{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WOPZQRYKLXNCK5YSITMWZUD6BW","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":"bdfe9efa280b23e82c4f24a2cf0c55108eafd97471587aa0e2880d12b3cbae33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-20T13:41:41Z","title_canon_sha256":"b35714bf627299ecbe4b3ba753a4ee0fac82dbfea453ee6de09d39071219cbb7"},"schema_version":"1.0","source":{"id":"1410.5271","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5271","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5271v2","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5271","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"WOPZQRYKLXNC","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WOPZQRYKLXNCK5YS","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WOPZQRYK","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:0e9e0b1c37748de72e49d73bf1f7d879e04d49067f4b1b774933014d7af31ffd","target":"graph","created_at":"2026-05-18T02:39:39Z","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":"A group $G$ is invariably generated by a subset $S$ of $G$ if $G= s^{g(s)} \\mid s\\in S$ for each choice of $g(s) \\in G$, $s \\in S$. Answering two questions posed by Kantor, Lubotzky and Shalev, we prove that the free prosoluble group of rank $d \\ge 2$ cannot be invariably generated by a finite set of elements, while the free solvable profinite group of rank $d$ and derived length $l$ is invariably generated by precisely $l(d-1)+1$ elements.","authors_text":"Andrea Lucchini, Eloisa Detomi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-20T13:41:41Z","title":"Invariable generation of prosoluble groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5271","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:c7f2737a4b5b2211be0b4b157ee645a7ac0ae01b32c905bd150c7534c9e06edc","target":"record","created_at":"2026-05-18T02:39:39Z","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":"bdfe9efa280b23e82c4f24a2cf0c55108eafd97471587aa0e2880d12b3cbae33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-10-20T13:41:41Z","title_canon_sha256":"b35714bf627299ecbe4b3ba753a4ee0fac82dbfea453ee6de09d39071219cbb7"},"schema_version":"1.0","source":{"id":"1410.5271","kind":"arxiv","version":2}},"canonical_sha256":"b39f98470a5dda25771244d96cd07e0da97ed99078caae5cc678abc82eb8e43c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b39f98470a5dda25771244d96cd07e0da97ed99078caae5cc678abc82eb8e43c","first_computed_at":"2026-05-18T02:39:39.856428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:39.856428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lbln3PtjldieOBZyd04mS+VtVHwQHoC5AboY0HE8NJBDa2L2uSuOykunfvdWRuhTOwtc9klC5kpBGkqwwUSNBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:39.857042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5271","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7f2737a4b5b2211be0b4b157ee645a7ac0ae01b32c905bd150c7534c9e06edc","sha256:0e9e0b1c37748de72e49d73bf1f7d879e04d49067f4b1b774933014d7af31ffd"],"state_sha256":"68b6859bae5ecd55d0b39cd3ff67d9bb891cbc76c6225ee31e1f67d8bedf17eb"}