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We show that the triples $u_k = (G_k,H_k,T_k)$ are mixed Beauville structures if $k$ is not a power of 2. This is the first known infinite family of 2-groups admitting mixed Beauville structures. Moreover, the associated Beauville surface $S(u_3)$ is real and, for $k > 3$ not a power of 2, the Beauville surface $S(u_k)$ is not biholomorphic to $\\bar{S(u_k)}$."},"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":"1304.4480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-16T14:57:57Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"797aeddbc87846c4f183c27759c250b4db8969f03daf1daaffcc1ab6c25133b1","abstract_canon_sha256":"2797bbe0347d5170404bcaf219b8f8945c1f8e2dd07d0d528daa92d345ceedd6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:52.890494Z","signature_b64":"GhjPmT3XP7mfPaS+jh6n4nCxqivChgJRJduP4V2xUYqR7cLT7agIi3FkeJepWEHFhTwk3/ebEaaRpfI+5K4ABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35e3bcc579f98cc925617f7626691f4875e9a8dc19e72d6f5aca6603f7b5056b","last_reissued_at":"2026-05-18T03:27:52.889999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:52.889999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An infinite family of 2-groups with mixed Beauville structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Alina Vdovina, Nathan Barker, Nigel Boston, Norbert Peyerimhoff","submitted_at":"2013-04-16T14:57:57Z","abstract_excerpt":"We construct an infinite family of triples $(G_k,H_k,T_k)$, where $G_k$ are 2-groups of increasing order, $H_k$ are index-2 subgroups of $G_k$, and $T_k$ are pairs of generators of $H_k$. We show that the triples $u_k = (G_k,H_k,T_k)$ are mixed Beauville structures if $k$ is not a power of 2. This is the first known infinite family of 2-groups admitting mixed Beauville structures. Moreover, the associated Beauville surface $S(u_3)$ is real and, for $k > 3$ not a power of 2, the Beauville surface $S(u_k)$ is not biholomorphic to $\\bar{S(u_k)}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4480","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":"1304.4480","created_at":"2026-05-18T03:27:52.890080+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.4480v1","created_at":"2026-05-18T03:27:52.890080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4480","created_at":"2026-05-18T03:27:52.890080+00:00"},{"alias_kind":"pith_short_12","alias_value":"GXR3ZRLZ7GGM","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"GXR3ZRLZ7GGMSJLB","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"GXR3ZRLZ","created_at":"2026-05-18T12:27:46.883200+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/GXR3ZRLZ7GGMSJLBP53CM2I7JB","json":"https://pith.science/pith/GXR3ZRLZ7GGMSJLBP53CM2I7JB.json","graph_json":"https://pith.science/api/pith-number/GXR3ZRLZ7GGMSJLBP53CM2I7JB/graph.json","events_json":"https://pith.science/api/pith-number/GXR3ZRLZ7GGMSJLBP53CM2I7JB/events.json","paper":"https://pith.science/paper/GXR3ZRLZ"},"agent_actions":{"view_html":"https://pith.science/pith/GXR3ZRLZ7GGMSJLBP53CM2I7JB","download_json":"https://pith.science/pith/GXR3ZRLZ7GGMSJLBP53CM2I7JB.json","view_paper":"https://pith.science/paper/GXR3ZRLZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.4480&json=true","fetch_graph":"https://pith.science/api/pith-number/GXR3ZRLZ7GGMSJLBP53CM2I7JB/graph.json","fetch_events":"https://pith.science/api/pith-number/GXR3ZRLZ7GGMSJLBP53CM2I7JB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GXR3ZRLZ7GGMSJLBP53CM2I7JB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GXR3ZRLZ7GGMSJLBP53CM2I7JB/action/storage_attestation","attest_author":"https://pith.science/pith/GXR3ZRLZ7GGMSJLBP53CM2I7JB/action/author_attestation","sign_citation":"https://pith.science/pith/GXR3ZRLZ7GGMSJLBP53CM2I7JB/action/citation_signature","submit_replication":"https://pith.science/pith/GXR3ZRLZ7GGMSJLBP53CM2I7JB/action/replication_record"}},"created_at":"2026-05-18T03:27:52.890080+00:00","updated_at":"2026-05-18T03:27:52.890080+00:00"}