{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KFPTZO5ATXDRAEMHG5H62LGLHM","short_pith_number":"pith:KFPTZO5A","canonical_record":{"source":{"id":"2607.00625","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-07-01T08:42:40Z","cross_cats_sorted":[],"title_canon_sha256":"ecaa784c824929d61c3cbe663f5a7a256dc9069fa54db9fcee3528b39eaca815","abstract_canon_sha256":"1bae48aa669007b8f0b2407ad4b3bdb3760ac2d4e611dcac293f1642b226de2d"},"schema_version":"1.0"},"canonical_sha256":"515f3cbba09dc7101187374fed2ccb3b0e1a7198d3dc7e054294dc0a793bd45b","source":{"kind":"arxiv","id":"2607.00625","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00625","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00625v1","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00625","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"pith_short_12","alias_value":"KFPTZO5ATXDR","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"pith_short_16","alias_value":"KFPTZO5ATXDRAEMH","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"pith_short_8","alias_value":"KFPTZO5A","created_at":"2026-07-02T01:17:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KFPTZO5ATXDRAEMHG5H62LGLHM","target":"record","payload":{"canonical_record":{"source":{"id":"2607.00625","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-07-01T08:42:40Z","cross_cats_sorted":[],"title_canon_sha256":"ecaa784c824929d61c3cbe663f5a7a256dc9069fa54db9fcee3528b39eaca815","abstract_canon_sha256":"1bae48aa669007b8f0b2407ad4b3bdb3760ac2d4e611dcac293f1642b226de2d"},"schema_version":"1.0"},"canonical_sha256":"515f3cbba09dc7101187374fed2ccb3b0e1a7198d3dc7e054294dc0a793bd45b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:17:49.545939Z","signature_b64":"fEF+t9t2FbMOqU9Lq57lUM0H5zTqrG8wnxHVNzQA0tXvHoQCb5GnS/1i/hyRvW1D62CvVRGCtJTMNlvM+nT3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"515f3cbba09dc7101187374fed2ccb3b0e1a7198d3dc7e054294dc0a793bd45b","last_reissued_at":"2026-07-02T01:17:49.545436Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:17:49.545436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.00625","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":"2026-07-02T01:17:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Psq03qFgpvfFdIPDu3ogGW1ZTF+goHIPPFzbqVFsVY434X+6OgUpPIGpbQ0UBUsLVkMA+s/j40NByA4HnI8GAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:35:48.730439Z"},"content_sha256":"9962db49185fb11531b38f8329274fae5e35f24895fbded40c3b6c9ef3e693ae","schema_version":"1.0","event_id":"sha256:9962db49185fb11531b38f8329274fae5e35f24895fbded40c3b6c9ef3e693ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KFPTZO5ATXDRAEMHG5H62LGLHM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive and Negative Determinant Strategies in Repeated Games with Behavior-Value Inconsistency","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Bin Wu, Yakun Wang, Yuan Liu","submitted_at":"2026-07-01T08:42:40Z","abstract_excerpt":"Direct reciprocity, based on the repeated interactions, is a fundamental mechanism to promote cooperation. Zero-determinant (ZD) strategies have opened an avenue for unilateral payoff control. However, previous studies neglect internal costs provided what agents do differ from what agents think, which is crucial for decision making of intelligent agents. Motivated by this, we establish a game theoretical framework by assuming that an individual pays the internal cost if the behavior is inconsistent with the internal thought. We prove that ZD strategy does not exist if the cost via behavior-val"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00625","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.00625/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-02T01:17:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TndUNBfUZZQpOfp7+kVvEbjb6vWM+QqF5sNPGKEOriB4O9SpHaOQOYQXOa/e+9ghAnjqmmxvVv50iuDu36ubAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:35:48.731157Z"},"content_sha256":"b5c1eeb1f6c06a302992fce827e1a58ceb674ec810d637286f1a74736efecab2","schema_version":"1.0","event_id":"sha256:b5c1eeb1f6c06a302992fce827e1a58ceb674ec810d637286f1a74736efecab2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KFPTZO5ATXDRAEMHG5H62LGLHM/bundle.json","state_url":"https://pith.science/pith