{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UXOGRQ4AZ6VNQIKLFIVGI6UPSH","short_pith_number":"pith:UXOGRQ4A","canonical_record":{"source":{"id":"1102.1096","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-02-05T19:46:56Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"197c998b409934ad746d7ece7a877a20bead8afd063c00a2cf8563c740bdb300","abstract_canon_sha256":"71fabb8bdb29e382006d81d0f9dcda96b5e8b81776b9109b305932d40ad9c98d"},"schema_version":"1.0"},"canonical_sha256":"a5dc68c380cfaad8214b2a2a647a8f91f802799601d8dc644291951607874e5d","source":{"kind":"arxiv","id":"1102.1096","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1096","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1096v2","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1096","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"pith_short_12","alias_value":"UXOGRQ4AZ6VN","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UXOGRQ4AZ6VNQIKL","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UXOGRQ4A","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UXOGRQ4AZ6VNQIKLFIVGI6UPSH","target":"record","payload":{"canonical_record":{"source":{"id":"1102.1096","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-02-05T19:46:56Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"197c998b409934ad746d7ece7a877a20bead8afd063c00a2cf8563c740bdb300","abstract_canon_sha256":"71fabb8bdb29e382006d81d0f9dcda96b5e8b81776b9109b305932d40ad9c98d"},"schema_version":"1.0"},"canonical_sha256":"a5dc68c380cfaad8214b2a2a647a8f91f802799601d8dc644291951607874e5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:25:37.615996Z","signature_b64":"O0aacvhdSv47KMIZKxFUaotOy3bi0+QRGCqaN71jsDWiFX+s/2yNYHnIs8JeMGDbJE6AX2pfDiaTm2hWsmPPDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5dc68c380cfaad8214b2a2a647a8f91f802799601d8dc644291951607874e5d","last_reissued_at":"2026-05-18T04:25:37.615439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:25:37.615439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.1096","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":"2026-05-18T04:25:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ksAl1Lwtcv5hVOudy6pwuzQIIJ2+sW1W6d2BGxgqdN7w6s1vlgKQHFvwz3nHBCKafvtfvXfW2E4Egzw+I7CsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:05:03.316498Z"},"content_sha256":"5d8a166e4eca60b85cd9fc26bd29607409c238ac6e03c9fd6591994df79a85c3","schema_version":"1.0","event_id":"sha256:5d8a166e4eca60b85cd9fc26bd29607409c238ac6e03c9fd6591994df79a85c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UXOGRQ4AZ6VNQIKLFIVGI6UPSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Repeated Matching Pennies with Limited Randomness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.GT","authors_text":"Lance Fortnow, Michele Budinich","submitted_at":"2011-02-05T19:46:56Z","abstract_excerpt":"We consider a repeated Matching Pennies game in which players have limited access to randomness. Playing the (unique) Nash equilibrium in this n-stage game requires n random bits. Can there be Nash equilibria that use less than n random coins?\n  Our main results are as follows: We give a full characterization of approximate equilibria, showing that, for any e in [0, 1], the game has a e-Nash equilibrium if and only if both players have (1 - e)n random coins. When players are bound to run in polynomial time, Nash equilibria can exist if and only if one-way functions exist. It is possible to tra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1096","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":"2026-05-18T04:25:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UuCouGrAZWPJUvxhtdjOsrT6vrWlZDYuASC2Aq0iNLZkRmG7LIbtu5eOeWmSoE3WZbEE2NZ+WsnYaLn4Of3tBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:05:03.317150Z"},"content_sha256":"d043112ddccf808354dad8e52fd63b6e97077940c82cf74d57502bc8ec8a899b","schema_version":"1.0","event_id":"sha256:d043112ddccf808354dad8e52fd63b6e97077940c82cf74d57502bc8ec8a899b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UXOGRQ4AZ6VNQIKLFIVGI6UPSH/bundle.json","state_url":"https://