{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:CFNSYFS5NBIVRRLSNZDAT3WZ52","short_pith_number":"pith:CFNSYFS5","canonical_record":{"source":{"id":"1009.0932","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-09-05T16:59:59Z","cross_cats_sorted":["cs.SY","math.PR","q-fin.GN"],"title_canon_sha256":"a0661610377e4a3efaece262161b985a9e4a27895530fc09a499b010eebb85a1","abstract_canon_sha256":"c31d53b60c0a22fee9fba176c145857bef2317babe00c561f62f056e84737267"},"schema_version":"1.0"},"canonical_sha256":"115b2c165d685158c5726e4609eed9ee8e1dc6c3de57cb9f0780f7d540415e89","source":{"kind":"arxiv","id":"1009.0932","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0932","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0932v8","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0932","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"CFNSYFS5NBIV","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"CFNSYFS5NBIVRRLS","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"CFNSYFS5","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:CFNSYFS5NBIVRRLSNZDAT3WZ52","target":"record","payload":{"canonical_record":{"source":{"id":"1009.0932","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-09-05T16:59:59Z","cross_cats_sorted":["cs.SY","math.PR","q-fin.GN"],"title_canon_sha256":"a0661610377e4a3efaece262161b985a9e4a27895530fc09a499b010eebb85a1","abstract_canon_sha256":"c31d53b60c0a22fee9fba176c145857bef2317babe00c561f62f056e84737267"},"schema_version":"1.0"},"canonical_sha256":"115b2c165d685158c5726e4609eed9ee8e1dc6c3de57cb9f0780f7d540415e89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:37.305048Z","signature_b64":"lzXVCtEluBoRSw9ipHX4wJb6XjoKDvYUlaKXj9gUZN1jzyZ2zScsTUVO7xDwWzLnIyFlq3wrAFFIpPjIF+eCAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"115b2c165d685158c5726e4609eed9ee8e1dc6c3de57cb9f0780f7d540415e89","last_reissued_at":"2026-05-18T03:36:37.304586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:37.304586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.0932","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3CyARAzjOHdWLI4sooTdbGzFJAStolF05iyfvbELrt3AmSLQrC9R0hwGiUO+vNOglOBXKzYgW+KcV01UC3wDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T17:41:23.670395Z"},"content_sha256":"3bb6d1799f6bf3cbc5f7aca4a598be70af93ac03b201626138395940c2c64ff3","schema_version":"1.0","event_id":"sha256:3bb6d1799f6bf3cbc5f7aca4a598be70af93ac03b201626138395940c2c64ff3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:CFNSYFS5NBIVRRLSNZDAT3WZ52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Multi-Dimensional Controller and Stopper Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.PR","q-fin.GN"],"primary_cat":"math.OC","authors_text":"Erhan Bayraktar, Yu-Jui Huang","submitted_at":"2010-09-05T16:59:59Z","abstract_excerpt":"We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the volatility terms of the state process. Under appropriate conditions, we show that the game has a value and the value function is the unique viscosity solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0932","kind":"arxiv","version":8},"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":"2026-05-18T03:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+lWOZ0KkC8DyN0v1Bf+L/Wd0lsQE8vA/mmUelFu5fYaENnoj1BgyhV9dneL2AYHvfzHRI0VeOSvI/p1H52cAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T17:41:23.670748Z"},"content_sha256":"b4ae0dfa52c6a13e1e94e1fca01de3e9f390a1403a9bc2bd1c19eb969a52b5a2","schema_version":"1.0","event_id":"sha256:b4ae0dfa52c6a13e1e94e1fca01de3e9f390a1403a9bc2bd1c19eb969a52b5a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFNSYFS5NBIVRRLSNZDAT3WZ52/bundle.json","state_url":"https://pith.science/pith/CFNSYFS5NBIVRRLSNZDAT3WZ52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFNSYFS5NBIVRRLSNZDAT3WZ52/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":"2026-05-20T17:41:23Z","links":{"resolver":"https://pith.science/pith/CFNSYFS5NBIVRRLSNZDAT3WZ52","bundle":"https://pith.science/pith/CFNSYFS5NBIVRRLSNZDAT3WZ52/bundle.json","state":"https://pith.science/pith/CFNSYFS5NBIVRRLSNZDAT3WZ52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFNSYFS5NBIVRRLSNZDAT3WZ52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CFNSYFS5NBIVRRLSNZDAT3WZ52","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":"c31d53b60c0a22fee9fba176c145857bef2317babe00c561f62f056e84737267","cross_cats_sorted":["cs.SY","math.PR","q-fin.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-09-05T16:59:59Z","title_canon_sha256":"a0661610377e4a3efaece262161b985a9e4a27895530fc09a499b010eebb85a1"},"schema_version":"1.0","source":{"id":"1009.0932","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0932","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0932v8","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0932","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"CFNSYFS5NBIV","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"CFNSYFS5NBIVRRLS","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"CFNSYFS5","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:b4ae0dfa52c6a13e1e94e1fca01de3e9f390a1403a9bc2bd1c19eb969a52b5a2","target":"graph","created_at":"2026-05-18T03:36:37Z","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 consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the volatility terms of the state process. Under appropriate conditions, we show that the game has a value and the value function is the unique viscosity solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation.","authors_text":"Erhan Bayraktar, Yu-Jui Huang","cross_cats":["cs.SY","math.PR","q-fin.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-09-05T16:59:59Z","title":"On the Multi-Dimensional Controller and Stopper Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0932","kind":"arxiv","version":8},"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":"sha256:3bb6d1799f6bf3cbc5f7aca4a598be70af93ac03b201626138395940c2c64ff3","target":"record","created_at":"2026-05-18T03:36:37Z","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":"c31d53b60c0a22fee9fba176c145857bef2317babe00c561f62f056e84737267","cross_cats_sorted":["cs.SY","math.PR","q-fin.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-09-05T16:59:59Z","title_canon_sha256":"a0661610377e4a3efaece262161b985a9e4a27895530fc09a499b010eebb85a1"},"schema_version":"1.0","source":{"id":"1009.0932","kind":"arxiv","version":8}},"canonical_sha256":"115b2c165d685158c5726e4609eed9ee8e1dc6c3de57cb9f0780f7d540415e89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"115b2c165d685158c5726e4609eed9ee8e1dc6c3de57cb9f0780f7d540415e89","first_computed_at":"2026-05-18T03:36:37.304586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:37.304586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lzXVCtEluBoRSw9ipHX4wJb6XjoKDvYUlaKXj9gUZN1jzyZ2zScsTUVO7xDwWzLnIyFlq3wrAFFIpPjIF+eCAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:37.305048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0932","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bb6d1799f6bf3cbc5f7aca4a598be70af93ac03b201626138395940c2c64ff3","sha256:b4ae0dfa52c6a13e1e94e1fca01de3e9f390a1403a9bc2bd1c19eb969a52b5a2"],"state_sha256":"e1d5e23217a81adac413bc929976acb737781bbb8ae87494ba102b9283aaed54"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AamXSPS8KqxsGoPy1pHGOo3KeHyDffkRoos1CZF/ZdjxOnDTPlXenDVjyMTKKVZTK4kh5k16m6J8yyiA6W3dBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T17:41:23.673791Z","bundle_sha256":"698ccdd6cf6b08209410ea50ea4bc6b918dac60c9c91968d782dc465a58cd8a1"}}