{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZDWZ2Q3GYANYVEMZWOZTU6F4VJ","short_pith_number":"pith:ZDWZ2Q3G","schema_version":"1.0","canonical_sha256":"c8ed9d4366c01b8a9199b3b33a78bcaa77cbd8b48e0a9ec257b0cf066d5bf16d","source":{"kind":"arxiv","id":"1608.00259","version":2},"attestation_state":"computed","paper":{"title":"Impartial achievement games for generating generalized dihedral groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Bret J. Benesh, Dana C. Ernst, Nandor Sieben","submitted_at":"2016-07-31T20:18:48Z","abstract_excerpt":"We study an impartial game introduced by Anderson and Harary. This game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nim-numbers of this game for generalized dihedral groups, which are of the form $\\operatorname{Dih}(A)= \\mathbb{Z}_2 \\ltimes A$ for a finite abelian group $A$."},"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":"1608.00259","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-31T20:18:48Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ffda3b5b43f0cf7f7273d5368c51bbd97818829caac95018c681c32d32bc179b","abstract_canon_sha256":"727be7823b529f4da403f5f38c345342224bb8203c51f1f01998059699df49f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:56.821475Z","signature_b64":"5PHn7uDa1DpBtPiwxoZaKvc3VK2CQVmDiA4BzebntROMCwOhP3o0CZUhsdlmslC8FLlr2TqkKDDO/aJ/YRmRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8ed9d4366c01b8a9199b3b33a78bcaa77cbd8b48e0a9ec257b0cf066d5bf16d","last_reissued_at":"2026-05-18T00:16:56.820755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:56.820755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Impartial achievement games for generating generalized dihedral groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Bret J. Benesh, Dana C. Ernst, Nandor Sieben","submitted_at":"2016-07-31T20:18:48Z","abstract_excerpt":"We study an impartial game introduced by Anderson and Harary. This game is played by two players who alternately choose previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins. We determine the nim-numbers of this game for generalized dihedral groups, which are of the form $\\operatorname{Dih}(A)= \\mathbb{Z}_2 \\ltimes A$ for a finite abelian group $A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00259","kind":"arxiv","version":2},"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":"1608.00259","created_at":"2026-05-18T00:16:56.820868+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.00259v2","created_at":"2026-05-18T00:16:56.820868+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00259","created_at":"2026-05-18T00:16:56.820868+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZDWZ2Q3GYANY","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZDWZ2Q3GYANYVEMZ","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZDWZ2Q3G","created_at":"2026-05-18T12:30:53.716459+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/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ","json":"https://pith.science/pith/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ.json","graph_json":"https://pith.science/api/pith-number/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ/graph.json","events_json":"https://pith.science/api/pith-number/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ/events.json","paper":"https://pith.science/paper/ZDWZ2Q3G"},"agent_actions":{"view_html":"https://pith.science/pith/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ","download_json":"https://pith.science/pith/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ.json","view_paper":"https://pith.science/paper/ZDWZ2Q3G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.00259&json=true","fetch_graph":"https://pith.science/api/pith-number/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ/action/storage_attestation","attest_author":"https://pith.science/pith/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ/action/author_attestation","sign_citation":"https://pith.science/pith/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ/action/citation_signature","submit_replication":"https://pith.science/pith/ZDWZ2Q3GYANYVEMZWOZTU6F4VJ/action/replication_record"}},"created_at":"2026-05-18T00:16:56.820868+00:00","updated_at":"2026-05-18T00:16:56.820868+00:00"}