{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U5YB2BSHEPVP73DV2NYWAJMY2F","short_pith_number":"pith:U5YB2BSH","canonical_record":{"source":{"id":"1301.5683","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-01-24T01:33:55Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"6326da0fe4d7c54e08dc1de1824f4d0135d06430c0435dbcaf77e7d348121e25","abstract_canon_sha256":"da34c9a31ac6cc9093c4963d7f68dc0c893fff8286dd13bc5e7ea600736a3e2c"},"schema_version":"1.0"},"canonical_sha256":"a7701d064723eaffec75d371602598d158d4acc5bd310dfca02533a7cffc28e6","source":{"kind":"arxiv","id":"1301.5683","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5683","created_at":"2026-05-18T03:35:37Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5683v1","created_at":"2026-05-18T03:35:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5683","created_at":"2026-05-18T03:35:37Z"},{"alias_kind":"pith_short_12","alias_value":"U5YB2BSHEPVP","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U5YB2BSHEPVP73DV","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U5YB2BSH","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U5YB2BSHEPVP73DV2NYWAJMY2F","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5683","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-01-24T01:33:55Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"6326da0fe4d7c54e08dc1de1824f4d0135d06430c0435dbcaf77e7d348121e25","abstract_canon_sha256":"da34c9a31ac6cc9093c4963d7f68dc0c893fff8286dd13bc5e7ea600736a3e2c"},"schema_version":"1.0"},"canonical_sha256":"a7701d064723eaffec75d371602598d158d4acc5bd310dfca02533a7cffc28e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:37.710197Z","signature_b64":"ISm7Z9bYBGUqVvjB2ri3AYD8jxnh6dmUch+qSxg76/dAgBWn1d35L6jlaKtRsOeAptNTdyd+rl7PiBjpiQV5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7701d064723eaffec75d371602598d158d4acc5bd310dfca02533a7cffc28e6","last_reissued_at":"2026-05-18T03:35:37.709332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:37.709332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5683","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":"2026-05-18T03:35:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t5lbkWMfn+Wddg4jPajePdghFOqKKfRa91H8zrbZDUNT/3vcibNK1glAc7/ufDKTxwGxGn1wxzZUNDVgMSoiCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T19:34:49.797865Z"},"content_sha256":"5e6d0ffdbe42a07dfb7fa5455f607465f7f7b229f0d8f2ec208af63e122d0b39","schema_version":"1.0","event_id":"sha256:5e6d0ffdbe42a07dfb7fa5455f607465f7f7b229f0d8f2ec208af63e122d0b39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U5YB2BSHEPVP73DV2NYWAJMY2F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When is tit-for-tat unbeatable?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"cs.GT","authors_text":"Burkhard C. Schipper, Joerg Oechssler, Peter Duersch","submitted_at":"2013-01-24T01:33:55Z","abstract_excerpt":"We characterize the class of symmetric two-player games in which tit-for-tat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes tit-for-tat but also imitate-the-best and imitate-if-better. Every decision rule in this class is essentially unbeatable in exact potential games. Our results apply to many interesting games including all symmetric 2x2 games, and standard examples of Cournot duopoly, price competition, public goods games, common pool re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5683","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":"2026-05-18T03:35:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fFToA0h47khehfK5u1vdqKt4P5khEscZSwx7K0zW24ZrEuSdks0nuXgakYYHL/E2cqszFn0h26hAN27bPId4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T19:34:49.798541Z"},"content_sha256":"9d76c305ff0637042e362679f940cd1ce8bb5d7827842c627c4973fc2c91c685","schema_version":"1.0","event_id":"sha256:9d76c305ff0637042e362679f940cd1ce8bb5d7827842c627c4973fc2c91c685"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U5YB2BSHEPVP73DV2NYWAJMY2F/bundle.json","state_url":"https://pith.science/pith/U5YB2BSHEPVP73DV2NYWAJMY2F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U5YB2BSHEPVP73DV2NYWAJMY2F/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":"2026-05-24T19:34:49Z","links":{"resolver":"https://pith.science/pith/U5YB2BSHEPVP73DV2NYWAJMY2F","bundle":"https://pith.science/pith/U5YB2BSHEPVP73DV2NYWAJMY2F/bundle.json","state":"https://pith.science/pith/U5YB2BSHEPVP73DV2NYWAJMY2F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U5YB2BSHEPVP73DV2NYWAJMY2F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U5YB2BSHEPVP73DV2NYWAJMY2F","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":"da34c9a31ac6cc9093c4963d7f68dc0c893fff8286dd13bc5e7ea600736a3e2c","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-01-24T01:33:55Z","title_canon_sha256":"6326da0fe4d7c54e08dc1de1824f4d0135d06430c0435dbcaf77e7d348121e25"},"schema_version":"1.0","source":{"id":"1301.5683","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5683","created_at":"2026-05-18T03:35:37Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5683v1","created_at":"2026-05-18T03:35:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5683","created_at":"2026-05-18T03:35:37Z"},{"alias_kind":"pith_short_12","alias_value":"U5YB2BSHEPVP","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U5YB2BSHEPVP73DV","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U5YB2BSH","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:9d76c305ff0637042e362679f940cd1ce8bb5d7827842c627c4973fc2c91c685","target":"graph","created_at":"2026-05-18T03:35:37Z","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 characterize the class of symmetric two-player games in which tit-for-tat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes tit-for-tat but also imitate-the-best and imitate-if-better. Every decision rule in this class is essentially unbeatable in exact potential games. Our results apply to many interesting games including all symmetric 2x2 games, and standard examples of Cournot duopoly, price competition, public goods games, common pool re","authors_text":"Burkhard C. Schipper, Joerg Oechssler, Peter Duersch","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-01-24T01:33:55Z","title":"When is tit-for-tat unbeatable?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5683","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":"sha256:5e6d0ffdbe42a07dfb7fa5455f607465f7f7b229f0d8f2ec208af63e122d0b39","target":"record","created_at":"2026-05-18T03:35:37Z","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":"da34c9a31ac6cc9093c4963d7f68dc0c893fff8286dd13bc5e7ea600736a3e2c","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2013-01-24T01:33:55Z","title_canon_sha256":"6326da0fe4d7c54e08dc1de1824f4d0135d06430c0435dbcaf77e7d348121e25"},"schema_version":"1.0","source":{"id":"1301.5683","kind":"arxiv","version":1}},"canonical_sha256":"a7701d064723eaffec75d371602598d158d4acc5bd310dfca02533a7cffc28e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7701d064723eaffec75d371602598d158d4acc5bd310dfca02533a7cffc28e6","first_computed_at":"2026-05-18T03:35:37.709332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:37.709332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ISm7Z9bYBGUqVvjB2ri3AYD8jxnh6dmUch+qSxg76/dAgBWn1d35L6jlaKtRsOeAptNTdyd+rl7PiBjpiQV5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:37.710197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5683","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e6d0ffdbe42a07dfb7fa5455f607465f7f7b229f0d8f2ec208af63e122d0b39","sha256:9d76c305ff0637042e362679f940cd1ce8bb5d7827842c627c4973fc2c91c685"],"state_sha256":"db29def28bc4f647620df1c13da1882866a285e0a02b36f2d318476493077aa8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qai0qQwn9HC/vJvZyQsTMHo0POOvSbR5VbwLGYgUrP8Rz+jQvQ4j0V3+iSk5Lt17OxkyNoQ0ggOgP7ZsqacFDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T19:34:49.801493Z","bundle_sha256":"604883344bf1ca1c9d6ae1a481be5c4f8045a6a019d83c1883448803c2c35fc0"}}