{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7A7PGUSPXJGCA3VOCNPVMDQ4GN","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":"19313cd3b481b0236037d6d929f1b163689494224dbf3623ccdf7adfdfa793fc","cross_cats_sorted":["math.GM","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-10-28T15:08:00Z","title_canon_sha256":"c378aba11a4442c7af5f5b447b4903b88754d43090f30c79ed60cbef4c37e80a"},"schema_version":"1.0","source":{"id":"1010.5987","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5987","created_at":"2026-05-18T04:20:24Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5987v2","created_at":"2026-05-18T04:20:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5987","created_at":"2026-05-18T04:20:24Z"},{"alias_kind":"pith_short_12","alias_value":"7A7PGUSPXJGC","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7A7PGUSPXJGCA3VO","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7A7PGUSP","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:919e703fd0696f9955d5ea2b2d655cdbab0abdc45f8090619e6b081177b2cc96","target":"graph","created_at":"2026-05-18T04:20:24Z","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 show that the Heisenberg type group $H_X=(\\Bbb{Z}_2 \\oplus V) \\leftthreetimes V^{\\ast}$, with the discrete Boolean group $V:=C(X,\\Z_2)$, canonically defined by any Stone space $X$, is always minimal. That is, $H_X$ does not admit any strictly coarser Hausdorff group topology. This leads us to the following result: for every (locally compact) non-archimedean $G$ there exists a (resp., locally compact) non-archimedean minimal group $M$ such that $G$ is a group retract of $M.$ For discrete groups $G$ the latter was proved by S. Dierolf and U. Schwanengel. We unify some old and new characteriza","authors_text":"Menachem Shlossberg, Michael Megrelishvili","cross_cats":["math.GM","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-10-28T15:08:00Z","title":"Notes on non-archimedean topological groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5987","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:dffe03064c3aae1cb4c0dd73c8bb0bc82c1e9b06bb8a03b05f50cc03b5be0d5d","target":"record","created_at":"2026-05-18T04:20:24Z","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":"19313cd3b481b0236037d6d929f1b163689494224dbf3623ccdf7adfdfa793fc","cross_cats_sorted":["math.GM","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2010-10-28T15:08:00Z","title_canon_sha256":"c378aba11a4442c7af5f5b447b4903b88754d43090f30c79ed60cbef4c37e80a"},"schema_version":"1.0","source":{"id":"1010.5987","kind":"arxiv","version":2}},"canonical_sha256":"f83ef3524fba4c206eae135f560e1c3353eaad69f9f2851765826008c6319d5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f83ef3524fba4c206eae135f560e1c3353eaad69f9f2851765826008c6319d5d","first_computed_at":"2026-05-18T04:20:24.881026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:24.881026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uAsAqEKVto7YItCIYVUSQM8Hi8uDKQ/b18Nb2mEcxPzS4Wxi9N7ff9dJSbQtjluNAhUZeEu/CKeH+gUwpt9tDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:24.881549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5987","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dffe03064c3aae1cb4c0dd73c8bb0bc82c1e9b06bb8a03b05f50cc03b5be0d5d","sha256:919e703fd0696f9955d5ea2b2d655cdbab0abdc45f8090619e6b081177b2cc96"],"state_sha256":"37da3183cc7d5f9838d1e66e6838e4eeaf54ecbaa0a8b4153c9f6db066ab5dc1"}