{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GNGUP7XGXHHO7RXXTOENIBUU42","short_pith_number":"pith:GNGUP7XG","canonical_record":{"source":{"id":"2605.26516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-05-26T03:57:59Z","cross_cats_sorted":[],"title_canon_sha256":"1672b5c9ac4cf4ff8be39882bb88f811b08bb6b1f1f98371a66c52b8ec4266d4","abstract_canon_sha256":"299fd25059ecbbdb0307c33ff41c8f108d7891d89359d956142dcdf05c2b1081"},"schema_version":"1.0"},"canonical_sha256":"334d47fee6b9ceefc6f79b88d40694e68fb58b14a6ba9f899e77226bc8f81437","source":{"kind":"arxiv","id":"2605.26516","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26516","created_at":"2026-05-27T01:05:24Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26516v1","created_at":"2026-05-27T01:05:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26516","created_at":"2026-05-27T01:05:24Z"},{"alias_kind":"pith_short_12","alias_value":"GNGUP7XGXHHO","created_at":"2026-05-27T01:05:24Z"},{"alias_kind":"pith_short_16","alias_value":"GNGUP7XGXHHO7RXX","created_at":"2026-05-27T01:05:24Z"},{"alias_kind":"pith_short_8","alias_value":"GNGUP7XG","created_at":"2026-05-27T01:05:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GNGUP7XGXHHO7RXXTOENIBUU42","target":"record","payload":{"canonical_record":{"source":{"id":"2605.26516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-05-26T03:57:59Z","cross_cats_sorted":[],"title_canon_sha256":"1672b5c9ac4cf4ff8be39882bb88f811b08bb6b1f1f98371a66c52b8ec4266d4","abstract_canon_sha256":"299fd25059ecbbdb0307c33ff41c8f108d7891d89359d956142dcdf05c2b1081"},"schema_version":"1.0"},"canonical_sha256":"334d47fee6b9ceefc6f79b88d40694e68fb58b14a6ba9f899e77226bc8f81437","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:05:24.038224Z","signature_b64":"3rFURPW79cLLI+4ZJcDCPWEuqTLH//mLXXa8KdfQcARXxHSt98Bqelyctzz3H+9G9zzC8o8FHuKvBpfX4Ro+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"334d47fee6b9ceefc6f79b88d40694e68fb58b14a6ba9f899e77226bc8f81437","last_reissued_at":"2026-05-27T01:05:24.037423Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:05:24.037423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.26516","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":"2026-05-27T01:05:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/KeEZiCVtEQJmD/CNuHHJYQLObhwzCYjkENyOuN4zF6s5x3zsYT0t8PqXrltl0R/kXZ1EMEMMR8DIbYRMYxKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:43:20.147098Z"},"content_sha256":"b3edc4e83c3fe42ff7b1fa66c28ad03bce2f9796e16b9708612454ce0f7cea51","schema_version":"1.0","event_id":"sha256:b3edc4e83c3fe42ff7b1fa66c28ad03bce2f9796e16b9708612454ce0f7cea51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GNGUP7XGXHHO7RXXTOENIBUU42","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"State-Robust Nash Predictions In Population Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"econ.TH","authors_text":"Junfei Guo, Rui Sun","submitted_at":"2026-05-26T03:57:59Z","abstract_excerpt":"This paper introduces state-robust equilibrium (SRE), a local validity test for Nash predictions in finite-strategy population games when the payoff-relevant aggregate state may be misspecified. The reported prescription and payoff map are held fixed; only the state used to evaluate payoff comparisons varies. SRE is equivalent to local best-response invariance, absence of structural exposure, and validity along every vanishing interior aggregate-state error. In affine games, the tangent-cone, normal-cone, and linear-program tests characterize exposure and identify the exposing population, the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26516","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/2605.26516/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":"2026-05-27T01:05:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2FVPPD2MvwxqRdv44aEz47H9CKM+bAXJWM5KHuYOVKxENNVqJOrj+ZvpAIPRx/FCKY8oaq/FDc1lhpp8ozJKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:43:20.147607Z"},"content_sha256":"b1ddbab641905f6351124c7790696a8bd76371d954d0c38d57c5e453d35bb4c0","schema_version":"1.0","event_id":"sha256:b1ddbab641905f6351124c7790696a8bd76371d954d0c38d57c5e453d35bb4c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GNGUP7XGXHHO7RXXTOENIBUU42/bundle.json","state_url":"https