{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6CW7BWDSWZIZD45L4RMTHRQTT6","short_pith_number":"pith:6CW7BWDS","schema_version":"1.0","canonical_sha256":"f0adf0d872b65191f3abe45933c6139f90d0b4dbd449db3edca46898c3484200","source":{"kind":"arxiv","id":"1511.04035","version":1},"attestation_state":"computed","paper":{"title":"NIM with Cash","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Douglas Ulrich, John Purtilo, William Gasarch","submitted_at":"2015-11-12T19:58:48Z","abstract_excerpt":"Let A be a finite subset of $\\nat$. Then NIM(A;n) is the following 2-player game: initially there are $n$ stones on the board and the players alternate removing $a\\in A$ stones. The first player who cannot move loses. This game has been well studied.\n  We investigate an extension of the game where Player I starts out with d dollars, Player II starts out with e dollars, and when a player removes a\\in A he loses a dollars. The first player who cannot move loses; however, note this can happen for two different reasons: (1) the number of stones is less than min(A), (2) the player has less than $\\m"},"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":"1511.04035","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-12T19:58:48Z","cross_cats_sorted":[],"title_canon_sha256":"3e1ccc83fda022a1f57308a42ddbc3669cd22bf8355ed9a7bd933e6bf9058501","abstract_canon_sha256":"8938a3dedf1a4d01b88394b8718b43b9dba4674f44e1176c6f190513584c57fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:06.204427Z","signature_b64":"hcWfYPJvaG4V0vEaLto1GFohPDICBd73FI6swjkr7Uzn7+cDHfs+82R38IW17vxhoOKCsW+s6/LavJdcQT/xCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0adf0d872b65191f3abe45933c6139f90d0b4dbd449db3edca46898c3484200","last_reissued_at":"2026-05-18T01:27:06.203600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:06.203600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"NIM with Cash","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Douglas Ulrich, John Purtilo, William Gasarch","submitted_at":"2015-11-12T19:58:48Z","abstract_excerpt":"Let A be a finite subset of $\\nat$. Then NIM(A;n) is the following 2-player game: initially there are $n$ stones on the board and the players alternate removing $a\\in A$ stones. The first player who cannot move loses. This game has been well studied.\n  We investigate an extension of the game where Player I starts out with d dollars, Player II starts out with e dollars, and when a player removes a\\in A he loses a dollars. The first player who cannot move loses; however, note this can happen for two different reasons: (1) the number of stones is less than min(A), (2) the player has less than $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04035","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":"1511.04035","created_at":"2026-05-18T01:27:06.203750+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.04035v1","created_at":"2026-05-18T01:27:06.203750+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04035","created_at":"2026-05-18T01:27:06.203750+00:00"},{"alias_kind":"pith_short_12","alias_value":"6CW7BWDSWZIZ","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6CW7BWDSWZIZD45L","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6CW7BWDS","created_at":"2026-05-18T12:29:07.941421+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/6CW7BWDSWZIZD45L4RMTHRQTT6","json":"https://pith.science/pith/6CW7BWDSWZIZD45L4RMTHRQTT6.json","graph_json":"https://pith.science/api/pith-number/6CW7BWDSWZIZD45L4RMTHRQTT6/graph.json","events_json":"https://pith.science/api/pith-number/6CW7BWDSWZIZD45L4RMTHRQTT6/events.json","paper":"https://pith.science/paper/6CW7BWDS"},"agent_actions":{"view_html":"https://pith.science/pith/6CW7BWDSWZIZD45L4RMTHRQTT6","download_json":"https://pith.science/pith/6CW7BWDSWZIZD45L4RMTHRQTT6.json","view_paper":"https://pith.science/paper/6CW7BWDS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.04035&json=true","fetch_graph":"https://pith.science/api/pith-number/6CW7BWDSWZIZD45L4RMTHRQTT6/graph.json","fetch_events":"https://pith.science/api/pith-number/6CW7BWDSWZIZD45L4RMTHRQTT6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6CW7BWDSWZIZD45L4RMTHRQTT6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6CW7BWDSWZIZD45L4RMTHRQTT6/action/storage_attestation","attest_author":"https://pith.science/pith/6CW7BWDSWZIZD45L4RMTHRQTT6/action/author_attestation","sign_citation":"https://pith.science/pith/6CW7BWDSWZIZD45L4RMTHRQTT6/action/citation_signature","submit_replication":"https://pith.science/pith/6CW7BWDSWZIZD45L4RMTHRQTT6/action/replication_record"}},"created_at":"2026-05-18T01:27:06.203750+00:00","updated_at":"2026-05-18T01:27:06.203750+00:00"}