{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HVWB7CYGGKY5SM7Q6QXSZG5OZA","short_pith_number":"pith:HVWB7CYG","canonical_record":{"source":{"id":"1512.00216","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-01T10:40:18Z","cross_cats_sorted":[],"title_canon_sha256":"35b6318b80c2dce07e6f6edcfde14fc6260087cdef2e9c947155456dd795452c","abstract_canon_sha256":"1dce6aea3dd50e5d0e4c52e4ee23bce92b0a90d88eb9c84b9e8f43f5c485d4bd"},"schema_version":"1.0"},"canonical_sha256":"3d6c1f8b0632b1d933f0f42f2c9baec831553c96b4e61bdbe54079aaa1af5ef3","source":{"kind":"arxiv","id":"1512.00216","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00216","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00216v3","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00216","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"HVWB7CYGGKY5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HVWB7CYGGKY5SM7Q","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HVWB7CYG","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HVWB7CYGGKY5SM7Q6QXSZG5OZA","target":"record","payload":{"canonical_record":{"source":{"id":"1512.00216","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-01T10:40:18Z","cross_cats_sorted":[],"title_canon_sha256":"35b6318b80c2dce07e6f6edcfde14fc6260087cdef2e9c947155456dd795452c","abstract_canon_sha256":"1dce6aea3dd50e5d0e4c52e4ee23bce92b0a90d88eb9c84b9e8f43f5c485d4bd"},"schema_version":"1.0"},"canonical_sha256":"3d6c1f8b0632b1d933f0f42f2c9baec831553c96b4e61bdbe54079aaa1af5ef3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:02.308208Z","signature_b64":"sQUJnB9jl8li0RNkRHnMXcaPY50X8risZh3q0CKVE5FLAV4iPZIzqDWzv0jsnIXIJheWaWBgvnMv8Mx1oxrpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d6c1f8b0632b1d933f0f42f2c9baec831553c96b4e61bdbe54079aaa1af5ef3","last_reissued_at":"2026-05-18T00:41:02.307468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:02.307468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.00216","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":"2026-05-18T00:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8J3272m9tt8A7rOVjsQepdb8y44hhYAZ2a/Ys2iDUouII+7LACTL3VBfv99CG8GpmIZ8C72P+dDvAq0p5IZ1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T12:34:26.094221Z"},"content_sha256":"a3a182d599cbcb1d11ac533b8b79a7fd7fa4e7097daa968e091e3e31164ce40d","schema_version":"1.0","event_id":"sha256:a3a182d599cbcb1d11ac533b8b79a7fd7fa4e7097daa968e091e3e31164ce40d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HVWB7CYGGKY5SM7Q6QXSZG5OZA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal control of Markov jump processes : Asymptotic analysis, algorithms and applications to the modelling of chemical reaction systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carsten Hartmann, Max von Kleist, Wei Zhang","submitted_at":"2015-12-01T10:40:18Z","abstract_excerpt":"Markov jump processes are widely used to model natural and engineered processes. In the context of biological or chemical applications one typically refers to the chemical master equation (CME), which models the evolution of the probability mass of any copy-number combination of the interacting particles. When many interacting particles (\"species\") are considered, the complexity of the CME quickly increases, making direct numerical simulations impossible. This is even more problematic when one aims at controlling the Markov jump processes defined by the CME. In this work, we study both open lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00216","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":"2026-05-18T00:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s8oI+T8UhBy1wz6vYbKSIwEd3Q3zqZJMYDq1ZtXkI+QmO1qTaRKBA+nT63m38Qcci4CiCV68YNDCyo7LS/u/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T12:34:26.094627Z"},"content_sha256":"4631502e0e6415eab45ce16a6416e2d5db354e9bc61ddeed1542b7d7989fbb04","schema_version":"1.0","event_id":"sha256:4631502e0e6415eab45ce16a6416e2d5db354e9bc61ddeed1542b7d7989fbb04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HVWB7CYGGKY5SM7Q6QXSZG5OZA/bundle.json","state_url":"https://pith.science