{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3TULL6WKQQ7ZTOQBY6E7I4HLKT","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":"736860c1867411f236211c2d3f4db70af5ae6ba683378e336ae4cbcb3ed28c61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-27T07:24:39Z","title_canon_sha256":"5bbf0f2931194c2eb0194b533e2f70f05701ee7e5a40a2214ba17e1b3752a7e3"},"schema_version":"1.0","source":{"id":"1303.6755","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6755","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6755v1","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6755","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"pith_short_12","alias_value":"3TULL6WKQQ7Z","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3TULL6WKQQ7ZTOQB","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3TULL6WK","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:ccbc493c89f540c5054fe1e9cd1256746d72ffb91f0c968a0cdbf84df8e4d825","target":"graph","created_at":"2026-05-18T02:51:57Z","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 announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with open normaliser, and show that its properties reflect the global structure of the ambient group.","authors_text":"Colin D. Reid, George A. Willis, Pierre-Emmanuel Caprace","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-27T07:24:39Z","title":"Locally normal subgroups of simple locally compact groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6755","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":"sha256:3f6a92cd9f21eafc7bad7f884fd273e4cda805f1f958a14e65e1139b2ee72178","target":"record","created_at":"2026-05-18T02:51:57Z","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":"736860c1867411f236211c2d3f4db70af5ae6ba683378e336ae4cbcb3ed28c61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-27T07:24:39Z","title_canon_sha256":"5bbf0f2931194c2eb0194b533e2f70f05701ee7e5a40a2214ba17e1b3752a7e3"},"schema_version":"1.0","source":{"id":"1303.6755","kind":"arxiv","version":1}},"canonical_sha256":"dce8b5faca843f99ba01c789f470eb54edde4c63ddee7c82059a624d0f521210","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dce8b5faca843f99ba01c789f470eb54edde4c63ddee7c82059a624d0f521210","first_computed_at":"2026-05-18T02:51:57.145716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:57.145716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LQBH/wbCF4WTWeclHMJm5cZIsvBRqamkRAF21A4V0VUJrAQAbgNpueNsi6Ske4utH4KZMKNs7seSjqOFjYWoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:57.146190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6755","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f6a92cd9f21eafc7bad7f884fd273e4cda805f1f958a14e65e1139b2ee72178","sha256:ccbc493c89f540c5054fe1e9cd1256746d72ffb91f0c968a0cdbf84df8e4d825"],"state_sha256":"ec21d16fe85684a63e4d2d43206060e5d4aa90d22ec76c10888a79100a0b01a0"}