{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6R3BNN37CKV64JSZUEAX2XQMN7","short_pith_number":"pith:6R3BNN37","canonical_record":{"source":{"id":"1506.09184","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-30T18:08:10Z","cross_cats_sorted":["math.OC","q-fin.MF"],"title_canon_sha256":"33116ba0590d8d6a997dff561ce8fd7c18a6265fa27f03b0f0602b5a1abe3c47","abstract_canon_sha256":"aaa3a73500b6d171a18e49e226bd3c0424634f9b981e10e3b2a3e1ab250b2113"},"schema_version":"1.0"},"canonical_sha256":"f47616b77f12abee2659a1017d5e0c6febd411b6373b28e7c1e666dd6b7bff3b","source":{"kind":"arxiv","id":"1506.09184","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.09184","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1506.09184v3","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.09184","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"6R3BNN37CKV6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6R3BNN37CKV64JSZ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6R3BNN37","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6R3BNN37CKV64JSZUEAX2XQMN7","target":"record","payload":{"canonical_record":{"source":{"id":"1506.09184","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-30T18:08:10Z","cross_cats_sorted":["math.OC","q-fin.MF"],"title_canon_sha256":"33116ba0590d8d6a997dff561ce8fd7c18a6265fa27f03b0f0602b5a1abe3c47","abstract_canon_sha256":"aaa3a73500b6d171a18e49e226bd3c0424634f9b981e10e3b2a3e1ab250b2113"},"schema_version":"1.0"},"canonical_sha256":"f47616b77f12abee2659a1017d5e0c6febd411b6373b28e7c1e666dd6b7bff3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:50.546273Z","signature_b64":"ozsCNXprgtLfD+GW0V/tF29O+s5+HrcHY8ueXHMETbjLl23aI2i5lV3Tp3RfiEfvj7Ve52sbE1pm59R+RQ7oDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f47616b77f12abee2659a1017d5e0c6febd411b6373b28e7c1e666dd6b7bff3b","last_reissued_at":"2026-05-18T01:04:50.545856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:50.545856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.09184","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i2i+kOUJAQTSDVaNu7RKcv1h1DnXAidwwTdr5IvY4/oU+Vj4k0a6xjBMNFZj3KqrGjknZdeUapUYEW6Rh/8ADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T12:31:49.316850Z"},"content_sha256":"25566f1b23c4c320d1410993432304be45dbc2b2775741ff45b5aa31e5426195","schema_version":"1.0","event_id":"sha256:25566f1b23c4c320d1410993432304be45dbc2b2775741ff45b5aa31e5426195"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6R3BNN37CKV64JSZUEAX2XQMN7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Robust Dynkin Game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","q-fin.MF"],"primary_cat":"math.PR","authors_text":"Erhan Bayraktar, Song Yao","submitted_at":"2015-06-30T18:08:10Z","abstract_excerpt":"We study a robust Dynkin game over a set of mutually singular probabilities. We first prove that for the conservative player of the game, her lower and upper value processes coincide (i.e. She has a value process $V $ in the game). Such a result helps people connect the robust Dynkin game with second-order doubly reflected backward stochastic differential equations. Also, we show that the value process $V$ is a submartingale under an appropriately defined nonlinear expectations up to the first time $\\tau_*$ when $V$ meets the lower payoff process $L$. If the probability set is weakly compact, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.09184","kind":"arxiv","version":3},"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":"2026-05-18T01:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jQisEqm+9fGDaBWfPeCtk9h0RGCewaCoa4BbJEw9Vlp0/t5lDVTCmDe/tUFOREG6UzfumjFXl0Odp2D427nlDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T12:31:49.317206Z"},"content_sha256":"d98eded146a3eea8fa084ff80dc91c680254a86cde611a576651f70c8bd1ae54","schema_version":"1.0","event_id":"sha256:d98eded146a3eea8fa084ff80dc91c680254a86cde611a576651f70c8bd1ae54"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6R3BNN37CKV64JSZUEAX2XQMN7/bundle.json","state_url":"https://pith.science/pith/6R3BNN37CKV64JSZUEAX2XQMN7