{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RABIWRCXPS536CBSSSQEDJ7NGX","short_pith_number":"pith:RABIWRCX","canonical_record":{"source":{"id":"1502.04068","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-02-13T17:50:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e013da38a38008d84bdac12bd83f85ee27e746614b149c757681f09c8bd85c8f","abstract_canon_sha256":"fd5846ba2ce80b869d1c4891ce991a1cffff1568ece6b2626328a39509c25b84"},"schema_version":"1.0"},"canonical_sha256":"88028b44577cbbbf083294a041a7ed35d232699b172060e61ffd10a5ec1be551","source":{"kind":"arxiv","id":"1502.04068","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04068","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04068v2","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04068","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"RABIWRCXPS53","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RABIWRCXPS536CBS","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RABIWRCX","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RABIWRCXPS536CBSSSQEDJ7NGX","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04068","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-02-13T17:50:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e013da38a38008d84bdac12bd83f85ee27e746614b149c757681f09c8bd85c8f","abstract_canon_sha256":"fd5846ba2ce80b869d1c4891ce991a1cffff1568ece6b2626328a39509c25b84"},"schema_version":"1.0"},"canonical_sha256":"88028b44577cbbbf083294a041a7ed35d232699b172060e61ffd10a5ec1be551","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:42.043442Z","signature_b64":"PfYoIOBWDtU18LuW12dElVNF+ruDJnsxR6sBWRff0iPE/sSvtFcUlUEwcKvuW9goGpK+QT/56RnagUcNtD9CBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88028b44577cbbbf083294a041a7ed35d232699b172060e61ffd10a5ec1be551","last_reissued_at":"2026-05-18T01:34:42.042458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:42.042458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04068","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T/fdE+GyCc935uWwrtL2DA9YRkU938gH6feDd+ZeawraaoMBFg2C0wVHkKuj6TDwj1FKPw6RUkmRkcxyKUMFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:03:27.839440Z"},"content_sha256":"d042648c6461279440d37494509eaeb928d647cc77b771458fc62a86b65bbac0","schema_version":"1.0","event_id":"sha256:d042648c6461279440d37494509eaeb928d647cc77b771458fc62a86b65bbac0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RABIWRCXPS536CBSSSQEDJ7NGX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Building Nim","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Eric Duch\\^ene, Matthieu Dufour, Silvia Heubach, Urban Larsson","submitted_at":"2015-02-13T17:50:35Z","abstract_excerpt":"The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new spin: building nim. With given finite numbers of tokens and stacks, this two-player game is played in two stages (thus belonging to the same family of games as e.g. nine-men's morris): first building, where players alternate to put one token on one of the, initially empty, stacks until all tokens have been used. Then, the players play nim. Of course, because "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04068","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hqPuNdObcj6+0kk/E6UnOrs9gCIa3wghJ3eXqiMu4hCCxan21VpSoitESuM0cnOdXwUG5IB9RKVHrQj/LZj7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:03:27.839789Z"},"content_sha256":"2d3ae2cfa6e96f0ce3211389c53ef7e2c8280d8b6bd3af2011d7f83f9fe69c4c","schema_version":"1.0","event_id":"sha256:2d3ae2cfa6e96f0ce3211389c53ef7e2c8280d8b6bd3af2011d7f83f9fe69c4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RABIWRCXPS536CBSSSQEDJ7NGX/bundle.json","state_url":"https://pith.science/pith/RABIWRCXPS536CBSSSQEDJ7NGX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RABIWRCXPS536CBSSSQEDJ7NGX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T05:03:27Z","links":{"resolver":"https://pith.science/pith/RABIWRCXPS536CBSSSQEDJ7NGX","bundle":"https://pith.science/pith/RABIWRCXPS536CBSSSQEDJ7NGX/bundle.json","state":"https://pith.science/pith/RABIWRCXPS536CBSSSQEDJ7NGX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RABIWRCXPS536CBSSSQEDJ7NGX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RABIWRCXPS536CBSSSQEDJ7NGX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fd5846ba2ce80b869d1c4891ce991a1cffff1568ece6b2626328a39509c25b84","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-02-13T17:50:35Z","title_canon_sha256":"e013da38a38008d84bdac12bd83f85ee27e746614b149c757681f09c8bd85c8f"},"schema_version":"1.0","source":{"id":"1502.04068","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04068","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04068v2","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04068","created_at":"2026-05-18T01:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"RABIWRCXPS53","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RABIWRCXPS536CBS","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RABIWRCX","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:2d3ae2cfa6e96f0ce3211389c53ef7e2c8280d8b6bd3af2011d7f83f9fe69c4c","target":"graph","created_at":"2026-05-18T01:34:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new spin: building nim. With given finite numbers of tokens and stacks, this two-player game is played in two stages (thus belonging to the same family of games as e.g. nine-men's morris): first building, where players alternate to put one token on one of the, initially empty, stacks until all tokens have been used. Then, the players play nim. Of course, because ","authors_text":"Eric Duch\\^ene, Matthieu Dufour, Silvia Heubach, Urban Larsson","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-02-13T17:50:35Z","title":"Building Nim"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04068","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d042648c6461279440d37494509eaeb928d647cc77b771458fc62a86b65bbac0","target":"record","created_at":"2026-05-18T01:34:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fd5846ba2ce80b869d1c4891ce991a1cffff1568ece6b2626328a39509c25b84","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-02-13T17:50:35Z","title_canon_sha256":"e013da38a38008d84bdac12bd83f85ee27e746614b149c757681f09c8bd85c8f"},"schema_version":"1.0","source":{"id":"1502.04068","kind":"arxiv","version":2}},"canonical_sha256":"88028b44577cbbbf083294a041a7ed35d232699b172060e61ffd10a5ec1be551","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88028b44577cbbbf083294a041a7ed35d232699b172060e61ffd10a5ec1be551","first_computed_at":"2026-05-18T01:34:42.042458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:42.042458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PfYoIOBWDtU18LuW12dElVNF+ruDJnsxR6sBWRff0iPE/sSvtFcUlUEwcKvuW9goGpK+QT/56RnagUcNtD9CBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:42.043442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04068","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d042648c6461279440d37494509eaeb928d647cc77b771458fc62a86b65bbac0","sha256:2d3ae2cfa6e96f0ce3211389c53ef7e2c8280d8b6bd3af2011d7f83f9fe69c4c"],"state_sha256":"47a68be4d7634af2537bbbe27369fb9ccf605ba934f74691e046e657c425be57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yf0dAdWFo/jVyHCNtuvKc9QNXy8ht/froqGgbmjIkwJdfMyYmqcvSGW5QHxaPyMp1ixyY35glk2WXfNPIeuRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:03:27.841777Z","bundle_sha256":"289d1c741ebbbe68305c4f3b27ac976cd349ecd6d53b55df29a5cfcb3fe30ba8"}}