{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:Z4WPXQJ6NZTACBO2GCPAMGEBK2","short_pith_number":"pith:Z4WPXQJ6","schema_version":"1.0","canonical_sha256":"cf2cfbc13e6e660105da309e061881568e1891331d98dc4f7259bf9bc747c6bd","source":{"kind":"arxiv","id":"math/0411466","version":6},"attestation_state":"computed","paper":{"title":"Strongly bounded groups and infinite powers of finite groups","license":"","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"Yves de Cornulier","submitted_at":"2004-11-21T22:41:44Z","abstract_excerpt":"We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently introduced by G. Bergman.\n  Our main result is that G^I is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that omega_1-existentially closed groups are strongly bounded."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0411466","kind":"arxiv","version":6},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2004-11-21T22:41:44Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"0c5b0d9af567752ea9e6702cef8a817f5b4bc818b29d5c198819031c699e117a","abstract_canon_sha256":"8ef05d9083b6731756b7a79b58d8b3b74dca373426f0058bad5fa1296d4bf53c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:36.349453Z","signature_b64":"9qHxMg5MDUxMxRHp39W6C8rHaX0X+sW7XoWYSiAEx9q9P2QKFqoKT7LdgMDYQeyn6V67yUB1z56l2ZmiCKc1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf2cfbc13e6e660105da309e061881568e1891331d98dc4f7259bf9bc747c6bd","last_reissued_at":"2026-05-18T04:42:36.348911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:36.348911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strongly bounded groups and infinite powers of finite groups","license":"","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"Yves de Cornulier","submitted_at":"2004-11-21T22:41:44Z","abstract_excerpt":"We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently introduced by G. Bergman.\n  Our main result is that G^I is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that omega_1-existentially closed groups are strongly bounded."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411466","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0411466","created_at":"2026-05-18T04:42:36.348994+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0411466v6","created_at":"2026-05-18T04:42:36.348994+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411466","created_at":"2026-05-18T04:42:36.348994+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z4WPXQJ6NZTA","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z4WPXQJ6NZTACBO2","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z4WPXQJ6","created_at":"2026-05-18T12:25:52.687210+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z4WPXQJ6NZTACBO2GCPAMGEBK2","json":"https://pith.science/pith/Z4WPXQJ6NZTACBO2GCPAMGEBK2.json","graph_json":"https://pith.science/api/pith-number/Z4WPXQJ6NZTACBO2GCPAMGEBK2/graph.json","events_json":"https://pith.science/api/pith-number/Z4WPXQJ6NZTACBO2GCPAMGEBK2/events.json","paper":"https://pith.science/paper/Z4WPXQJ6"},"agent_actions":{"view_html":"https://pith.science/pith/Z4WPXQJ6NZTACBO2GCPAMGEBK2","download_json":"https://pith.science/pith/Z4WPXQJ6NZTACBO2GCPAMGEBK2.json","view_paper":"https://pith.science/paper/Z4WPXQJ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0411466&json=true","fetch_graph":"https://pith.science/api/pith-number/Z4WPXQJ6NZTACBO2GCPAMGEBK2/graph.json","fetch_events":"https://pith.science/api/pith-number/Z4WPXQJ6NZTACBO2GCPAMGEBK2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z4WPXQJ6NZTACBO2GCPAMGEBK2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z4WPXQJ6NZTACBO2GCPAMGEBK2/action/storage_attestation","attest_author":"https://pith.science/pith/Z4WPXQJ6NZTACBO2GCPAMGEBK2/action/author_attestation","sign_citation":"https://pith.science/pith/Z4WPXQJ6NZTACBO2GCPAMGEBK2/action/citation_signature","submit_replication":"https://pith.science/pith/Z4WPXQJ6NZTACBO2GCPAMGEBK2/action/replication_record"}},"created_at":"2026-05-18T04:42:36.348994+00:00","updated_at":"2026-05-18T04:42:36.348994+00:00"}