{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:THFWSF56OALPMX73LYKYHRQZP5","short_pith_number":"pith:THFWSF56","canonical_record":{"source":{"id":"math/0401154","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2004-01-14T15:32:01Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"624e1d23dc3188911bb2059445c1d13a028173eb9ea9dfb8d407bb66b6c69f42","abstract_canon_sha256":"550c584fa2b4177bace7e9262be1298d310640195b6f957af5f2bc7f41fedc5a"},"schema_version":"1.0"},"canonical_sha256":"99cb6917be7016f65ffb5e1583c6197f4e459e26f9079d7f4e1c785f3c800740","source":{"kind":"arxiv","id":"math/0401154","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401154","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401154v4","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401154","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"THFWSF56OALP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"THFWSF56OALPMX73","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"THFWSF56","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:THFWSF56OALPMX73LYKYHRQZP5","target":"record","payload":{"canonical_record":{"source":{"id":"math/0401154","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2004-01-14T15:32:01Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"624e1d23dc3188911bb2059445c1d13a028173eb9ea9dfb8d407bb66b6c69f42","abstract_canon_sha256":"550c584fa2b4177bace7e9262be1298d310640195b6f957af5f2bc7f41fedc5a"},"schema_version":"1.0"},"canonical_sha256":"99cb6917be7016f65ffb5e1583c6197f4e459e26f9079d7f4e1c785f3c800740","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:44.946172Z","signature_b64":"QZJEMFQk6jbhZfUbZBQwMqIVvhGZmU+xx1k16pxX2kBgmQ8v5HgOZ0/00BgiAdUZMaLLeZ3/EnygVt/3/LIDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99cb6917be7016f65ffb5e1583c6197f4e459e26f9079d7f4e1c785f3c800740","last_reissued_at":"2026-05-18T04:42:44.945633Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:44.945633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0401154","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:42:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+S/NR3SxCvn+Rmb3xX7u/Cw6vPh0h7Gs6LMJqaTMHDIFesjlIkoE1sdebmbEpFStdkcHkI5QEjJbCkicIEuTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:35:52.866120Z"},"content_sha256":"623ddf9bcf45913ecdd357c4413dc44a81c49f318110cbe76723fe9f62caf2c8","schema_version":"1.0","event_id":"sha256:623ddf9bcf45913ecdd357c4413dc44a81c49f318110cbe76723fe9f62caf2c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:THFWSF56OALPMX73LYKYHRQZP5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random strategies with memory for the Robin Hood game","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Boaz Tsaban","submitted_at":"2004-01-14T15:32:01Z","abstract_excerpt":"The_Robin_Hood_ game is played as follows: On day i, the Sheriff puts s(i) bags of gold in the cave. On night i, Robin removes r(i) bags from the cave. The game is played for each natural nymber i. Robin wins if each bag which was put in the cave is eventually removed from it; otherwise the Sheriff wins.\n  Gasarch, Golub, and Srinivasan studied the Robin Hood game in the case of random strategies where Robin has no historical memory. We extend their main result to the case of bounded historical memory, and obtain a hierarchy of provably distinct games."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401154","kind":"arxiv","version":4},"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":"2026-05-18T04:42:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vdQgZd6w38hTKYfkKmxatmMC7fwsSkFb1KF1nBOW3aWYK2IDRmvWyZJYLEdUKJ1pxETdmsQQeuancP/HcYJ5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:35:52.866479Z"},"content_sha256":"948fffe4331d5cf373cff648a6230a8dd4e0d8ff5eb7fd1bd0ee396702025b95","schema_version":"1.0","event_id":"sha256:948fffe4331d5cf373cff648a6230a8dd4e0d8ff5eb7fd1bd0ee396702025b95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/THFWSF56OALPMX73LYKYHRQZP5/bundle.json","state_url":"https://pith.science/pith/THFWSF56OALPMX73LYKYHRQZP5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/THFWSF56OALPMX73LYKYHRQZP5/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":"2026-06-03T03:35:52Z","links":{"resolver":"https://pith.science/pith/THFWSF56OALPMX73LYKYHRQZP5","bundle":"https://pith.science/pith/THFWSF56OALPMX73LYKYHRQZP5/bundle.json","state":"https://pith.science/pith/THFWSF56OALPMX73LYKYHRQZP5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/THFWSF56OALPMX73LYKYHRQZP5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:THFWSF56OALPMX73LYKYHRQZP5","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":"550c584fa2b4177bace7e9262be1298d310640195b6f957af5f2bc7f41fedc5a","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.CO","submitted_at":"2004-01-14T15:32:01Z","title_canon_sha256":"624e1d23dc3188911bb2059445c1d13a028173eb9ea9dfb8d407bb66b6c69f42"},"schema_version":"1.0","source":{"id":"math/0401154","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401154","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401154v4","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401154","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"THFWSF56OALP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"THFWSF56OALPMX73","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"THFWSF56","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:948fffe4331d5cf373cff648a6230a8dd4e0d8ff5eb7fd1bd0ee396702025b95","target":"graph","created_at":"2026-05-18T04:42:44Z","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_Robin_Hood_ game is played as follows: On day i, the Sheriff puts s(i) bags of gold in the cave. On night i, Robin removes r(i) bags from the cave. The game is played for each natural nymber i. Robin wins if each bag which was put in the cave is eventually removed from it; otherwise the Sheriff wins.\n  Gasarch, Golub, and Srinivasan studied the Robin Hood game in the case of random strategies where Robin has no historical memory. We extend their main result to the case of bounded historical memory, and obtain a hierarchy of provably distinct games.","authors_text":"Boaz Tsaban","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2004-01-14T15:32:01Z","title":"Random strategies with memory for the Robin Hood game"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401154","kind":"arxiv","version":4},"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":"sha256:623ddf9bcf45913ecdd357c4413dc44a81c49f318110cbe76723fe9f62caf2c8","target":"record","created_at":"2026-05-18T04:42:44Z","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":"550c584fa2b4177bace7e9262be1298d310640195b6f957af5f2bc7f41fedc5a","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"math.CO","submitted_at":"2004-01-14T15:32:01Z","title_canon_sha256":"624e1d23dc3188911bb2059445c1d13a028173eb9ea9dfb8d407bb66b6c69f42"},"schema_version":"1.0","source":{"id":"math/0401154","kind":"arxiv","version":4}},"canonical_sha256":"99cb6917be7016f65ffb5e1583c6197f4e459e26f9079d7f4e1c785f3c800740","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99cb6917be7016f65ffb5e1583c6197f4e459e26f9079d7f4e1c785f3c800740","first_computed_at":"2026-05-18T04:42:44.945633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:44.945633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QZJEMFQk6jbhZfUbZBQwMqIVvhGZmU+xx1k16pxX2kBgmQ8v5HgOZ0/00BgiAdUZMaLLeZ3/EnygVt/3/LIDDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:44.946172Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0401154","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:623ddf9bcf45913ecdd357c4413dc44a81c49f318110cbe76723fe9f62caf2c8","sha256:948fffe4331d5cf373cff648a6230a8dd4e0d8ff5eb7fd1bd0ee396702025b95"],"state_sha256":"02efab11c8c7097012989c16ad78aaa33bfb715cca49f8ae6408b740c3562099"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+K/ntolARSyNgZkfHG3yYA5eXfm4PPK7xFXssFCFpI1MqagWYmUolvQHrPkuR9AKWt7KqZbJFQAAaXxbt2fUAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:35:52.868311Z","bundle_sha256":"f3203a3095890a4c067907eb3091b9b55c10cd84dc1627c0ffa8d29843114aa8"}}