/pith/HVWB7CYGGKY5SM7Q6QXSZG5OZA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HVWB7CYGGKY5SM7Q6QXSZG5OZA/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":"2026-06-24T12:34:26Z","links":{"resolver":"https://pith.science/pith/HVWB7CYGGKY5SM7Q6QXSZG5OZA","bundle":"https://pith.science/pith/HVWB7CYGGKY5SM7Q6QXSZG5OZA/bundle.json","state":"https://pith.science/pith/HVWB7CYGGKY5SM7Q6QXSZG5OZA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HVWB7CYGGKY5SM7Q6QXSZG5OZA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HVWB7CYGGKY5SM7Q6QXSZG5OZA","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":"1dce6aea3dd50e5d0e4c52e4ee23bce92b0a90d88eb9c84b9e8f43f5c485d4bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-01T10:40:18Z","title_canon_sha256":"35b6318b80c2dce07e6f6edcfde14fc6260087cdef2e9c947155456dd795452c"},"schema_version":"1.0","source":{"id":"1512.00216","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00216","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00216v3","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00216","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"HVWB7CYGGKY5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HVWB7CYGGKY5SM7Q","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HVWB7CYG","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:4631502e0e6415eab45ce16a6416e2d5db354e9bc61ddeed1542b7d7989fbb04","target":"graph","created_at":"2026-05-18T00:41:02Z","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":"Markov jump processes are widely used to model natural and engineered processes. In the context of biological or chemical applications one typically refers to the chemical master equation (CME), which models the evolution of the probability mass of any copy-number combination of the interacting particles. When many interacting particles (\"species\") are considered, the complexity of the CME quickly increases, making direct numerical simulations impossible. This is even more problematic when one aims at controlling the Markov jump processes defined by the CME. In this work, we study both open lo","authors_text":"Carsten Hartmann, Max von Kleist, Wei Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-01T10:40:18Z","title":"Optimal control of Markov jump processes : Asymptotic analysis, algorithms and applications to the modelling of chemical reaction systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00216","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:a3a182d599cbcb1d11ac533b8b79a7fd7fa4e7097daa968e091e3e31164ce40d","target":"record","created_at":"2026-05-18T00:41:02Z","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":"1dce6aea3dd50e5d0e4c52e4ee23bce92b0a90d88eb9c84b9e8f43f5c485d4bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-01T10:40:18Z","title_canon_sha256":"35b6318b80c2dce07e6f6edcfde14fc6260087cdef2e9c947155456dd795452c"},"schema_version":"1.0","source":{"id":"1512.00216","kind":"arxiv","version":3}},"canonical_sha256":"3d6c1f8b0632b1d933f0f42f2c9baec831553c96b4e61bdbe54079aaa1af5ef3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d6c1f8b0632b1d933f0f42f2c9baec831553c96b4e61bdbe54079aaa1af5ef3","first_computed_at":"2026-05-18T00:41:02.307468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:02.307468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sQUJnB9jl8li0RNkRHnMXcaPY50X8risZh3q0CKVE5FLAV4iPZIzqDWzv0jsnIXIJheWaWBgvnMv8Mx1oxrpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:02.308208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00216","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3a182d599cbcb1d11ac533b8b79a7fd7fa4e7097daa968e091e3e31164ce40d","sha256:4631502e0e6415eab45ce16a6416e2d5db354e9bc61ddeed1542b7d7989fbb04"],"state_sha256":"9671c0b4b162134b18d91fee02906a7eab50b23d0ec7dab845e13dc06ba2741e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x28N+UmfrcI2HRdQMZcPD+vazaqJNIb7hlQfUuUnNBmD2yzCH6rfPWG9eplPXV5TK2DZf5Z76/GDDnR8j2EzBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T12:34:26.096582Z","bundle_sha256":"fe6742488043f1e0b37a7b60c2a00117523f9150638180e9f53b07d6703cc674"}}