbNA+HK2wzI9TYVZjx1FQDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:38.474851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:437033141bd463f93bc14ea90470da7102e652b03b9278c7b7b9ee13ffc99416","sha256:a83a6c529430b1085c4dcbf6fa9829b3c7574273272ffb8876edc7171d953ba5"],"state_sha256":"e8130744d6617e613ce8e520a89ecc5eac81bf00b9a353c736925fd0f5d00b7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hwvVN1IhgfTe4sDP8sDP326s6ksowng8UFFSpk1NHBBgHbLjztX1J9c2Thy2+BtMltY/B2I9o2BTSY++cmbAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:28:51.527306Z","bundle_sha256":"7937564be96813ca426e24caab5ab36d3fcd5d74ff862a0c8a6dee9a3d125924"}}