{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SH3DPYPFAMSGVEGHCKZWZQK2X2","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":"fbf6cf8a9bce4973c7eba646befc28ee8fd8b96ae631c2acfef5249966349a7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-14T14:56:24Z","title_canon_sha256":"6b59d9f39ad8a14cce98c0bfce51669fc3b5e1ab20b7e989f1846e0b001de1b5"},"schema_version":"1.0","source":{"id":"1611.04403","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04403","created_at":"2026-05-18T00:59:16Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04403v1","created_at":"2026-05-18T00:59:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04403","created_at":"2026-05-18T00:59:16Z"},{"alias_kind":"pith_short_12","alias_value":"SH3DPYPFAMSG","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SH3DPYPFAMSGVEGH","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SH3DPYPF","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:ce8ce58d890d01069c24f8e783a96d8a7f1370ba218caadad38f4a7473b75d23","target":"graph","created_at":"2026-05-18T00:59:16Z","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 prove that an isomorphism between saturated fusion systems over the same finite p-group is detected on the elementary abelian subgroups of the hyperfocal subgroup if p is odd, and on the abelian subgroups of the hyperfocal subgroup of exponent at most 4 if p = 2. For odd p, this has implications for mod p group cohomology.","authors_text":"Ellen Henke, Jun Liao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-14T14:56:24Z","title":"Control of Fusion by Abelian Subgroups of the Hyperfocal Subgroup"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04403","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":"sha256:7384a6196b62e4f18aa3aeb1c4df11dbb1e49759d64c1dd27080ce0ced4c01c0","target":"record","created_at":"2026-05-18T00:59:16Z","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":"fbf6cf8a9bce4973c7eba646befc28ee8fd8b96ae631c2acfef5249966349a7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-11-14T14:56:24Z","title_canon_sha256":"6b59d9f39ad8a14cce98c0bfce51669fc3b5e1ab20b7e989f1846e0b001de1b5"},"schema_version":"1.0","source":{"id":"1611.04403","kind":"arxiv","version":1}},"canonical_sha256":"91f637e1e503246a90c712b36cc15abe8a99eaa855b4e750bb897e894e61d876","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91f637e1e503246a90c712b36cc15abe8a99eaa855b4e750bb897e894e61d876","first_computed_at":"2026-05-18T00:59:16.752279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:16.752279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rMY912M5NYPjNqIIQG51D9Pt6S62BCsxkuW9L7+jsbo5ViAA0a6hYAV4Sd3c0fDZ7qMcBkE7VToTopWb6lVLAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:16.752966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04403","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7384a6196b62e4f18aa3aeb1c4df11dbb1e49759d64c1dd27080ce0ced4c01c0","sha256:ce8ce58d890d01069c24f8e783a96d8a7f1370ba218caadad38f4a7473b75d23"],"state_sha256":"b8f4ab8350a49e08f55c33c229162f58dcaa30ec573c291732b928aa64c056b9"}