{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GYRRZOKLFXDQZNXCKQBHLJGANR","short_pith_number":"pith:GYRRZOKL","schema_version":"1.0","canonical_sha256":"36231cb94b2dc70cb6e2540275a4c06c70235f244d441fc4225b069518e5cfb7","source":{"kind":"arxiv","id":"1707.03066","version":1},"attestation_state":"computed","paper":{"title":"On expansions of non-abelian free groups by cosets of a finite index subgroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"Javier de la Nuez Gonz\\'alez","submitted_at":"2017-07-10T21:19:34Z","abstract_excerpt":"Let $F$ be a finitely generated non-abelian free group and $Q$ a finite quotient. Denote by $L_Q$ the language obtained by adding unary predicates $P_q$, $q\\in Q$ to the language of groups. Using a slight generalization of some of the techniques involved in Zlil Sela's solution to Tarski\\'s problem on the elementary theory of non-abelian free groups, we provide a few basic results on the validity of first order entences in the $L_Q$-expansion of $F$ in which every $P_q$ is interpreted as the preimage of $q$ in $F$. In particular we prove an analogous result to Sela's generalization of Merzlyak"},"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":"1707.03066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-07-10T21:19:34Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"0189ee25197dc977cb31ac603fbfd18d6381397d62292c762fc626908eef1747","abstract_canon_sha256":"f8ed9cdcb3bb171df14bab9785e9e38453a3ec41a5c1dc634180736c9b4d2fb8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:34.431358Z","signature_b64":"SJ2Xiectj8V9loajwe1bNpfZ4hhfcOgujDoiukGRF0XM/r8K9m/84XMH1Xp4K14dLa574p8WMcLJkk2HbWeAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36231cb94b2dc70cb6e2540275a4c06c70235f244d441fc4225b069518e5cfb7","last_reissued_at":"2026-05-18T00:40:34.430670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:34.430670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On expansions of non-abelian free groups by cosets of a finite index subgroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"Javier de la Nuez Gonz\\'alez","submitted_at":"2017-07-10T21:19:34Z","abstract_excerpt":"Let $F$ be a finitely generated non-abelian free group and $Q$ a finite quotient. Denote by $L_Q$ the language obtained by adding unary predicates $P_q$, $q\\in Q$ to the language of groups. Using a slight generalization of some of the techniques involved in Zlil Sela's solution to Tarski\\'s problem on the elementary theory of non-abelian free groups, we provide a few basic results on the validity of first order entences in the $L_Q$-expansion of $F$ in which every $P_q$ is interpreted as the preimage of $q$ in $F$. In particular we prove an analogous result to Sela's generalization of Merzlyak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03066","kind":"arxiv","version":1},"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":"1707.03066","created_at":"2026-05-18T00:40:34.430773+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.03066v1","created_at":"2026-05-18T00:40:34.430773+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03066","created_at":"2026-05-18T00:40:34.430773+00:00"},{"alias_kind":"pith_short_12","alias_value":"GYRRZOKLFXDQ","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GYRRZOKLFXDQZNXC","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GYRRZOKL","created_at":"2026-05-18T12:31:18.294218+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/GYRRZOKLFXDQZNXCKQBHLJGANR","json":"https://pith.science/pith/GYRRZOKLFXDQZNXCKQBHLJGANR.json","graph_json":"https://pith.science/api/pith-number/GYRRZOKLFXDQZNXCKQBHLJGANR/graph.json","events_json":"https://pith.science/api/pith-number/GYRRZOKLFXDQZNXCKQBHLJGANR/events.json","paper":"https://pith.science/paper/GYRRZOKL"},"agent_actions":{"view_html":"https://pith.science/pith/GYRRZOKLFXDQZNXCKQBHLJGANR","download_json":"https://pith.science/pith/GYRRZOKLFXDQZNXCKQBHLJGANR.json","view_paper":"https://pith.science/paper/GYRRZOKL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.03066&json=true","fetch_graph":"https://pith.science/api/pith-number/GYRRZOKLFXDQZNXCKQBHLJGANR/graph.json","fetch_events":"https://pith.science/api/pith-number/GYRRZOKLFXDQZNXCKQBHLJGANR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GYRRZOKLFXDQZNXCKQBHLJGANR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GYRRZOKLFXDQZNXCKQBHLJGANR/action/storage_attestation","attest_author":"https://pith.science/pith/GYRRZOKLFXDQZNXCKQBHLJGANR/action/author_attestation","sign_citation":"https://pith.science/pith/GYRRZOKLFXDQZNXCKQBHLJGANR/action/citation_signature","submit_replication":"https://pith.science/pith/GYRRZOKLFXDQZNXCKQBHLJGANR/action/replication_record"}},"created_at":"2026-05-18T00:40:34.430773+00:00","updated_at":"2026-05-18T00:40:34.430773+00:00"}