pith.science/pith/UXOGRQ4AZ6VNQIKLFIVGI6UPSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UXOGRQ4AZ6VNQIKLFIVGI6UPSH/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":"2026-05-27T07:05:03Z","links":{"resolver":"https://pith.science/pith/UXOGRQ4AZ6VNQIKLFIVGI6UPSH","bundle":"https://pith.science/pith/UXOGRQ4AZ6VNQIKLFIVGI6UPSH/bundle.json","state":"https://pith.science/pith/UXOGRQ4AZ6VNQIKLFIVGI6UPSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UXOGRQ4AZ6VNQIKLFIVGI6UPSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UXOGRQ4AZ6VNQIKLFIVGI6UPSH","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":"71fabb8bdb29e382006d81d0f9dcda96b5e8b81776b9109b305932d40ad9c98d","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-02-05T19:46:56Z","title_canon_sha256":"197c998b409934ad746d7ece7a877a20bead8afd063c00a2cf8563c740bdb300"},"schema_version":"1.0","source":{"id":"1102.1096","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1096","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1096v2","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1096","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"pith_short_12","alias_value":"UXOGRQ4AZ6VN","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UXOGRQ4AZ6VNQIKL","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UXOGRQ4A","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:d043112ddccf808354dad8e52fd63b6e97077940c82cf74d57502bc8ec8a899b","target":"graph","created_at":"2026-05-18T04:25:37Z","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":"We consider a repeated Matching Pennies game in which players have limited access to randomness. Playing the (unique) Nash equilibrium in this n-stage game requires n random bits. Can there be Nash equilibria that use less than n random coins?\n  Our main results are as follows: We give a full characterization of approximate equilibria, showing that, for any e in [0, 1], the game has a e-Nash equilibrium if and only if both players have (1 - e)n random coins. When players are bound to run in polynomial time, Nash equilibria can exist if and only if one-way functions exist. It is possible to tra","authors_text":"Lance Fortnow, Michele Budinich","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-02-05T19:46:56Z","title":"Repeated Matching Pennies with Limited Randomness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1096","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":"sha256:5d8a166e4eca60b85cd9fc26bd29607409c238ac6e03c9fd6591994df79a85c3","target":"record","created_at":"2026-05-18T04:25:37Z","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":"71fabb8bdb29e382006d81d0f9dcda96b5e8b81776b9109b305932d40ad9c98d","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2011-02-05T19:46:56Z","title_canon_sha256":"197c998b409934ad746d7ece7a877a20bead8afd063c00a2cf8563c740bdb300"},"schema_version":"1.0","source":{"id":"1102.1096","kind":"arxiv","version":2}},"canonical_sha256":"a5dc68c380cfaad8214b2a2a647a8f91f802799601d8dc644291951607874e5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5dc68c380cfaad8214b2a2a647a8f91f802799601d8dc644291951607874e5d","first_computed_at":"2026-05-18T04:25:37.615439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:37.615439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O0aacvhdSv47KMIZKxFUaotOy3bi0+QRGCqaN71jsDWiFX+s/2yNYHnIs8JeMGDbJE6AX2pfDiaTm2hWsmPPDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:37.615996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1096","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d8a166e4eca60b85cd9fc26bd29607409c238ac6e03c9fd6591994df79a85c3","sha256:d043112ddccf808354dad8e52fd63b6e97077940c82cf74d57502bc8ec8a899b"],"state_sha256":"ee1f81ba8947009b5e1ba3be062a70e9192931bc0f24622d4ecdbf4a15db3b63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xf81kqeFD+0BwEvYpVMtM99Y3X+BGkiUqtqoOjYErD4n0lMmJ5plJRODu3IPGXC8myB58LEvmjj5bwD5EXTGCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:05:03.320567Z","bundle_sha256":"4700ef350c7c6ce465df826930cd2c0e736ff5f88bd48e5e64b1d80e065331c3"}}