://pith.science/pith/GNGUP7XGXHHO7RXXTOENIBUU42/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GNGUP7XGXHHO7RXXTOENIBUU42/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":"2026-08-08T17:43:20Z","links":{"resolver":"https://pith.science/pith/GNGUP7XGXHHO7RXXTOENIBUU42","bundle":"https://pith.science/pith/GNGUP7XGXHHO7RXXTOENIBUU42/bundle.json","state":"https://pith.science/pith/GNGUP7XGXHHO7RXXTOENIBUU42/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GNGUP7XGXHHO7RXXTOENIBUU42/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GNGUP7XGXHHO7RXXTOENIBUU42","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":"299fd25059ecbbdb0307c33ff41c8f108d7891d89359d956142dcdf05c2b1081","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-05-26T03:57:59Z","title_canon_sha256":"1672b5c9ac4cf4ff8be39882bb88f811b08bb6b1f1f98371a66c52b8ec4266d4"},"schema_version":"1.0","source":{"id":"2605.26516","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26516","created_at":"2026-05-27T01:05:24Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26516v1","created_at":"2026-05-27T01:05:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26516","created_at":"2026-05-27T01:05:24Z"},{"alias_kind":"pith_short_12","alias_value":"GNGUP7XGXHHO","created_at":"2026-05-27T01:05:24Z"},{"alias_kind":"pith_short_16","alias_value":"GNGUP7XGXHHO7RXX","created_at":"2026-05-27T01:05:24Z"},{"alias_kind":"pith_short_8","alias_value":"GNGUP7XG","created_at":"2026-05-27T01:05:24Z"}],"graph_snapshots":[{"event_id":"sha256:b1ddbab641905f6351124c7790696a8bd76371d954d0c38d57c5e453d35bb4c0","target":"graph","created_at":"2026-05-27T01:05:24Z","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/2605.26516/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces state-robust equilibrium (SRE), a local validity test for Nash predictions in finite-strategy population games when the payoff-relevant aggregate state may be misspecified. The reported prescription and payoff map are held fixed; only the state used to evaluate payoff comparisons varies. SRE is equivalent to local best-response invariance, absence of structural exposure, and validity along every vanishing interior aggregate-state error. In affine games, the tangent-cone, normal-cone, and linear-program tests characterize exposure and identify the exposing population, the ","authors_text":"Junfei Guo, Rui Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-05-26T03:57:59Z","title":"State-Robust Nash Predictions In Population Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26516","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:b3edc4e83c3fe42ff7b1fa66c28ad03bce2f9796e16b9708612454ce0f7cea51","target":"record","created_at":"2026-05-27T01:05:24Z","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":"299fd25059ecbbdb0307c33ff41c8f108d7891d89359d956142dcdf05c2b1081","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2026-05-26T03:57:59Z","title_canon_sha256":"1672b5c9ac4cf4ff8be39882bb88f811b08bb6b1f1f98371a66c52b8ec4266d4"},"schema_version":"1.0","source":{"id":"2605.26516","kind":"arxiv","version":1}},"canonical_sha256":"334d47fee6b9ceefc6f79b88d40694e68fb58b14a6ba9f899e77226bc8f81437","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"334d47fee6b9ceefc6f79b88d40694e68fb58b14a6ba9f899e77226bc8f81437","first_computed_at":"2026-05-27T01:05:24.037423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:05:24.037423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3rFURPW79cLLI+4ZJcDCPWEuqTLH//mLXXa8KdfQcARXxHSt98Bqelyctzz3H+9G9zzC8o8FHuKvBpfX4Ro+BA==","signature_status":"signed_v1","signed_at":"2026-05-27T01:05:24.038224Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.26516","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3edc4e83c3fe42ff7b1fa66c28ad03bce2f9796e16b9708612454ce0f7cea51","sha256:b1ddbab641905f6351124c7790696a8bd76371d954d0c38d57c5e453d35bb4c0"],"state_sha256":"69525e9f8ca97de47c037cfff5e6d0f5a20494ac38668826b62586e7699d5454"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BPsK0BeKytXnhjNQyHWFf4jmCTv4qG9GZm3F3AWdPOj+8zQaAW4iQkkNfUDbOzG0V+W+qHNIXvFCCIYXdthBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T17:43:20.151799Z","bundle_sha256":"8a7d72e5ad27c44e7d3c8003027ba54fe389b2a147fe7b0f909dd4e33047aad3"}}