{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GXKHIW4ZSCNOCNDV2HGGKDEAKL","short_pith_number":"pith:GXKHIW4Z","canonical_record":{"source":{"id":"1506.01307","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-06-03T16:47:25Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"21b0ca2cbe43b545a7e715e7154a4e517801365851593764b36355e257b126f2","abstract_canon_sha256":"1b0edf403f93b4983aaa210865b00a16a6b283408d51663f7095b21c2c5c7bcd"},"schema_version":"1.0"},"canonical_sha256":"35d4745b99909ae13475d1cc650c8052d4730c29135b40b978d4b96158890610","source":{"kind":"arxiv","id":"1506.01307","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01307","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01307v2","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01307","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"pith_short_12","alias_value":"GXKHIW4ZSCNO","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GXKHIW4ZSCNOCNDV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GXKHIW4Z","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GXKHIW4ZSCNOCNDV2HGGKDEAKL","target":"record","payload":{"canonical_record":{"source":{"id":"1506.01307","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-06-03T16:47:25Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"21b0ca2cbe43b545a7e715e7154a4e517801365851593764b36355e257b126f2","abstract_canon_sha256":"1b0edf403f93b4983aaa210865b00a16a6b283408d51663f7095b21c2c5c7bcd"},"schema_version":"1.0"},"canonical_sha256":"35d4745b99909ae13475d1cc650c8052d4730c29135b40b978d4b96158890610","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:47.274381Z","signature_b64":"LYufLIpoT4I1+Wtjf+KzDW/xXxglUPSiLrFw8glsAVEiTXEizwTj/TyGk0boO9Feug9ZoOyhbVmkpmuOarENBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35d4745b99909ae13475d1cc650c8052d4730c29135b40b978d4b96158890610","last_reissued_at":"2026-05-18T00:26:47.273925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:47.273925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.01307","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EqCRXXaR0kw+yB7EHIx3P4aTGUlLVkrMTaJM611KdOe/fzu5D8BltCRU4HdpQ3cTcEd9GZ6YRhjhqgRUWUgXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:20:55.108123Z"},"content_sha256":"a47dec130527f02343808d802eba089836feed3adbb125b330d8ed77309e5069","schema_version":"1.0","event_id":"sha256:a47dec130527f02343808d802eba089836feed3adbb125b330d8ed77309e5069"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GXKHIW4ZSCNOCNDV2HGGKDEAKL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Control of fixed points and existence and uniqueness of centric linking systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"George Glauberman, Justin Lynd","submitted_at":"2015-06-03T16:47:25Z","abstract_excerpt":"A. Chermak has recently proved that to each saturated fusion system over a finite $p$-group, there is a unique associated centric linking system. B. Oliver extended Chermak's proof by showing that all the higher cohomological obstruction groups relevant to unique existence of centric linking systems vanish. Both proofs indirectly assume the classification of finite simple groups. We show how to remove this assumption, thereby giving a classification-free proof of the Martino-Priddy conjecture concerning the $p$-completed classifying spaces of finite groups. Our main tool is a 1971 result of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01307","kind":"arxiv","version":2},"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":"2026-05-18T00:26:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GipGyQURFXIU49OLPGR8ggq37z5fOXDLVWoy2khPsd9Kv4FwRGD66+pyiCo57Kd+bSj2MeAMqFTKmSsbiUGKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:20:55.108476Z"},"content_sha256":"66c14e48be06f974c855bbdf427229aa2fefa59cf72a7485abaa096211c2da1a","schema_version":"1.0","event_id":"sha256:66c14e48be06f974c855bbdf427229aa2fefa59cf72a7485abaa096211c2da1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GXKHIW4ZSCNOCNDV2HGGKDEAKL/bundle.json","state_url":"https://pith.science/pith/GXKHIW4ZSCNOCNDV2HGGKDEAKL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GXKHIW4ZSCNOCNDV2HGGKDEAKL/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":"2026-06-22T12:20:55Z","links":{"resolver":"https://pith.science/pith/GXKHIW4ZSCNOCNDV2HGGKDEAKL","bundle":"https://pith.science/pith/GXKHIW4ZSCNOCNDV2HGGKDEAKL/bundle.json","state":"https://pith.science/pith/GXKHIW4ZSCNOCNDV2HGGKDEAKL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GXKHIW4ZSCNOCNDV2HGGKDEAKL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GXKHIW4ZSCNOCNDV2HGGKDEAKL","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":"1b0edf403f93b4983aaa210865b00a16a6b283408d51663f7095b21c2c5c7bcd","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-06-03T16:47:25Z","title_canon_sha256":"21b0ca2cbe43b545a7e715e7154a4e517801365851593764b36355e257b126f2"},"schema_version":"1.0","source":{"id":"1506.01307","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01307","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01307v2","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01307","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"pith_short_12","alias_value":"GXKHIW4ZSCNO","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GXKHIW4ZSCNOCNDV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GXKHIW4Z","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:66c14e48be06f974c855bbdf427229aa2fefa59cf72a7485abaa096211c2da1a","target":"graph","created_at":"2026-05-18T00:26:47Z","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. Chermak has recently proved that to each saturated fusion system over a finite $p$-group, there is a unique associated centric linking system. B. Oliver extended Chermak's proof by showing that all the higher cohomological obstruction groups relevant to unique existence of centric linking systems vanish. Both proofs indirectly assume the classification of finite simple groups. We show how to remove this assumption, thereby giving a classification-free proof of the Martino-Priddy conjecture concerning the $p$-completed classifying spaces of finite groups. Our main tool is a 1971 result of th","authors_text":"George Glauberman, Justin Lynd","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-06-03T16:47:25Z","title":"Control of fixed points and existence and uniqueness of centric linking systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01307","kind":"arxiv","version":2},"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:a47dec130527f02343808d802eba089836feed3adbb125b330d8ed77309e5069","target":"record","created_at":"2026-05-18T00:26:47Z","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":"1b0edf403f93b4983aaa210865b00a16a6b283408d51663f7095b21c2c5c7bcd","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-06-03T16:47:25Z","title_canon_sha256":"21b0ca2cbe43b545a7e715e7154a4e517801365851593764b36355e257b126f2"},"schema_version":"1.0","source":{"id":"1506.01307","kind":"arxiv","version":2}},"canonical_sha256":"35d4745b99909ae13475d1cc650c8052d4730c29135b40b978d4b96158890610","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35d4745b99909ae13475d1cc650c8052d4730c29135b40b978d4b96158890610","first_computed_at":"2026-05-18T00:26:47.273925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:47.273925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LYufLIpoT4I1+Wtjf+KzDW/xXxglUPSiLrFw8glsAVEiTXEizwTj/TyGk0boO9Feug9ZoOyhbVmkpmuOarENBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:47.274381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01307","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a47dec130527f02343808d802eba089836feed3adbb125b330d8ed77309e5069","sha256:66c14e48be06f974c855bbdf427229aa2fefa59cf72a7485abaa096211c2da1a"],"state_sha256":"148a19ff9c8df12a467244dccb1c7d421e98a18b72efd0c599c6292aab57d593"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wck+4L8aH0vmU7W8Aa5puMzOVIhugumap6Rdg7fivOKhL3FXyeM1VbHEBBaK9CDfpLPZayh+I0kWb3bLSNE7Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:20:55.110368Z","bundle_sha256":"305305b7278c849d0a3d4a1b9187d89d7ff8ec0c28ed0303d9727b36628cf374"}}