{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4XZ7ZOMQ3AOQF65JGG3RZCW5N5","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":"470b3061988793e24d37efd98251a5849d972cbf58699e6c8de118aed5997955","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-23T11:44:28Z","title_canon_sha256":"75c7ffa797165ccb222b77fc7e07a54fc43bde80cc11f8f0b6a061ee5471a39d"},"schema_version":"1.0","source":{"id":"1304.6246","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6246","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6246v1","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6246","created_at":"2026-05-18T02:51:57Z"},{"alias_kind":"pith_short_12","alias_value":"4XZ7ZOMQ3AOQ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4XZ7ZOMQ3AOQF65J","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4XZ7ZOMQ","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:000fe1ac4609280ba32a374ed7dc597d7bb951227118f68d3bf4a2d8f95b7c52","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":"The Tits core G^+ of a totally disconnected locally compact group G is defined as the abstract subgroup generated by the closures of the contraction groups of all its elements. We show that a dense subgroup is normalised by the Tits core if and only if it contains it. It follows that every dense subnormal subgroup contains the Tits core. In particular, if G is topologically simple, then the Tits core is abstractly simple, and if G^+ is non-trivial then it is the unique minimal dense normal subgroup. The proofs are based on the fact, of independent interest, that the map which associates to an ","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":"2013-04-23T11:44:28Z","title":"Limits of contraction groups and the Tits core"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6246","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":"sha256:50f9fcb25934f29d98e6950e089ae7a729ccd13bc36aa02888938cd3361dca9e","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":"470b3061988793e24d37efd98251a5849d972cbf58699e6c8de118aed5997955","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-23T11:44:28Z","title_canon_sha256":"75c7ffa797165ccb222b77fc7e07a54fc43bde80cc11f8f0b6a061ee5471a39d"},"schema_version":"1.0","source":{"id":"1304.6246","kind":"arxiv","version":1}},"canonical_sha256":"e5f3fcb990d81d02fba931b71c8add6f48ea48e14cf7229a51968faea513dad3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5f3fcb990d81d02fba931b71c8add6f48ea48e14cf7229a51968faea513dad3","first_computed_at":"2026-05-18T02:51:57.120214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:57.120214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QOE0hz2x0i3GzET2yaE0ztoIRg9+uOiLYTxuBONaxzIRs9KuuKcfQBAgI6tmLLXx1LjDQcp5GW2z93u7bN0WDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:57.120736Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6246","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50f9fcb25934f29d98e6950e089ae7a729ccd13bc36aa02888938cd3361dca9e","sha256:000fe1ac4609280ba32a374ed7dc597d7bb951227118f68d3bf4a2d8f95b7c52"],"state_sha256":"a3010c7202a71c6310c2498dbb50f6edb992f2268070b0f8c606ce62b4c5e82f"}