{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BPISTSYZ3RKJKHHM3CYEIJYZTP","short_pith_number":"pith:BPISTSYZ","schema_version":"1.0","canonical_sha256":"0bd129cb19dc54951cecd8b04427199bf7e9d2cb81807f397f4ea036cc7e6414","source":{"kind":"arxiv","id":"1907.09219","version":1},"attestation_state":"computed","paper":{"title":"Totalitarian random Tug-of-War games in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fernando Charro, Marcos Ant\\'on, Peiyong Wang","submitted_at":"2019-07-22T10:19:49Z","abstract_excerpt":"In this work we discuss a random Tug-of-War game in graphs where one of the players has the power to decide at each turn whether to play a round of classical random Tug-of-War, or let the other player choose the new game position in exchange of a fixed payoff. We prove that this game has a value using a discrete comparison principle and viscosity tools, as well as probabilistic arguments. This game is related to Jensen's extremal equations, which have a key role in Jensen's celebrated proof of uniqueness of infinity harmonic functions."},"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":"1907.09219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-22T10:19:49Z","cross_cats_sorted":[],"title_canon_sha256":"e6f405706059ee18e3ca8f599c037ec04e0471589697511cefa9eddc328c14ad","abstract_canon_sha256":"e3b075b8977790e12ed939433fb7614531459449d4699e131beb9dcbc3675d2a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:59.805630Z","signature_b64":"RNkuwS31N6nPT0bvzz5QgUyQFF2rp0pkN20J0nZhFR4yp2MhmHwFTYh9R8h6guleIzgcteLXAvOTej0nULjxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bd129cb19dc54951cecd8b04427199bf7e9d2cb81807f397f4ea036cc7e6414","last_reissued_at":"2026-05-17T23:39:59.805065Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:59.805065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Totalitarian random Tug-of-War games in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fernando Charro, Marcos Ant\\'on, Peiyong Wang","submitted_at":"2019-07-22T10:19:49Z","abstract_excerpt":"In this work we discuss a random Tug-of-War game in graphs where one of the players has the power to decide at each turn whether to play a round of classical random Tug-of-War, or let the other player choose the new game position in exchange of a fixed payoff. We prove that this game has a value using a discrete comparison principle and viscosity tools, as well as probabilistic arguments. This game is related to Jensen's extremal equations, which have a key role in Jensen's celebrated proof of uniqueness of infinity harmonic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09219","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":"1907.09219","created_at":"2026-05-17T23:39:59.805166+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.09219v1","created_at":"2026-05-17T23:39:59.805166+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.09219","created_at":"2026-05-17T23:39:59.805166+00:00"},{"alias_kind":"pith_short_12","alias_value":"BPISTSYZ3RKJ","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"BPISTSYZ3RKJKHHM","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"BPISTSYZ","created_at":"2026-05-18T12:33:12.712433+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/BPISTSYZ3RKJKHHM3CYEIJYZTP","json":"https://pith.science/pith/BPISTSYZ3RKJKHHM3CYEIJYZTP.json","graph_json":"https://pith.science/api/pith-number/BPISTSYZ3RKJKHHM3CYEIJYZTP/graph.json","events_json":"https://pith.science/api/pith-number/BPISTSYZ3RKJKHHM3CYEIJYZTP/events.json","paper":"https://pith.science/paper/BPISTSYZ"},"agent_actions":{"view_html":"https://pith.science/pith/BPISTSYZ3RKJKHHM3CYEIJYZTP","download_json":"https://pith.science/pith/BPISTSYZ3RKJKHHM3CYEIJYZTP.json","view_paper":"https://pith.science/paper/BPISTSYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.09219&json=true","fetch_graph":"https://pith.science/api/pith-number/BPISTSYZ3RKJKHHM3CYEIJYZTP/graph.json","fetch_events":"https://pith.science/api/pith-number/BPISTSYZ3RKJKHHM3CYEIJYZTP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BPISTSYZ3RKJKHHM3CYEIJYZTP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BPISTSYZ3RKJKHHM3CYEIJYZTP/action/storage_attestation","attest_author":"https://pith.science/pith/BPISTSYZ3RKJKHHM3CYEIJYZTP/action/author_attestation","sign_citation":"https://pith.science/pith/BPISTSYZ3RKJKHHM3CYEIJYZTP/action/citation_signature","submit_replication":"https://pith.science/pith/BPISTSYZ3RKJKHHM3CYEIJYZTP/action/replication_record"}},"created_at":"2026-05-17T23:39:59.805166+00:00","updated_at":"2026-05-17T23:39:59.805166+00:00"}