{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3PUSJISH54W3B5JFBIBHBUZXAI","short_pith_number":"pith:3PUSJISH","canonical_record":{"source":{"id":"1709.10345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-27T21:53:11Z","cross_cats_sorted":[],"title_canon_sha256":"2919fe59f5fba5c4647c03ace72d920d6d9ca1229e6bdc1d55e581782c16cb4c","abstract_canon_sha256":"e6aa2343e5830da52c1fa2f6d85f2f281f8046c6a043d252310dbc70465215f4"},"schema_version":"1.0"},"canonical_sha256":"dbe924a247ef2db0f5250a0270d33702011e730e49a21f0428a0f6c00cd72c61","source":{"kind":"arxiv","id":"1709.10345","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10345","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10345v1","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10345","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"3PUSJISH54W3","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3PUSJISH54W3B5JF","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3PUSJISH","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3PUSJISH54W3B5JFBIBHBUZXAI","target":"record","payload":{"canonical_record":{"source":{"id":"1709.10345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-27T21:53:11Z","cross_cats_sorted":[],"title_canon_sha256":"2919fe59f5fba5c4647c03ace72d920d6d9ca1229e6bdc1d55e581782c16cb4c","abstract_canon_sha256":"e6aa2343e5830da52c1fa2f6d85f2f281f8046c6a043d252310dbc70465215f4"},"schema_version":"1.0"},"canonical_sha256":"dbe924a247ef2db0f5250a0270d33702011e730e49a21f0428a0f6c00cd72c61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:03.455433Z","signature_b64":"6NkAkXd9lsQaBsDq9EG80QwFIgfEskeh+zWv1+YTfvHQAsz9whKwLDg1Nb/JbDFH7+vkYRf807OyWUqxo+8wBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbe924a247ef2db0f5250a0270d33702011e730e49a21f0428a0f6c00cd72c61","last_reissued_at":"2026-05-18T00:34:03.454875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:03.454875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.10345","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vTrJcV/gNa+3qwd2edZs4bbAhi21Db6OQzbo7qwG3++ajG2sPnmqEXY5sdGuPbLb0utK5VGjhDq48D2Uob6BDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T13:06:08.966588Z"},"content_sha256":"b67ff877afebcceb4ab04dbb68e6cc37252ca0636ae584fd7416e196e109b740","schema_version":"1.0","event_id":"sha256:b67ff877afebcceb4ab04dbb68e6cc37252ca0636ae584fd7416e196e109b740"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3PUSJISH54W3B5JFBIBHBUZXAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Control of Time-Varying Epidemic-Like Stochastic Processes and Their Mean-Field Limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chai Wah Wu, Mark S. Squillante, Yingdong Lu","submitted_at":"2017-09-27T21:53:11Z","abstract_excerpt":"The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially important to include time-varying parameters that impact viral epidemic-like propagation. We connect the control of such stochastic processes with time-varying behavior to the stochastic shortest path problem and obtain solutions for various cost functions. Then, under a mean-field scaling, this general class of stochastic processes is shown to converge to a corresponding dynamical system. We analogously establish that the optimal control of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10345","kind":"arxiv","version":1},"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":"2026-05-18T00:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1VXQILr0Z4BC8GE2wF0AZMBeBTxTSQF0ai4e3mebTDyfTSZA1vlzMmwQ4SVOJ4Tyef4IxJVVVGkIvUFQgfSkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T13:06:08.967260Z"},"content_sha256":"dfeb2f153535cdff84282e37fb0dc05b70d95e191599329ab2e1ed7d5f946bd9","schema_version":"1.0","event_id":"sha256:dfeb2f153535cdff84282e37fb0dc05b70d95e191599329ab2e1ed7d5f946bd9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3PUSJISH54W3B5JFBIBHBUZXAI/bundle.json","state_url":"https://pith.science/pith/3PUSJISH54W3B5JFBIBHBUZXAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3PUSJISH54W3B5JFBIBHBUZXAI/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":"2026-05-23T13:06:08Z","links":{"resolver":"https://pith.science/pith/3PUSJISH54W3B5JFBIBHBUZXAI","bundle":"https://pith.science/pith/3PUSJISH54W3B5JFBIBHBUZXAI/bundle.json","state":"https://pith.science/pith/3PUSJISH54W3B5JFBIBHBUZXAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3PUSJISH54W3B5JFBIBHBUZXAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3PUSJISH54W3B5JFBIBHBUZXAI","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":"e6aa2343e5830da52c1fa2f6d85f2f281f8046c6a043d252310dbc70465215f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-27T21:53:11Z","title_canon_sha256":"2919fe59f5fba5c4647c03ace72d920d6d9ca1229e6bdc1d55e581782c16cb4c"},"schema_version":"1.0","source":{"id":"1709.10345","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10345","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10345v1","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10345","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"3PUSJISH54W3","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3PUSJISH54W3B5JF","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3PUSJISH","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:dfeb2f153535cdff84282e37fb0dc05b70d95e191599329ab2e1ed7d5f946bd9","target":"graph","created_at":"2026-05-18T00:34:03Z","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":"The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially important to include time-varying parameters that impact viral epidemic-like propagation. We connect the control of such stochastic processes with time-varying behavior to the stochastic shortest path problem and obtain solutions for various cost functions. Then, under a mean-field scaling, this general class of stochastic processes is shown to converge to a corresponding dynamical system. We analogously establish that the optimal control of t","authors_text":"Chai Wah Wu, Mark S. Squillante, Yingdong Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-27T21:53:11Z","title":"Control of Time-Varying Epidemic-Like Stochastic Processes and Their Mean-Field Limits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10345","kind":"arxiv","version":1},"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:b67ff877afebcceb4ab04dbb68e6cc37252ca0636ae584fd7416e196e109b740","target":"record","created_at":"2026-05-18T00:34:03Z","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":"e6aa2343e5830da52c1fa2f6d85f2f281f8046c6a043d252310dbc70465215f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-09-27T21:53:11Z","title_canon_sha256":"2919fe59f5fba5c4647c03ace72d920d6d9ca1229e6bdc1d55e581782c16cb4c"},"schema_version":"1.0","source":{"id":"1709.10345","kind":"arxiv","version":1}},"canonical_sha256":"dbe924a247ef2db0f5250a0270d33702011e730e49a21f0428a0f6c00cd72c61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbe924a247ef2db0f5250a0270d33702011e730e49a21f0428a0f6c00cd72c61","first_computed_at":"2026-05-18T00:34:03.454875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:03.454875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6NkAkXd9lsQaBsDq9EG80QwFIgfEskeh+zWv1+YTfvHQAsz9whKwLDg1Nb/JbDFH7+vkYRf807OyWUqxo+8wBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:03.455433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.10345","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b67ff877afebcceb4ab04dbb68e6cc37252ca0636ae584fd7416e196e109b740","sha256:dfeb2f153535cdff84282e37fb0dc05b70d95e191599329ab2e1ed7d5f946bd9"],"state_sha256":"0addbd1b361e37b3e9d33b3d351a6e8375dcdef6e56516f68d0159e9b153d534"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z2kfZ8SIggyfiZCqB3Wq1eFqM4iHYBVcUlzGoul3cuBrRkz6d0zSMr9QwDLVsQm82GdLl33XHOJXzoxLTwn2Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T13:06:08.971065Z","bundle_sha256":"36222e64c19b98fa480a578a2dcf40d49e6d27c2e6591dc7cae8f7d7aebac497"}}