{"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"}