/KFPTZO5ATXDRAEMHG5H62LGLHM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KFPTZO5ATXDRAEMHG5H62LGLHM/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":"2026-08-13T17:35:48Z","links":{"resolver":"https://pith.science/pith/KFPTZO5ATXDRAEMHG5H62LGLHM","bundle":"https://pith.science/pith/KFPTZO5ATXDRAEMHG5H62LGLHM/bundle.json","state":"https://pith.science/pith/KFPTZO5ATXDRAEMHG5H62LGLHM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KFPTZO5ATXDRAEMHG5H62LGLHM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KFPTZO5ATXDRAEMHG5H62LGLHM","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":"1bae48aa669007b8f0b2407ad4b3bdb3760ac2d4e611dcac293f1642b226de2d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-07-01T08:42:40Z","title_canon_sha256":"ecaa784c824929d61c3cbe663f5a7a256dc9069fa54db9fcee3528b39eaca815"},"schema_version":"1.0","source":{"id":"2607.00625","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00625","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00625v1","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00625","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"pith_short_12","alias_value":"KFPTZO5ATXDR","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"pith_short_16","alias_value":"KFPTZO5ATXDRAEMH","created_at":"2026-07-02T01:17:49Z"},{"alias_kind":"pith_short_8","alias_value":"KFPTZO5A","created_at":"2026-07-02T01:17:49Z"}],"graph_snapshots":[{"event_id":"sha256:b5c1eeb1f6c06a302992fce827e1a58ceb674ec810d637286f1a74736efecab2","target":"graph","created_at":"2026-07-02T01:17:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.00625/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Direct reciprocity, based on the repeated interactions, is a fundamental mechanism to promote cooperation. Zero-determinant (ZD) strategies have opened an avenue for unilateral payoff control. However, previous studies neglect internal costs provided what agents do differ from what agents think, which is crucial for decision making of intelligent agents. Motivated by this, we establish a game theoretical framework by assuming that an individual pays the internal cost if the behavior is inconsistent with the internal thought. We prove that ZD strategy does not exist if the cost via behavior-val","authors_text":"Bin Wu, Yakun Wang, Yuan Liu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-07-01T08:42:40Z","title":"Positive and Negative Determinant Strategies in Repeated Games with Behavior-Value Inconsistency"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00625","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":"sha256:9962db49185fb11531b38f8329274fae5e35f24895fbded40c3b6c9ef3e693ae","target":"record","created_at":"2026-07-02T01:17:49Z","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":"1bae48aa669007b8f0b2407ad4b3bdb3760ac2d4e611dcac293f1642b226de2d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-07-01T08:42:40Z","title_canon_sha256":"ecaa784c824929d61c3cbe663f5a7a256dc9069fa54db9fcee3528b39eaca815"},"schema_version":"1.0","source":{"id":"2607.00625","kind":"arxiv","version":1}},"canonical_sha256":"515f3cbba09dc7101187374fed2ccb3b0e1a7198d3dc7e054294dc0a793bd45b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"515f3cbba09dc7101187374fed2ccb3b0e1a7198d3dc7e054294dc0a793bd45b","first_computed_at":"2026-07-02T01:17:49.545436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:17:49.545436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fEF+t9t2FbMOqU9Lq57lUM0H5zTqrG8wnxHVNzQA0tXvHoQCb5GnS/1i/hyRvW1D62CvVRGCtJTMNlvM+nT3Bw==","signature_status":"signed_v1","signed_at":"2026-07-02T01:17:49.545939Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00625","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9962db49185fb11531b38f8329274fae5e35f24895fbded40c3b6c9ef3e693ae","sha256:b5c1eeb1f6c06a302992fce827e1a58ceb674ec810d637286f1a74736efecab2"],"state_sha256":"4cab6bd503558aad828368e9c9f2fc44ae935b298db4881256aceed0a1edf19d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DlqQAp4kZ+NWzzKD1MVdtpL2LBO6sHvzpSdG5f41Q0AbDAkNPqMEJVIaTldjtY8U/Yf8KMRu3B3sUHlYXWmhAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T17:35:48.737795Z","bundle_sha256":"e6b55d08163430d65561f7d54421d9a89c40a1ac801857f7aea2b9e160007426"}}