{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BJFWO57AE5RE73U7K37OPJVO4W","short_pith_number":"pith:BJFWO57A","schema_version":"1.0","canonical_sha256":"0a4b6777e027624fee9f56fee7a6aee5981c87aba05b505f4109d09a76cf1912","source":{"kind":"arxiv","id":"1610.06655","version":2},"attestation_state":"computed","paper":{"title":"Immune Therapeutic Strategies Using Optimal Controls with $L^1$ and $L^2$ Type Objectives","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Judy Day, Ouassim Bara, Seddik Djouadi, Suzanne Lenhart","submitted_at":"2016-10-21T02:41:56Z","abstract_excerpt":"Therapeutic strategies to correct an excessive immune response to pathogenic infection is investigated as an optimal control problem. The control problem is formulated around a four dimensional mathematical model describing the inflammatory response to a pathogenic insult with two therapeutic control inputs which have either a direct pro- or anti-inflammatory effect in the given system. We use Pontryagin's maximum principle and discuss necessary optimality conditions. We consider both an $L^1$ type objective functional as well as an $L^2$ type objective. For the former, the presence of singula"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.06655","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2016-10-21T02:41:56Z","cross_cats_sorted":[],"title_canon_sha256":"05c24e25b63c74b52afccb8a9691f821e474f236ba551737130baa713207532d","abstract_canon_sha256":"7cc734ff91f4281f2a0348532d6db1b6396fb97d57c673c8fdd398633ca743ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:07.932844Z","signature_b64":"/YtLdS+1q1ArR8M7LfCKIqrK8wc4Y7XBtFkO1Ih3V0mf/5c5i40b6q6O2yetn76fkPfy3DHGsa8C2ksgPUGpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a4b6777e027624fee9f56fee7a6aee5981c87aba05b505f4109d09a76cf1912","last_reissued_at":"2026-05-18T00:46:07.932440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:07.932440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Immune Therapeutic Strategies Using Optimal Controls with $L^1$ and $L^2$ Type Objectives","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Judy Day, Ouassim Bara, Seddik Djouadi, Suzanne Lenhart","submitted_at":"2016-10-21T02:41:56Z","abstract_excerpt":"Therapeutic strategies to correct an excessive immune response to pathogenic infection is investigated as an optimal control problem. The control problem is formulated around a four dimensional mathematical model describing the inflammatory response to a pathogenic insult with two therapeutic control inputs which have either a direct pro- or anti-inflammatory effect in the given system. We use Pontryagin's maximum principle and discuss necessary optimality conditions. We consider both an $L^1$ type objective functional as well as an $L^2$ type objective. For the former, the presence of singula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06655","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.06655","created_at":"2026-05-18T00:46:07.932499+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.06655v2","created_at":"2026-05-18T00:46:07.932499+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06655","created_at":"2026-05-18T00:46:07.932499+00:00"},{"alias_kind":"pith_short_12","alias_value":"BJFWO57AE5RE","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"BJFWO57AE5RE73U7","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"BJFWO57A","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BJFWO57AE5RE73U7K37OPJVO4W","json":"https://pith.science/pith/BJFWO57AE5RE73U7K37OPJVO4W.json","graph_json":"https://pith.science/api/pith-number/BJFWO57AE5RE73U7K37OPJVO4W/graph.json","events_json":"https://pith.science/api/pith-number/BJFWO57AE5RE73U7K37OPJVO4W/events.json","paper":"https://pith.science/paper/BJFWO57A"},"agent_actions":{"view_html":"https://pith.science/pith/BJFWO57AE5RE73U7K37OPJVO4W","download_json":"https://pith.science/pith/BJFWO57AE5RE73U7K37OPJVO4W.json","view_paper":"https://pith.science/paper/BJFWO57A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.06655&json=true","fetch_graph":"https://pith.science/api/pith-number/BJFWO57AE5RE73U7K37OPJVO4W/graph.json","fetch_events":"https://pith.science/api/pith-number/BJFWO57AE5RE73U7K37OPJVO4W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BJFWO57AE5RE73U7K37OPJVO4W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BJFWO57AE5RE73U7K37OPJVO4W/action/storage_attestation","attest_author":"https://pith.science/pith/BJFWO57AE5RE73U7K37OPJVO4W/action/author_attestation","sign_citation":"https://pith.science/pith/BJFWO57AE5RE73U7K37OPJVO4W/action/citation_signature","submit_replication":"https://pith.science/pith/BJFWO57AE5RE73U7K37OPJVO4W/action/replication_record"}},"created_at":"2026-05-18T00:46:07.932499+00:00","updated_at":"2026-05-18T00:46:07.932499+00:00"}