{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2DFX5OWZQU2XM7DXYKTFXJ6P2P","short_pith_number":"pith:2DFX5OWZ","canonical_record":{"source":{"id":"1302.3973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-16T14:20:42Z","cross_cats_sorted":[],"title_canon_sha256":"8a3383136c15e15f511e7131e7759a8879f3f30abc004dfcbb99a1c223180583","abstract_canon_sha256":"c430874ac9b8f25e5ec14c25ce68ab6e0d4618c7069073fe8c92a91cf984ad12"},"schema_version":"1.0"},"canonical_sha256":"d0cb7ebad98535767c77c2a65ba7cfd3f7ac697afa8661085e4d7d0edcbf6e25","source":{"kind":"arxiv","id":"1302.3973","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3973","created_at":"2026-05-18T01:37:38Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3973v2","created_at":"2026-05-18T01:37:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3973","created_at":"2026-05-18T01:37:38Z"},{"alias_kind":"pith_short_12","alias_value":"2DFX5OWZQU2X","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2DFX5OWZQU2XM7DX","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2DFX5OWZ","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2DFX5OWZQU2XM7DXYKTFXJ6P2P","target":"record","payload":{"canonical_record":{"source":{"id":"1302.3973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-16T14:20:42Z","cross_cats_sorted":[],"title_canon_sha256":"8a3383136c15e15f511e7131e7759a8879f3f30abc004dfcbb99a1c223180583","abstract_canon_sha256":"c430874ac9b8f25e5ec14c25ce68ab6e0d4618c7069073fe8c92a91cf984ad12"},"schema_version":"1.0"},"canonical_sha256":"d0cb7ebad98535767c77c2a65ba7cfd3f7ac697afa8661085e4d7d0edcbf6e25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:38.279790Z","signature_b64":"lmuddBR2zKfQ44cu/QXubihjKI60r/9/brP6Vc3QOPCWF7/lhNEf0Jksfg4T/DyBP6y9yd3T05HzfUTQl2ziDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0cb7ebad98535767c77c2a65ba7cfd3f7ac697afa8661085e4d7d0edcbf6e25","last_reissued_at":"2026-05-18T01:37:38.279230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:38.279230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.3973","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":"2026-05-18T01:37:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KYZ1f/mMCSDcclJ3ZkLJK9iZ4yJJZvmJK8l7fiGTR1SYSikhn90TzEOCskciq9kjzZc6GajImoZ7aEm3vIM8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:52:00.365197Z"},"content_sha256":"3fbcbd1bf0e8438b2f874957a457fcb0a850cfb2748b794a908877d541b0148a","schema_version":"1.0","event_id":"sha256:3fbcbd1bf0e8438b2f874957a457fcb0a850cfb2748b794a908877d541b0148a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2DFX5OWZQU2XM7DXYKTFXJ6P2P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite sequential Nash equilibrium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Stephane Le Roux","submitted_at":"2013-02-16T14:20:42Z","abstract_excerpt":"In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play in turn. Two existing results are relevant here: first, all finite such games have a Nash equilibrium (w.r.t. some given preferences) iff all the given preferences are acyclic; second, all infinite such games have a Nash equilibrium, if they involve two agents who compete for victory and if the actual plays making a given agent win (and the opponent lose) for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3973","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":"2026-05-18T01:37:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i3TJRbI//wwlvQ6R43uTJHUeOWovJg1OCe66Bpz/VxwphmBzXiMgQOiCzybhlr3p/BHQqkA9bTLfpXX8J2jwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:52:00.365944Z"},"content_sha256":"9519cd533e484e82c7d1ecb2bc49e12ddc1a5aaf78da4e35b44ed2dca850857c","schema_version":"1.0","event_id":"sha256:9519cd533e484e82c7d1ecb2bc49e12ddc1a5aaf78da4e35b44ed2dca850857c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2DFX5OWZQU2XM7DXYKTFXJ6P2P/bundle.json","state_url":"https://pith.science/pith/