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We prove that if $G$ is periodic then the quotients $G/\\st_G(n)$ are Beauville groups for every $n\\geq 2$ if $p\\geq 5$ and $n\\geq 3$ if $p=3$. On the other hand, if $G$ is non-periodic, then none of the quotients $G/\\st_G(n)$ are Beauville groups."},"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":"1803.04879","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-03-13T15:27:08Z","cross_cats_sorted":[],"title_canon_sha256":"55d6cae9e175c43068e415032341fb2563dbac21b7e86d21b9555fa6b646b6e4","abstract_canon_sha256":"81c95f48ea1f29520986da939a3fbc97a397988cd75c488d2eaf6587faa58ea5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:15.556283Z","signature_b64":"FEreLK89W0rmVpG2xDxAkzpPGM8pOAytieuQI4rD0dG74PmviNcw7rpWjGsDIXThJ/9rTiQ5X7KofSrqXoZKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f082180476a89d8b4149b7cbe6226e90f54ac5560e86e94b6a572858cbacb04b","last_reissued_at":"2026-05-18T00:21:15.555854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:15.555854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Grigorchuk-Gupta-Sidki groups as a source for Beauville surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"\\c{S}\\\"ukran G\\\"ul, Jone Uria-Albizuri","submitted_at":"2018-03-13T15:27:08Z","abstract_excerpt":"If $G$ is a Grigorchuk-Gupta-Sidki group defined over a $p$-adic tree, where $p$ is an odd prime, we study the existence of Beauville surfaces associated to the quotients of $G$ by its level stabilizers $\\st_G(n)$. We prove that if $G$ is periodic then the quotients $G/\\st_G(n)$ are Beauville groups for every $n\\geq 2$ if $p\\geq 5$ and $n\\geq 3$ if $p=3$. On the other hand, if $G$ is non-periodic, then none of the quotients $G/\\st_G(n)$ are Beauville groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04879","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":"1803.04879","created_at":"2026-05-18T00:21:15.555932+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.04879v1","created_at":"2026-05-18T00:21:15.555932+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04879","created_at":"2026-05-18T00:21:15.555932+00:00"},{"alias_kind":"pith_short_12","alias_value":"6CBBQBDWVCOY","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"6CBBQBDWVCOYWQKJ","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"6CBBQBDW","created_at":"2026-05-18T12:32:08.215937+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/6CBBQBDWVCOYWQKJW7F6MITOSD","json":"https://pith.science/pith/6CBBQBDWVCOYWQKJW7F6MITOSD.json","graph_json":"https://pith.science/api/pith-number/6CBBQBDWVCOYWQKJW7F6MITOSD/graph.json","events_json":"https://pith.science/api/pith-number/6CBBQBDWVCOYWQKJW7F6MITOSD/events.json","paper":"https://pith.science/paper/6CBBQBDW"},"agent_actions":{"view_html":"https://pith.science/pith/6CBBQBDWVCOYWQKJW7F6MITOSD","download_json":"https://pith.science/pith/6CBBQBDWVCOYWQKJW7F6MITOSD.json","view_paper":"https://pith.science/paper/6CBBQBDW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.04879&json=true","fetch_graph":"https://pith.science/api/pith-number/6CBBQBDWVCOYWQKJW7F6MITOSD/graph.json","fetch_events":"https://pith.science/api/pith-number/6CBBQBDWVCOYWQKJW7F6MITOSD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6CBBQBDWVCOYWQKJW7F6MITOSD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6CBBQBDWVCOYWQKJW7F6MITOSD/action/storage_attestation","attest_author":"https://pith.science/pith/6CBBQBDWVCOYWQKJW7F6MITOSD/action/author_attestation","sign_citation":"https://pith.science/pith/6CBBQBDWVCOYWQKJW7F6MITOSD/action/citation_signature","submit_replication":"https://pith.science/pith/6CBBQBDWVCOYWQKJW7F6MITOSD/action/replication_record"}},"created_at":"2026-05-18T00:21:15.555932+00:00","updated_at":"2026-05-18T00:21:15.555932+00:00"}