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6R3BNN37CKV64JSZUEAX2XQMN7/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":"2026-05-21T12:31:49Z","links":{"resolver":"https://pith.science/pith/6R3BNN37CKV64JSZUEAX2XQMN7","bundle":"https://pith.science/pith/6R3BNN37CKV64JSZUEAX2XQMN7/bundle.json","state":"https://pith.science/pith/6R3BNN37CKV64JSZUEAX2XQMN7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6R3BNN37CKV64JSZUEAX2XQMN7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6R3BNN37CKV64JSZUEAX2XQMN7","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":"aaa3a73500b6d171a18e49e226bd3c0424634f9b981e10e3b2a3e1ab250b2113","cross_cats_sorted":["math.OC","q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-30T18:08:10Z","title_canon_sha256":"33116ba0590d8d6a997dff561ce8fd7c18a6265fa27f03b0f0602b5a1abe3c47"},"schema_version":"1.0","source":{"id":"1506.09184","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.09184","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1506.09184v3","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.09184","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"6R3BNN37CKV6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6R3BNN37CKV64JSZ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6R3BNN37","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:d98eded146a3eea8fa084ff80dc91c680254a86cde611a576651f70c8bd1ae54","target":"graph","created_at":"2026-05-18T01:04:50Z","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 study a robust Dynkin game over a set of mutually singular probabilities. We first prove that for the conservative player of the game, her lower and upper value processes coincide (i.e. She has a value process $V $ in the game). Such a result helps people connect the robust Dynkin game with second-order doubly reflected backward stochastic differential equations. Also, we show that the value process $V$ is a submartingale under an appropriately defined nonlinear expectations up to the first time $\\tau_*$ when $V$ meets the lower payoff process $L$. If the probability set is weakly compact, ","authors_text":"Erhan Bayraktar, Song Yao","cross_cats":["math.OC","q-fin.MF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-30T18:08:10Z","title":"On the Robust Dynkin Game"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.09184","kind":"arxiv","version":3},"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":"sha256:25566f1b23c4c320d1410993432304be45dbc2b2775741ff45b5aa31e5426195","target":"record","created_at":"2026-05-18T01:04:50Z","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":"aaa3a73500b6d171a18e49e226bd3c0424634f9b981e10e3b2a3e1ab250b2113","cross_cats_sorted":["math.OC","q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-30T18:08:10Z","title_canon_sha256":"33116ba0590d8d6a997dff561ce8fd7c18a6265fa27f03b0f0602b5a1abe3c47"},"schema_version":"1.0","source":{"id":"1506.09184","kind":"arxiv","version":3}},"canonical_sha256":"f47616b77f12abee2659a1017d5e0c6febd411b6373b28e7c1e666dd6b7bff3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f47616b77f12abee2659a1017d5e0c6febd411b6373b28e7c1e666dd6b7bff3b","first_computed_at":"2026-05-18T01:04:50.545856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:50.545856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ozsCNXprgtLfD+GW0V/tF29O+s5+HrcHY8ueXHMETbjLl23aI2i5lV3Tp3RfiEfvj7Ve52sbE1pm59R+RQ7oDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:50.546273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.09184","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25566f1b23c4c320d1410993432304be45dbc2b2775741ff45b5aa31e5426195","sha256:d98eded146a3eea8fa084ff80dc91c680254a86cde611a576651f70c8bd1ae54"],"state_sha256":"618eb9ac4f351820ddcd4d222d562f75845ee5e2e0756404844cf0553d70a105"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m8/fHVvJwvwMcRgJO7wgHRuPHNcQNp5mrcJSb0bgCjrsz6dFUazQUkuNv7DRBGzx5CSGjTB/bw1lJ1dPrk3jBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T12:31:49.319660Z","bundle_sha256":"02ade43356f54416b4e7066c94db5758fce564448cf111286122f6ec8ae65f86"}}