{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:56QERC4ZFRP4ASVXRDTY4O426Q","short_pith_number":"pith:56QERC4Z","canonical_record":{"source":{"id":"1204.2498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-11T17:01:54Z","cross_cats_sorted":[],"title_canon_sha256":"3040c61e5520bf84565f59374dee0a450faf8f4b9845fff1e51a2434ca5ca868","abstract_canon_sha256":"f3783744d24b6e2509366a2f529f90121ea165d9bc7e07f029d796ac1efd1278"},"schema_version":"1.0"},"canonical_sha256":"efa0488b992c5fc04ab788e78e3b9af4112e7a8c9e9ecd5a37ca02abf309dffa","source":{"kind":"arxiv","id":"1204.2498","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2498","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2498v2","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2498","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"56QERC4ZFRP4","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"56QERC4ZFRP4ASVX","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"56QERC4Z","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:56QERC4ZFRP4ASVXRDTY4O426Q","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-11T17:01:54Z","cross_cats_sorted":[],"title_canon_sha256":"3040c61e5520bf84565f59374dee0a450faf8f4b9845fff1e51a2434ca5ca868","abstract_canon_sha256":"f3783744d24b6e2509366a2f529f90121ea165d9bc7e07f029d796ac1efd1278"},"schema_version":"1.0"},"canonical_sha256":"efa0488b992c5fc04ab788e78e3b9af4112e7a8c9e9ecd5a37ca02abf309dffa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:10.324862Z","signature_b64":"FuJg95C3P7YlPk6udYIEKpvWa+gu6FV+No0Wu6jJS7/KJOkv1f4Rqp51pr4ZdsBq/LdjZUpyPAaCag1/cuGLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efa0488b992c5fc04ab788e78e3b9af4112e7a8c9e9ecd5a37ca02abf309dffa","last_reissued_at":"2026-05-18T03:27:10.324368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:10.324368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2498","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":"2026-05-18T03:27:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"30c+aBI3zChWplFxFNOGI+XFmGxWHW4fcRKby35okFNbssEGH4w0QV/kaYxgURoPl9tC9jimoDZR3IqRfqJDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:53:14.200260Z"},"content_sha256":"647591bfdd939b09122ada27ebd22f6635d2cdbb624291a56393fc4031604217","schema_version":"1.0","event_id":"sha256:647591bfdd939b09122ada27ebd22f6635d2cdbb624291a56393fc4031604217"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:56QERC4ZFRP4ASVXRDTY4O426Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An explicit solution of a non-linear quadratic constrained stochastic control problem with an application to optimal liquidation in dark pools with adverse selection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Peter Kratz","submitted_at":"2012-04-11T17:01:54Z","abstract_excerpt":"We study a constrained stochastic control problem with jumps; the jump times of the controlled process are given by a Poisson process. The cost functional comprises quadratic components for an absolutely continuous control and the controlled process and an absolute value component for the control of the jump size of the process. We characterize the value function by a \"polynomial\" of degree two whose coefficients depend on the state of the system; these coefficients are given by a coupled system of ODEs. The problem hence reduces from solving the Hamilton Jacobi Bellman (HJB) equation (i.e., a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2498","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":"2026-05-18T03:27:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VLFLuXSiwPASO45JqHiOQotP2QCt4OGzo0yfiZswbhDfMpDegLsZKheS+mg75P7DQIW6RrDWOBXZu6SzC36pCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:53:14.200619Z"},"content_sha256":"b606d5e40abf33a1f548f85573f02a814fe9fe396c72e78d7df8fd78f04fc7dd","schema_version":"1.0","event_id":"sha256:b606d5e40abf33a1f548f85573f02a814fe9fe396c72e78d7df8fd78f04fc7dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/56QERC4ZFRP4ASVXRDTY4O426Q/bundle.json","state_url":"https://pith.science/pith/56QERC4ZFRP4ASVXRDTY4O426Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/56QERC4ZFRP4ASVXRDTY4O426Q/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":"2026-06-25T12:53:14Z","links":{"resolver":"https://pith.science/pith/56QERC4ZFRP4ASVXRDTY4O426Q","bundle":"https://pith.science/pith/56QERC4ZFRP4ASVXRDTY4O426Q/bundle.json","state":"https://pith.science/pith/56QERC4ZFRP4ASVXRDTY4O426Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/56QERC4ZFRP4ASVXRDTY4O426Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:56QERC4ZFRP4ASVXRDTY4O426Q","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":"f3783744d24b6e2509366a2f529f90121ea165d9bc7e07f029d796ac1efd1278","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-11T17:01:54Z","title_canon_sha256":"3040c61e5520bf84565f59374dee0a450faf8f4b9845fff1e51a2434ca5ca868"},"schema_version":"1.0","source":{"id":"1204.2498","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2498","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2498v2","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2498","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"56QERC4ZFRP4","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"56QERC4ZFRP4ASVX","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"56QERC4Z","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:b606d5e40abf33a1f548f85573f02a814fe9fe396c72e78d7df8fd78f04fc7dd","target":"graph","created_at":"2026-05-18T03:27:10Z","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 constrained stochastic control problem with jumps; the jump times of the controlled process are given by a Poisson process. The cost functional comprises quadratic components for an absolutely continuous control and the controlled process and an absolute value component for the control of the jump size of the process. We characterize the value function by a \"polynomial\" of degree two whose coefficients depend on the state of the system; these coefficients are given by a coupled system of ODEs. The problem hence reduces from solving the Hamilton Jacobi Bellman (HJB) equation (i.e., a","authors_text":"Peter Kratz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-11T17:01:54Z","title":"An explicit solution of a non-linear quadratic constrained stochastic control problem with an application to optimal liquidation in dark pools with adverse selection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2498","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":"sha256:647591bfdd939b09122ada27ebd22f6635d2cdbb624291a56393fc4031604217","target":"record","created_at":"2026-05-18T03:27:10Z","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":"f3783744d24b6e2509366a2f529f90121ea165d9bc7e07f029d796ac1efd1278","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-04-11T17:01:54Z","title_canon_sha256":"3040c61e5520bf84565f59374dee0a450faf8f4b9845fff1e51a2434ca5ca868"},"schema_version":"1.0","source":{"id":"1204.2498","kind":"arxiv","version":2}},"canonical_sha256":"efa0488b992c5fc04ab788e78e3b9af4112e7a8c9e9ecd5a37ca02abf309dffa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efa0488b992c5fc04ab788e78e3b9af4112e7a8c9e9ecd5a37ca02abf309dffa","first_computed_at":"2026-05-18T03:27:10.324368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:10.324368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FuJg95C3P7YlPk6udYIEKpvWa+gu6FV+No0Wu6jJS7/KJOkv1f4Rqp51pr4ZdsBq/LdjZUpyPAaCag1/cuGLDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:10.324862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2498","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:647591bfdd939b09122ada27ebd22f6635d2cdbb624291a56393fc4031604217","sha256:b606d5e40abf33a1f548f85573f02a814fe9fe396c72e78d7df8fd78f04fc7dd"],"state_sha256":"49daed49f974826a2230219825048eb3c559f06f78dfc87b03a06a38300f101e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ncxGfIODEy+3Y6L1z0LIx+OUtN0t78rbKolscDZHTNkmZ6I9w4XrLMKve6g9sFCCK+cYbk3SEnt/EPX+ePkBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:53:14.202521Z","bundle_sha256":"da594720efd8e0469d01f5c20d0d0ab0e015a3017fef67472238a00b2e3ac4d2"}}