{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6Y3LJICZKO5TF7NFURKHLH5DJ7","short_pith_number":"pith:6Y3LJICZ","canonical_record":{"source":{"id":"1303.5996","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-24T21:31:31Z","cross_cats_sorted":[],"title_canon_sha256":"3874f610c4c9cd963a3a7fbe27b993777ec4f2bc1e513100a6fbdc320aeba771","abstract_canon_sha256":"d58ae4ab2f56bfd20d53546bd1fc25ed03646f0f535d6e59bfb2dea0590d6263"},"schema_version":"1.0"},"canonical_sha256":"f636b4a05953bb32fda5a454759fa34ff58458411b6154c6796f561af757a106","source":{"kind":"arxiv","id":"1303.5996","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5996","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5996v2","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5996","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"6Y3LJICZKO5T","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6Y3LJICZKO5TF7NF","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6Y3LJICZ","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6Y3LJICZKO5TF7NFURKHLH5DJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1303.5996","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-24T21:31:31Z","cross_cats_sorted":[],"title_canon_sha256":"3874f610c4c9cd963a3a7fbe27b993777ec4f2bc1e513100a6fbdc320aeba771","abstract_canon_sha256":"d58ae4ab2f56bfd20d53546bd1fc25ed03646f0f535d6e59bfb2dea0590d6263"},"schema_version":"1.0"},"canonical_sha256":"f636b4a05953bb32fda5a454759fa34ff58458411b6154c6796f561af757a106","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:02.475625Z","signature_b64":"GYJKSPQvfHudDZU/hTzCh7FXzF+7YBgep4QY4dC7JlGESDkIj9Kgl/cqmXl5KGHWKM8OZOESNNG2ak+3fblICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f636b4a05953bb32fda5a454759fa34ff58458411b6154c6796f561af757a106","last_reissued_at":"2026-05-18T00:52:02.474903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:02.474903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.5996","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":"2026-05-18T00:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mmTXkVCKJHmwpanma6Z8D6mrN92XhTiNpuRXrmDzCrj9+QFuu9MJNZmrLAjOTcbpD0n77rOnF8nyYDi7S1yhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:23:56.902552Z"},"content_sha256":"d0c22156c76ca514ef99584459844fc4e6d1dcb225b40e12e4f15a7f0bea5b9a","schema_version":"1.0","event_id":"sha256:d0c22156c76ca514ef99584459844fc4e6d1dcb225b40e12e4f15a7f0bea5b9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6Y3LJICZKO5TF7NFURKHLH5DJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Thompson-Lyons transfer lemma for fusion systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Justin Lynd","submitted_at":"2013-03-24T21:31:31Z","abstract_excerpt":"In this note, a generalization of the Thompson transfer lemma and its various extensions, most recently due to Lyons, is proven in the context of saturated fusion systems. A strengthening of Alperin's fusion theorem is also given in this setting, following Alperin's own \"up and down\" fusion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5996","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":"2026-05-18T00:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jdx8gPZrHWka78+8YuJev0atIUsfzw4IrE6uanTtzK9xTcgiPEwaIHlOIz0ppOhZLeSXEI288TmW4D70ufnWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:23:56.902890Z"},"content_sha256":"57e7f6ac96ab8bad755a7f4b00e4d7915a1a462d8cc1b40308f375b591f35796","schema_version":"1.0","event_id":"sha256:57e7f6ac96ab8bad755a7f4b00e4d7915a1a462d8cc1b40308f375b591f35796"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6Y3LJICZKO5TF7NFURKHLH5DJ7/bundle.json","state_url":"https://pith.science/pith/6Y3LJICZKO5TF7NFURKHLH5DJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6Y3LJICZKO5TF7NFURKHLH5DJ7/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":"2026-06-22T11:23:56Z","links":{"resolver":"https://pith.science/pith/6Y3LJICZKO5TF7NFURKHLH5DJ7","bundle":"https://pith.science/pith/6Y3LJICZKO5TF7NFURKHLH5DJ7/bundle.json","state":"https://pith.science/pith/6Y3LJICZKO5TF7NFURKHLH5DJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6Y3LJICZKO5TF7NFURKHLH5DJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6Y3LJICZKO5TF7NFURKHLH5DJ7","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":"d58ae4ab2f56bfd20d53546bd1fc25ed03646f0f535d6e59bfb2dea0590d6263","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-24T21:31:31Z","title_canon_sha256":"3874f610c4c9cd963a3a7fbe27b993777ec4f2bc1e513100a6fbdc320aeba771"},"schema_version":"1.0","source":{"id":"1303.5996","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5996","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5996v2","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5996","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"6Y3LJICZKO5T","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6Y3LJICZKO5TF7NF","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6Y3LJICZ","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:57e7f6ac96ab8bad755a7f4b00e4d7915a1a462d8cc1b40308f375b591f35796","target":"graph","created_at":"2026-05-18T00:52:02Z","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":"In this note, a generalization of the Thompson transfer lemma and its various extensions, most recently due to Lyons, is proven in the context of saturated fusion systems. A strengthening of Alperin's fusion theorem is also given in this setting, following Alperin's own \"up and down\" fusion.","authors_text":"Justin Lynd","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-24T21:31:31Z","title":"The Thompson-Lyons transfer lemma for fusion systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5996","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:d0c22156c76ca514ef99584459844fc4e6d1dcb225b40e12e4f15a7f0bea5b9a","target":"record","created_at":"2026-05-18T00:52:02Z","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":"d58ae4ab2f56bfd20d53546bd1fc25ed03646f0f535d6e59bfb2dea0590d6263","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-24T21:31:31Z","title_canon_sha256":"3874f610c4c9cd963a3a7fbe27b993777ec4f2bc1e513100a6fbdc320aeba771"},"schema_version":"1.0","source":{"id":"1303.5996","kind":"arxiv","version":2}},"canonical_sha256":"f636b4a05953bb32fda5a454759fa34ff58458411b6154c6796f561af757a106","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f636b4a05953bb32fda5a454759fa34ff58458411b6154c6796f561af757a106","first_computed_at":"2026-05-18T00:52:02.474903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:02.474903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GYJKSPQvfHudDZU/hTzCh7FXzF+7YBgep4QY4dC7JlGESDkIj9Kgl/cqmXl5KGHWKM8OZOESNNG2ak+3fblICQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:02.475625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.5996","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0c22156c76ca514ef99584459844fc4e6d1dcb225b40e12e4f15a7f0bea5b9a","sha256:57e7f6ac96ab8bad755a7f4b00e4d7915a1a462d8cc1b40308f375b591f35796"],"state_sha256":"0fdda24ebe45599db7db6dc617175503409a6d274f8c4f5506235fab05bdbb30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bdD0MevnN374Tox0WZ+coOD6x5mSX2peHGSkzAJtMQ0Oy2e8i/CoNtEugwHA2xpNHpJlJcC/QAggaZKJ21vqAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:23:56.904746Z","bundle_sha256":"fa7fda41f70d563113be2f5881760dcdc408a3ff842a87d76d1dfd4ee9b4d610"}}