{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TW27S3UEAGSV7R4KOHRVTLCKTQ","short_pith_number":"pith:TW27S3UE","canonical_record":{"source":{"id":"1805.07019","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2018-05-18T01:52:42Z","cross_cats_sorted":[],"title_canon_sha256":"4ddfde6567b202ad376beb47a6af1981b47b23dceb2dfca4818648616bd1cfce","abstract_canon_sha256":"cd6dc5ac53032c3b5d2a768a2c36eb546ef4c8c57ee8b81f888ff15bc05b55a3"},"schema_version":"1.0"},"canonical_sha256":"9db5f96e8401a55fc78a71e359ac4a9c227da349268beff0ae8d7a4ca629959f","source":{"kind":"arxiv","id":"1805.07019","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07019","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07019v1","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07019","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"pith_short_12","alias_value":"TW27S3UEAGSV","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TW27S3UEAGSV7R4K","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TW27S3UE","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TW27S3UEAGSV7R4KOHRVTLCKTQ","target":"record","payload":{"canonical_record":{"source":{"id":"1805.07019","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2018-05-18T01:52:42Z","cross_cats_sorted":[],"title_canon_sha256":"4ddfde6567b202ad376beb47a6af1981b47b23dceb2dfca4818648616bd1cfce","abstract_canon_sha256":"cd6dc5ac53032c3b5d2a768a2c36eb546ef4c8c57ee8b81f888ff15bc05b55a3"},"schema_version":"1.0"},"canonical_sha256":"9db5f96e8401a55fc78a71e359ac4a9c227da349268beff0ae8d7a4ca629959f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:41.336948Z","signature_b64":"a1HfLXGkSL5hTMh0tbpDWcbpzAv/++udVqZDsjNV78ZImlZFY8cpvwzbe4M15dfQd/pLl4SBqZ7pFdqrbsNBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9db5f96e8401a55fc78a71e359ac4a9c227da349268beff0ae8d7a4ca629959f","last_reissued_at":"2026-05-18T00:15:41.336368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:41.336368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.07019","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGGK38vUyBcTOwVCS942+VrDUYn0a/Qe49FGV4YlzqHXl9gv/Ker0cxZKWhmFJHAEm8PznVqRjgzQJd671LUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:30:58.596102Z"},"content_sha256":"9fd5fe6ba179cd34bcfabf8d745c03894138855045ce5dd2fa0543f936b9ad6a","schema_version":"1.0","event_id":"sha256:9fd5fe6ba179cd34bcfabf8d745c03894138855045ce5dd2fa0543f936b9ad6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TW27S3UEAGSV7R4KOHRVTLCKTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\mathcal{P}$ Play in Candy Nim","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Tholen, Nitya Mani, Rajiv Nelakanti, Simon Rubinstein-Salzedo","submitted_at":"2018-05-18T01:52:42Z","abstract_excerpt":"Candy Nim is a variant of Nim in which both players aim to take the last candy in a game of Nim, with the added simultaneous secondary goal of taking as many candies as possible. We give bounds on the number of candies the first and second players obtain in 3-pile $\\mathcal{P}$ positions as well as strategies that are provably optimal for some families of such games. We also show how to construct a game with $N$ candies such that the loser takes the largest possible number of candies and bound the number of candies the winner can take in an arbitrary $\\mathcal{P}$ position with $N$ total candi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07019","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pOsX7C1D5I3VIfRYeI/Y345M6BqVeaEykUj3ll73RuTq9AtXIRSbfubDHhDFlKwhKebGSi52cDU9b8uULvj2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:30:58.596468Z"},"content_sha256":"79b96bb7dbb88a1536609764718a567c73e010a008c035da8d0e6f1681f2448c","schema_version":"1.0","event_id":"sha256:79b96bb7dbb88a1536609764718a567c73e010a008c035da8d0e6f1681f2448c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TW27S3UEAGSV7R4KOHRVTLCKTQ/bundle.json","state_url":"https://pith.science/pith/TW27S3UEAGSV7R4KOHRVTLCKTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