{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SPEM5OYQOZXUKBTI2IPBIGLMFX","short_pith_number":"pith:SPEM5OYQ","canonical_record":{"source":{"id":"1611.09984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-30T03:23:36Z","cross_cats_sorted":["cs.SY","math.DS"],"title_canon_sha256":"42beab51fce99550184faeb37ca76ebeff39886d5fb19136fb1085e9fc02beb7","abstract_canon_sha256":"1acc1d7fb88ab67a1f3616d15c0279d28dd553c4cd4fc393189877573d2218e1"},"schema_version":"1.0"},"canonical_sha256":"93c8cebb10766f450668d21e14196c2df45332625028905adb8cbf2353820b43","source":{"kind":"arxiv","id":"1611.09984","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09984","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09984v1","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09984","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"SPEM5OYQOZXU","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SPEM5OYQOZXUKBTI","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SPEM5OYQ","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SPEM5OYQOZXUKBTI2IPBIGLMFX","target":"record","payload":{"canonical_record":{"source":{"id":"1611.09984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-30T03:23:36Z","cross_cats_sorted":["cs.SY","math.DS"],"title_canon_sha256":"42beab51fce99550184faeb37ca76ebeff39886d5fb19136fb1085e9fc02beb7","abstract_canon_sha256":"1acc1d7fb88ab67a1f3616d15c0279d28dd553c4cd4fc393189877573d2218e1"},"schema_version":"1.0"},"canonical_sha256":"93c8cebb10766f450668d21e14196c2df45332625028905adb8cbf2353820b43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:11.468627Z","signature_b64":"LNzrc/niDdTojv34+rtYtf8bTSQ4a7upUgTn1+ZIm/nJqM9z5LK00sA8umVxnR0UUnECSikR2gZ5QzKeZNA0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93c8cebb10766f450668d21e14196c2df45332625028905adb8cbf2353820b43","last_reissued_at":"2026-05-18T00:56:11.467962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:11.467962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.09984","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":"2026-05-18T00:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OB3TGtei3pf0FjEj49IVa3fJ6Wcd5tj48Kk6wAuedXDT+OUvUWd/1Rvgjgpz+cDRqMV+UWy9S8vdpEgz1agWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:14:34.487113Z"},"content_sha256":"a2f751915fdbcf53fe26a50c436a041cb58140378f28578878d424f6b11f800e","schema_version":"1.0","event_id":"sha256:a2f751915fdbcf53fe26a50c436a041cb58140378f28578878d424f6b11f800e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SPEM5OYQOZXUKBTI2IPBIGLMFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the optimal control problem for a class of monotone bilinear systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.DS"],"primary_cat":"math.OC","authors_text":"Anders Rantzer, Marcello Colombino, Mihailo R. Jovanovi\\'c, Neil K. Dhingra, Roy S. Smith","submitted_at":"2016-11-30T03:23:36Z","abstract_excerpt":"We consider a class of monotone systems in which the control signal multiplies the state. Among other applications, such bilinear systems can be used to model the evolutionary dynamics of HIV in the presence of combination drug therapy. For this class of systems, we formulate an infinite horizon optimal control problem, prove that the optimal control signal is constant over time, and show that it can be computed by solving a finite-dimensional non-smooth convex optimization problem. We provide an explicit expression for the subdifferential set of the objective function and use a subgradient al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09984","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":"2026-05-18T00:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8FqJofDZcY/TCdW0KxEcPa0slMcrI0MuqoyIGp8h1U9sYN0UXyEKvgLmZkwS5EzxOmwe8E4vu1EJPjd6pJRPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:14:34.487477Z"},"content_sha256":"91018cb70cbbc4bcf2d5f79eb8b09848cdc41a5a398baf5453917225d0351d81","schema_version":"1.0","event_id":"sha256:91018cb70cbbc4bcf2d5f79eb8b09848cdc41a5a398baf5453917225d0351d81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SPEM5OYQOZXUKBTI2IPBIGLMFX/bundle.json","state_url":"https://pith.science/pith/SPEM