{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:F3ZWU5S6TCILFJGRYNQUVXDR5T","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":"cdde0f720ac8591d63f7bda9c95bb32962834c0287074b157431b628b4b773be","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2007-06-19T04:38:54Z","title_canon_sha256":"a3615601d0c010afc9ea179c47bfd5bbf4e9755f10545d2c363458932ff81554"},"schema_version":"1.0","source":{"id":"0706.2713","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.2713","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"arxiv_version","alias_value":"0706.2713v1","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.2713","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"pith_short_12","alias_value":"F3ZWU5S6TCIL","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"F3ZWU5S6TCILFJGR","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"F3ZWU5S6","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:765a0eb12022a573e58fe8fe6e4a19e2bfd2156c8da73c547694fbc64e8b4cba","target":"graph","created_at":"2026-05-18T03:44:13Z","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":"Let $G$ be an abstract Kac-Moody group over a finite field and $\\bar{G}$ be the closure of the image of $G$ in the automorphism group of its positive building. We show that if the Dynkin diagram associated to $G$ is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in $\\bar{G}$ which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)","authors_text":"Bertrand Remy (ICJ), Jacqui Ramagge, Udo Baumgartner","cross_cats":[],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2007-06-19T04:38:54Z","title":"Contraction groups in complete Kac-Moody groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.2713","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:e66d490a4bcc8dad8a5b4fd598e2c381b1467a1996eb84e9cf0446742e06915f","target":"record","created_at":"2026-05-18T03:44:13Z","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":"cdde0f720ac8591d63f7bda9c95bb32962834c0287074b157431b628b4b773be","cross_cats_sorted":[],"license":"","primary_cat":"math.GR","submitted_at":"2007-06-19T04:38:54Z","title_canon_sha256":"a3615601d0c010afc9ea179c47bfd5bbf4e9755f10545d2c363458932ff81554"},"schema_version":"1.0","source":{"id":"0706.2713","kind":"arxiv","version":1}},"canonical_sha256":"2ef36a765e9890b2a4d1c3614adc71ece548d08d2a52378371508f1bee57aa7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ef36a765e9890b2a4d1c3614adc71ece548d08d2a52378371508f1bee57aa7b","first_computed_at":"2026-05-18T03:44:13.909261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:13.909261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jDc1ERjXCgW25cSoYx5jTCnaeArTNGR8UlsJsIBc4KNY5MVl68pJzmjqmlYuUtPv0c4BuKEDD/VHOgmfiUnWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:13.909758Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.2713","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e66d490a4bcc8dad8a5b4fd598e2c381b1467a1996eb84e9cf0446742e06915f","sha256:765a0eb12022a573e58fe8fe6e4a19e2bfd2156c8da73c547694fbc64e8b4cba"],"state_sha256":"50886ad5769f7b0bf7e91769954c08e909eb8983c960d1df8478d6686512b724"}