{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZM2WAYVDMDXCRSVQ3CLSRI7KPB","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":"b9732062365a7754c15fa57c104fce22d5bcddf4f97f6d0b3aeb3ae4091ca0bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-03-02T22:59:50Z","title_canon_sha256":"5cc998e4439e0aea4d06e009bbaab903b578966820752dbf2db65285a391c025"},"schema_version":"1.0","source":{"id":"1703.00979","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00979","created_at":"2026-05-18T00:49:37Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00979v1","created_at":"2026-05-18T00:49:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00979","created_at":"2026-05-18T00:49:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZM2WAYVDMDXC","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZM2WAYVDMDXCRSVQ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZM2WAYVD","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:d811aff5873d153ef64582599f0f0624021cc2d7a23c0b6f5c20059a794c4feb","target":"graph","created_at":"2026-05-18T00:49:37Z","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 $w$ be a multilinear commutator word. In the present paper we describe recent results that show that if $G$ is a profinite group in which all $w$-values are contained in a union of finitely (or in some cases countably) many subgroups with a prescribed property, then the verbal subgroup $w(G)$ has the same property as well. In particular, we show this in the case where the subgroups are periodic or of finite rank.","authors_text":"Cristina Acciarri, Pavel Shumyatsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-03-02T22:59:50Z","title":"On verbal subgroups in finite and profinite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00979","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":"sha256:33162a968733d95acedab2fe85605f738437794ec8237c07a6d63a9c30115b4d","target":"record","created_at":"2026-05-18T00:49:37Z","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":"b9732062365a7754c15fa57c104fce22d5bcddf4f97f6d0b3aeb3ae4091ca0bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-03-02T22:59:50Z","title_canon_sha256":"5cc998e4439e0aea4d06e009bbaab903b578966820752dbf2db65285a391c025"},"schema_version":"1.0","source":{"id":"1703.00979","kind":"arxiv","version":1}},"canonical_sha256":"cb356062a360ee28cab0d89728a3ea784bac9efa43830ed999d09146ee133ea1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb356062a360ee28cab0d89728a3ea784bac9efa43830ed999d09146ee133ea1","first_computed_at":"2026-05-18T00:49:37.377102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:37.377102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rayVab24sP8wp1+K5BNGDf3v5FNrJjuin3E/smnG4PiVJRBqxxVvmsNlElRSpPVoJXlw+goKqV6VMM+kJF1mDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:37.377760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00979","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33162a968733d95acedab2fe85605f738437794ec8237c07a6d63a9c30115b4d","sha256:d811aff5873d153ef64582599f0f0624021cc2d7a23c0b6f5c20059a794c4feb"],"state_sha256":"aede44774a29561949245337e6cd5d6ac006dd68e5e92d7a819918c823b64ebb"}