{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:SUOVQZ6I6WSH5WXKOBRM7OSZFF","short_pith_number":"pith:SUOVQZ6I","schema_version":"1.0","canonical_sha256":"951d5867c8f5a47edaea7062cfba5929696fa3671acd9184c45e226f6fbd7d83","source":{"kind":"arxiv","id":"2503.16770","version":1},"attestation_state":"computed","paper":{"title":"An Improved Upper Bound on the Threshold Bias of the Oriented-cycle game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abdallah Saffidine, Anita Liebenau, Jeffrey Yang","submitted_at":"2025-03-21T00:59:26Z","abstract_excerpt":"We study the $b$-biased Oriented-cycle game where two players, OMaker and OBreaker, take turns directing the edges of $K_n$ (the complete graph on $n$ vertices). In each round, OMaker directs one previously undirected edge followed by OBreaker directing between one and $b$ previously undirected edges. The game ends once all edges have been directed, and OMaker wins if and only if the resulting tournament contains a directed cycle. Bollob\\'as and Szab\\'o asked the following question: what is the largest value of the bias $b$ for which OMaker has a winning strategy? Ben-Eliezer, Krivelevich and "},"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":"2503.16770","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-03-21T00:59:26Z","cross_cats_sorted":[],"title_canon_sha256":"94a57b168e22228d296c4d7ad496d4eefab72ef825fc2bc57e255d233913e15c","abstract_canon_sha256":"58ad161b29e8f11a4334c8e819d3c8171d8e7edc2ec950b33fe4db0807affae6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:36:49.582907Z","signature_b64":"mAVGgMYAnaVqikE8j2vIVcBNuQQPO1kd3cmZPxX3U+UebiNYlfUprthEZ2+SIlS6n2WAbAx7zIQiB7h+VWl5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"951d5867c8f5a47edaea7062cfba5929696fa3671acd9184c45e226f6fbd7d83","last_reissued_at":"2026-07-05T10:36:49.582506Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:36:49.582506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Improved Upper Bound on the Threshold Bias of the Oriented-cycle game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abdallah Saffidine, Anita Liebenau, Jeffrey Yang","submitted_at":"2025-03-21T00:59:26Z","abstract_excerpt":"We study the $b$-biased Oriented-cycle game where two players, OMaker and OBreaker, take turns directing the edges of $K_n$ (the complete graph on $n$ vertices). In each round, OMaker directs one previously undirected edge followed by OBreaker directing between one and $b$ previously undirected edges. The game ends once all edges have been directed, and OMaker wins if and only if the resulting tournament contains a directed cycle. Bollob\\'as and Szab\\'o asked the following question: what is the largest value of the bias $b$ for which OMaker has a winning strategy? Ben-Eliezer, Krivelevich and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16770","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.16770/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2503.16770","created_at":"2026-07-05T10:36:49.582563+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.16770v1","created_at":"2026-07-05T10:36:49.582563+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.16770","created_at":"2026-07-05T10:36:49.582563+00:00"},{"alias_kind":"pith_short_12","alias_value":"SUOVQZ6I6WSH","created_at":"2026-07-05T10:36:49.582563+00:00"},{"alias_kind":"pith_short_16","alias_value":"SUOVQZ6I6WSH5WXK","created_at":"2026-07-05T10:36:49.582563+00:00"},{"alias_kind":"pith_short_8","alias_value":"SUOVQZ6I","created_at":"2026-07-05T10:36:49.582563+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/SUOVQZ6I6WSH5WXKOBRM7OSZFF","json":"https://pith.science/pith/SUOVQZ6I6WSH5WXKOBRM7OSZFF.json","graph_json":"https://pith.science/api/pith-number/SUOVQZ6I6WSH5WXKOBRM7OSZFF/graph.json","events_json":"https://pith.science/api/pith-number/SUOVQZ6I6WSH5WXKOBRM7OSZFF/events.json","paper":"https://pith.science/paper/SUOVQZ6I"},"agent_actions":{"view_html":"https://pith.science/pith/SUOVQZ6I6WSH5WXKOBRM7OSZFF","download_json":"https://pith.science/pith/SUOVQZ6I6WSH5WXKOBRM7OSZFF.json","view_paper":"https://pith.science/paper/SUOVQZ6I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.16770&json=true","fetch_graph":"https://pith.science/api/pith-number/SUOVQZ6I6WSH5WXKOBRM7OSZFF/graph.json","fetch_events":"https://pith.science/api/pith-number/SUOVQZ6I6WSH5WXKOBRM7OSZFF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SUOVQZ6I6WSH5WXKOBRM7OSZFF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SUOVQZ6I6WSH5WXKOBRM7OSZFF/action/storage_attestation","attest_author":"https://pith.science/pith/SUOVQZ6I6WSH5WXKOBRM7OSZFF/action/author_attestation","sign_citation":"https://pith.science/pith/SUOVQZ6I6WSH5WXKOBRM7OSZFF/action/citation_signature","submit_replication":"https://pith.science/pith/SUOVQZ6I6WSH5WXKOBRM7OSZFF/action/replication_record"}},"created_at":"2026-07-05T10:36:49.582563+00:00","updated_at":"2026-07-05T10:36:49.582563+00:00"}