5OYQOZXUKBTI2IPBIGLMFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SPEM5OYQOZXUKBTI2IPBIGLMFX/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":"2026-06-02T04:14:34Z","links":{"resolver":"https://pith.science/pith/SPEM5OYQOZXUKBTI2IPBIGLMFX","bundle":"https://pith.science/pith/SPEM5OYQOZXUKBTI2IPBIGLMFX/bundle.json","state":"https://pith.science/pith/SPEM5OYQOZXUKBTI2IPBIGLMFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SPEM5OYQOZXUKBTI2IPBIGLMFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SPEM5OYQOZXUKBTI2IPBIGLMFX","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":"1acc1d7fb88ab67a1f3616d15c0279d28dd553c4cd4fc393189877573d2218e1","cross_cats_sorted":["cs.SY","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-30T03:23:36Z","title_canon_sha256":"42beab51fce99550184faeb37ca76ebeff39886d5fb19136fb1085e9fc02beb7"},"schema_version":"1.0","source":{"id":"1611.09984","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09984","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09984v1","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09984","created_at":"2026-05-18T00:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"SPEM5OYQOZXU","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SPEM5OYQOZXUKBTI","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SPEM5OYQ","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:91018cb70cbbc4bcf2d5f79eb8b09848cdc41a5a398baf5453917225d0351d81","target":"graph","created_at":"2026-05-18T00:56:11Z","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 class of monotone systems in which the control signal multiplies the state. Among other applications, such bilinear systems can be used to model the evolutionary dynamics of HIV in the presence of combination drug therapy. For this class of systems, we formulate an infinite horizon optimal control problem, prove that the optimal control signal is constant over time, and show that it can be computed by solving a finite-dimensional non-smooth convex optimization problem. We provide an explicit expression for the subdifferential set of the objective function and use a subgradient al","authors_text":"Anders Rantzer, Marcello Colombino, Mihailo R. Jovanovi\\'c, Neil K. Dhingra, Roy S. Smith","cross_cats":["cs.SY","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-30T03:23:36Z","title":"On the optimal control problem for a class of monotone bilinear systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09984","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:a2f751915fdbcf53fe26a50c436a041cb58140378f28578878d424f6b11f800e","target":"record","created_at":"2026-05-18T00:56:11Z","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":"1acc1d7fb88ab67a1f3616d15c0279d28dd553c4cd4fc393189877573d2218e1","cross_cats_sorted":["cs.SY","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-30T03:23:36Z","title_canon_sha256":"42beab51fce99550184faeb37ca76ebeff39886d5fb19136fb1085e9fc02beb7"},"schema_version":"1.0","source":{"id":"1611.09984","kind":"arxiv","version":1}},"canonical_sha256":"93c8cebb10766f450668d21e14196c2df45332625028905adb8cbf2353820b43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93c8cebb10766f450668d21e14196c2df45332625028905adb8cbf2353820b43","first_computed_at":"2026-05-18T00:56:11.467962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:11.467962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LNzrc/niDdTojv34+rtYtf8bTSQ4a7upUgTn1+ZIm/nJqM9z5LK00sA8umVxnR0UUnECSikR2gZ5QzKeZNA0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:11.468627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09984","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2f751915fdbcf53fe26a50c436a041cb58140378f28578878d424f6b11f800e","sha256:91018cb70cbbc4bcf2d5f79eb8b09848cdc41a5a398baf5453917225d0351d81"],"state_sha256":"be664a2f233fcfd4855b19b52adaa22db537740be47bcb9b430fef393f28baaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tS3fcwlMU9XHfpIJQq0sPVBtVZpXX1unDk3GPM5zsMrMxJdU0UfW5tS5vwCjQ09je3ribQ7RF4aWONAkvhY8Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:14:34.489437Z","bundle_sha256":"df4092311d3275a357939ccb2df9b340d1186f737258d4f59b5b50228cd7f414"}}