TW27S3UEAGSV7R4KOHRVTLCKTQ/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":"2026-06-05T08:30:58Z","links":{"resolver":"https://pith.science/pith/TW27S3UEAGSV7R4KOHRVTLCKTQ","bundle":"https://pith.science/pith/TW27S3UEAGSV7R4KOHRVTLCKTQ/bundle.json","state":"https://pith.science/pith/TW27S3UEAGSV7R4KOHRVTLCKTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TW27S3UEAGSV7R4KOHRVTLCKTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TW27S3UEAGSV7R4KOHRVTLCKTQ","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":"cd6dc5ac53032c3b5d2a768a2c36eb546ef4c8c57ee8b81f888ff15bc05b55a3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2018-05-18T01:52:42Z","title_canon_sha256":"4ddfde6567b202ad376beb47a6af1981b47b23dceb2dfca4818648616bd1cfce"},"schema_version":"1.0","source":{"id":"1805.07019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07019","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07019v1","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07019","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"pith_short_12","alias_value":"TW27S3UEAGSV","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TW27S3UEAGSV7R4K","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TW27S3UE","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:79b96bb7dbb88a1536609764718a567c73e010a008c035da8d0e6f1681f2448c","target":"graph","created_at":"2026-05-18T00:15:41Z","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":"Candy Nim is a variant of Nim in which both players aim to take the last candy in a game of Nim, with the added simultaneous secondary goal of taking as many candies as possible. We give bounds on the number of candies the first and second players obtain in 3-pile $\\mathcal{P}$ positions as well as strategies that are provably optimal for some families of such games. We also show how to construct a game with $N$ candies such that the loser takes the largest possible number of candies and bound the number of candies the winner can take in an arbitrary $\\mathcal{P}$ position with $N$ total candi","authors_text":"Alex Tholen, Nitya Mani, Rajiv Nelakanti, Simon Rubinstein-Salzedo","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2018-05-18T01:52:42Z","title":"$\\mathcal{P}$ Play in Candy Nim"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07019","kind":"arxiv","version":1},"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":"sha256:9fd5fe6ba179cd34bcfabf8d745c03894138855045ce5dd2fa0543f936b9ad6a","target":"record","created_at":"2026-05-18T00:15:41Z","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":"cd6dc5ac53032c3b5d2a768a2c36eb546ef4c8c57ee8b81f888ff15bc05b55a3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2018-05-18T01:52:42Z","title_canon_sha256":"4ddfde6567b202ad376beb47a6af1981b47b23dceb2dfca4818648616bd1cfce"},"schema_version":"1.0","source":{"id":"1805.07019","kind":"arxiv","version":1}},"canonical_sha256":"9db5f96e8401a55fc78a71e359ac4a9c227da349268beff0ae8d7a4ca629959f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9db5f96e8401a55fc78a71e359ac4a9c227da349268beff0ae8d7a4ca629959f","first_computed_at":"2026-05-18T00:15:41.336368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:41.336368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a1HfLXGkSL5hTMh0tbpDWcbpzAv/++udVqZDsjNV78ZImlZFY8cpvwzbe4M15dfQd/pLl4SBqZ7pFdqrbsNBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:41.336948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fd5fe6ba179cd34bcfabf8d745c03894138855045ce5dd2fa0543f936b9ad6a","sha256:79b96bb7dbb88a1536609764718a567c73e010a008c035da8d0e6f1681f2448c"],"state_sha256":"6c8c8a2d43e1d8d526ef2aefea82cb440e9a35df48b91935f22095bd651304e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b6RN9BywJDpZstROwBQHNw8BBoUsLawC+rb2hwqwi2MFlpP2ghF4+itMPA6gqsu5MPWirp0VQaGcgku9kgQCCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:30:58.598415Z","bundle_sha256":"9ad7ca53acb3d44f8163167c6946cd48b2c78affba2321786eba8f17bd83a86f"}}