{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6HPSGGE4GDFS5XVELC5KJBHTIA","short_pith_number":"pith:6HPSGGE4","schema_version":"1.0","canonical_sha256":"f1df23189c30cb2edea458baa484f340362cbec58fd8b4308668eee748a611fa","source":{"kind":"arxiv","id":"2607.06550","version":1},"attestation_state":"computed","paper":{"title":"Quantum combinatorial games","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Bram Westerbaan, Dieks Scholten, Simona Samardjiska","submitted_at":"2026-07-07T17:53:52Z","abstract_excerpt":"A combinatorial game is a deterministic game with no hidden information played between two opponents such as tic-tac-toe, checkers or chess. In this paper we extend combinatorial games to the quantum setting, by first revisiting and reformulating existing theory of classical combinatorial games. We investigate in which case a quantum opponent has an advantage over a classical one. Surprisingly, our instantiation of Zermelo's classical theorem in the quantum setting shows that the effects of quantum mechanics do not convey an advantage against a classical player that plays a perfect classical s"},"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":"2607.06550","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-07-07T17:53:52Z","cross_cats_sorted":[],"title_canon_sha256":"2da8725ff6332d494c6d809eff8d8d9d2d30359431fad0cc0a7c5cc38f0ce448","abstract_canon_sha256":"28b485d54e6127391ccadc0b4de31d118c6e0006857ffbccfb185e3023c1ac05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-08T01:19:29.653363Z","signature_b64":"Vw9pCnh1r5qGqPWIvTPvsWLvGjo/E0Jh4Ju79Lygwh8gukN9AfmovNfwa9nw2pUiDWds7NPnfsE7YLCV4gJQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1df23189c30cb2edea458baa484f340362cbec58fd8b4308668eee748a611fa","last_reissued_at":"2026-07-08T01:19:29.652935Z","signature_status":"signed_v1","first_computed_at":"2026-07-08T01:19:29.652935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum combinatorial games","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Bram Westerbaan, Dieks Scholten, Simona Samardjiska","submitted_at":"2026-07-07T17:53:52Z","abstract_excerpt":"A combinatorial game is a deterministic game with no hidden information played between two opponents such as tic-tac-toe, checkers or chess. In this paper we extend combinatorial games to the quantum setting, by first revisiting and reformulating existing theory of classical combinatorial games. We investigate in which case a quantum opponent has an advantage over a classical one. Surprisingly, our instantiation of Zermelo's classical theorem in the quantum setting shows that the effects of quantum mechanics do not convey an advantage against a classical player that plays a perfect classical s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06550","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/2607.06550/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":"2607.06550","created_at":"2026-07-08T01:19:29.652994+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.06550v1","created_at":"2026-07-08T01:19:29.652994+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06550","created_at":"2026-07-08T01:19:29.652994+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HPSGGE4GDFS","created_at":"2026-07-08T01:19:29.652994+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HPSGGE4GDFS5XVE","created_at":"2026-07-08T01:19:29.652994+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HPSGGE4","created_at":"2026-07-08T01:19:29.652994+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/6HPSGGE4GDFS5XVELC5KJBHTIA","json":"https://pith.science/pith/6HPSGGE4GDFS5XVELC5KJBHTIA.json","graph_json":"https://pith.science/api/pith-number/6HPSGGE4GDFS5XVELC5KJBHTIA/graph.json","events_json":"https://pith.science/api/pith-number/6HPSGGE4GDFS5XVELC5KJBHTIA/events.json","paper":"https://pith.science/paper/6HPSGGE4"},"agent_actions":{"view_html":"https://pith.science/pith/6HPSGGE4GDFS5XVELC5KJBHTIA","download_json":"https://pith.science/pith/6HPSGGE4GDFS5XVELC5KJBHTIA.json","view_paper":"https://pith.science/paper/6HPSGGE4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.06550&json=true","fetch_graph":"https://pith.science/api/pith-number/6HPSGGE4GDFS5XVELC5KJBHTIA/graph.json","fetch_events":"https://pith.science/api/pith-number/6HPSGGE4GDFS5XVELC5KJBHTIA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HPSGGE4GDFS5XVELC5KJBHTIA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HPSGGE4GDFS5XVELC5KJBHTIA/action/storage_attestation","attest_author":"https://pith.science/pith/6HPSGGE4GDFS5XVELC5KJBHTIA/action/author_attestation","sign_citation":"https://pith.science/pith/6HPSGGE4GDFS5XVELC5KJBHTIA/action/citation_signature","submit_replication":"https://pith.science/pith/6HPSGGE4GDFS5XVELC5KJBHTIA/action/replication_record"}},"created_at":"2026-07-08T01:19:29.652994+00:00","updated_at":"2026-07-08T01:19:29.652994+00:00"}