2DFX5OWZQU2XM7DXYKTFXJ6P2P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2DFX5OWZQU2XM7DXYKTFXJ6P2P/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":"2026-06-11T16:52:00Z","links":{"resolver":"https://pith.science/pith/2DFX5OWZQU2XM7DXYKTFXJ6P2P","bundle":"https://pith.science/pith/2DFX5OWZQU2XM7DXYKTFXJ6P2P/bundle.json","state":"https://pith.science/pith/2DFX5OWZQU2XM7DXYKTFXJ6P2P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2DFX5OWZQU2XM7DXYKTFXJ6P2P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2DFX5OWZQU2XM7DXYKTFXJ6P2P","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":"c430874ac9b8f25e5ec14c25ce68ab6e0d4618c7069073fe8c92a91cf984ad12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-16T14:20:42Z","title_canon_sha256":"8a3383136c15e15f511e7131e7759a8879f3f30abc004dfcbb99a1c223180583"},"schema_version":"1.0","source":{"id":"1302.3973","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3973","created_at":"2026-05-18T01:37:38Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3973v2","created_at":"2026-05-18T01:37:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3973","created_at":"2026-05-18T01:37:38Z"},{"alias_kind":"pith_short_12","alias_value":"2DFX5OWZQU2X","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2DFX5OWZQU2XM7DX","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2DFX5OWZ","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:9519cd533e484e82c7d1ecb2bc49e12ddc1a5aaf78da4e35b44ed2dca850857c","target":"graph","created_at":"2026-05-18T01:37:38Z","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":"In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play in turn. Two existing results are relevant here: first, all finite such games have a Nash equilibrium (w.r.t. some given preferences) iff all the given preferences are acyclic; second, all infinite such games have a Nash equilibrium, if they involve two agents who compete for victory and if the actual plays making a given agent win (and the opponent lose) for","authors_text":"Stephane Le Roux","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-16T14:20:42Z","title":"Infinite sequential Nash equilibrium"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3973","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":"sha256:3fbcbd1bf0e8438b2f874957a457fcb0a850cfb2748b794a908877d541b0148a","target":"record","created_at":"2026-05-18T01:37:38Z","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":"c430874ac9b8f25e5ec14c25ce68ab6e0d4618c7069073fe8c92a91cf984ad12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-16T14:20:42Z","title_canon_sha256":"8a3383136c15e15f511e7131e7759a8879f3f30abc004dfcbb99a1c223180583"},"schema_version":"1.0","source":{"id":"1302.3973","kind":"arxiv","version":2}},"canonical_sha256":"d0cb7ebad98535767c77c2a65ba7cfd3f7ac697afa8661085e4d7d0edcbf6e25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0cb7ebad98535767c77c2a65ba7cfd3f7ac697afa8661085e4d7d0edcbf6e25","first_computed_at":"2026-05-18T01:37:38.279230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:38.279230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lmuddBR2zKfQ44cu/QXubihjKI60r/9/brP6Vc3QOPCWF7/lhNEf0Jksfg4T/DyBP6y9yd3T05HzfUTQl2ziDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:38.279790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3973","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fbcbd1bf0e8438b2f874957a457fcb0a850cfb2748b794a908877d541b0148a","sha256:9519cd533e484e82c7d1ecb2bc49e12ddc1a5aaf78da4e35b44ed2dca850857c"],"state_sha256":"098e243164ef116e0c74b3ddca90b91fa0ed58b7cd2e63348098df1bfa4448e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P0F0HFA0QLqhWCHCOxmyVs2HRuRMU16CyBLJE9CH3yoYd29zt7eAaBb3QvF9aqatjEH+MPUCnNDn7LOVDZ0bBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:52:00.369886Z","bundle_sha256":"10899fce19f308f53b8d4c515850746753d94d44881e534fe6aa2fe0642e5af6"}}