{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TUQ3HG4CAPCKUW5MKF6YSRT23N","short_pith_number":"pith:TUQ3HG4C","schema_version":"1.0","canonical_sha256":"9d21b39b8203c4aa5bac517d89467adb729efa3ad3645dd35ab49b553173a85a","source":{"kind":"arxiv","id":"2602.14325","version":2},"attestation_state":"computed","paper":{"title":"Two Dimensional Subtraction -- Transfer Games","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alon Danai, Paul Ellis, Thotsaporn Aek Thanatipanonda","submitted_at":"2026-02-15T22:26:26Z","abstract_excerpt":"We generalize the results and conjectures of Tam\\'{a}s Lengyel, showing that the \\textsc{nim}-values of a large class of two-dimensional subtraction-transfer games are periodic. These are impartial, normal-play games with two piles of tokens, where players alternate either taking some tokens from a pile or transferring tokens from one pile to the other. In many cases, we calculate the exact period. We also develop several new notions of periodicitiy."},"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":"2602.14325","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-02-15T22:26:26Z","cross_cats_sorted":[],"title_canon_sha256":"4955abeef01203579d381964df8c84419723d3f024d1a77ba68964e1e1dcc3a0","abstract_canon_sha256":"0c88f7b1b889dc524d1bd137c1c1ca3014405840ba471c4aa70a0baa53b0e4e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:15.365917Z","signature_b64":"3qWqZ0M5RiMEnMzIP3mPHlH0lW9LG2PoPt7ARubrLor1mPJqFm24MoVatL8Ak3DB10UKHzMvuClWpsdtUY1aDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d21b39b8203c4aa5bac517d89467adb729efa3ad3645dd35ab49b553173a85a","last_reissued_at":"2026-05-25T02:01:15.365083Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:15.365083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two Dimensional Subtraction -- Transfer Games","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alon Danai, Paul Ellis, Thotsaporn Aek Thanatipanonda","submitted_at":"2026-02-15T22:26:26Z","abstract_excerpt":"We generalize the results and conjectures of Tam\\'{a}s Lengyel, showing that the \\textsc{nim}-values of a large class of two-dimensional subtraction-transfer games are periodic. These are impartial, normal-play games with two piles of tokens, where players alternate either taking some tokens from a pile or transferring tokens from one pile to the other. In many cases, we calculate the exact period. We also develop several new notions of periodicitiy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.14325","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.14325/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":"2602.14325","created_at":"2026-05-25T02:01:15.365187+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.14325v2","created_at":"2026-05-25T02:01:15.365187+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.14325","created_at":"2026-05-25T02:01:15.365187+00:00"},{"alias_kind":"pith_short_12","alias_value":"TUQ3HG4CAPCK","created_at":"2026-05-25T02:01:15.365187+00:00"},{"alias_kind":"pith_short_16","alias_value":"TUQ3HG4CAPCKUW5M","created_at":"2026-05-25T02:01:15.365187+00:00"},{"alias_kind":"pith_short_8","alias_value":"TUQ3HG4C","created_at":"2026-05-25T02:01:15.365187+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/TUQ3HG4CAPCKUW5MKF6YSRT23N","json":"https://pith.science/pith/TUQ3HG4CAPCKUW5MKF6YSRT23N.json","graph_json":"https://pith.science/api/pith-number/TUQ3HG4CAPCKUW5MKF6YSRT23N/graph.json","events_json":"https://pith.science/api/pith-number/TUQ3HG4CAPCKUW5MKF6YSRT23N/events.json","paper":"https://pith.science/paper/TUQ3HG4C"},"agent_actions":{"view_html":"https://pith.science/pith/TUQ3HG4CAPCKUW5MKF6YSRT23N","download_json":"https://pith.science/pith/TUQ3HG4CAPCKUW5MKF6YSRT23N.json","view_paper":"https://pith.science/paper/TUQ3HG4C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.14325&json=true","fetch_graph":"https://pith.science/api/pith-number/TUQ3HG4CAPCKUW5MKF6YSRT23N/graph.json","fetch_events":"https://pith.science/api/pith-number/TUQ3HG4CAPCKUW5MKF6YSRT23N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TUQ3HG4CAPCKUW5MKF6YSRT23N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TUQ3HG4CAPCKUW5MKF6YSRT23N/action/storage_attestation","attest_author":"https://pith.science/pith/TUQ3HG4CAPCKUW5MKF6YSRT23N/action/author_attestation","sign_citation":"https://pith.science/pith/TUQ3HG4CAPCKUW5MKF6YSRT23N/action/citation_signature","submit_replication":"https://pith.science/pith/TUQ3HG4CAPCKUW5MKF6YSRT23N/action/replication_record"}},"created_at":"2026-05-25T02:01:15.365187+00:00","updated_at":"2026-05-25T02:01:15.365187+00:00"}