{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2TWCXUNDMKSVF65HHG3OWYHEQS","short_pith_number":"pith:2TWCXUND","schema_version":"1.0","canonical_sha256":"d4ec2bd1a362a552fba739b6eb60e484b39f74ae9084c7b8e928f3fffa46b5b8","source":{"kind":"arxiv","id":"2607.01347","version":1},"attestation_state":"computed","paper":{"title":"Bilinear control of age--space structured populations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jiguang Yu, Louis Shuo Wang","submitted_at":"2026-07-01T18:05:22Z","abstract_excerpt":"We study constrained bilinear optimal control for nonlocal age--space structured population equations with renewal boundary conditions and endogenous surveillance feedback. The control acts as a coefficient in a mixed transport--diffusion equation, while a scalar observable generated by the state enters both the interior dynamics and the renewal law. This produces a nonlinear closed-loop control-to-state map and a feedback-dependent adjoint system. Using a characteristic mild formulation rather than a standard Lions--Magenes argument, we establish closed-loop well-posedness and Frechet differe"},"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":"2607.01347","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-01T18:05:22Z","cross_cats_sorted":[],"title_canon_sha256":"319051fa92a187f51d73e9a8d7341742cac1850b3c07a03dcfa210d87200f334","abstract_canon_sha256":"b4069b0dd17a8270806902676bb9277e8a42e04f02e86e91b1ee95361b5e9dfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T00:16:58.013066Z","signature_b64":"9KKxRdoaTnplqJXK7lOgURpjW9acwPxN/3syMM2G/vm3r818iuCT2zIZrsQrzTSd8+Tg6TChDXhbd8utogQaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4ec2bd1a362a552fba739b6eb60e484b39f74ae9084c7b8e928f3fffa46b5b8","last_reissued_at":"2026-07-03T00:16:58.012732Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T00:16:58.012732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bilinear control of age--space structured populations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jiguang Yu, Louis Shuo Wang","submitted_at":"2026-07-01T18:05:22Z","abstract_excerpt":"We study constrained bilinear optimal control for nonlocal age--space structured population equations with renewal boundary conditions and endogenous surveillance feedback. The control acts as a coefficient in a mixed transport--diffusion equation, while a scalar observable generated by the state enters both the interior dynamics and the renewal law. This produces a nonlinear closed-loop control-to-state map and a feedback-dependent adjoint system. Using a characteristic mild formulation rather than a standard Lions--Magenes argument, we establish closed-loop well-posedness and Frechet differe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01347","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.01347/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.01347","created_at":"2026-07-03T00:16:58.012786+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.01347v1","created_at":"2026-07-03T00:16:58.012786+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01347","created_at":"2026-07-03T00:16:58.012786+00:00"},{"alias_kind":"pith_short_12","alias_value":"2TWCXUNDMKSV","created_at":"2026-07-03T00:16:58.012786+00:00"},{"alias_kind":"pith_short_16","alias_value":"2TWCXUNDMKSVF65H","created_at":"2026-07-03T00:16:58.012786+00:00"},{"alias_kind":"pith_short_8","alias_value":"2TWCXUND","created_at":"2026-07-03T00:16:58.012786+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/2TWCXUNDMKSVF65HHG3OWYHEQS","json":"https://pith.science/pith/2TWCXUNDMKSVF65HHG3OWYHEQS.json","graph_json":"https://pith.science/api/pith-number/2TWCXUNDMKSVF65HHG3OWYHEQS/graph.json","events_json":"https://pith.science/api/pith-number/2TWCXUNDMKSVF65HHG3OWYHEQS/events.json","paper":"https://pith.science/paper/2TWCXUND"},"agent_actions":{"view_html":"https://pith.science/pith/2TWCXUNDMKSVF65HHG3OWYHEQS","download_json":"https://pith.science/pith/2TWCXUNDMKSVF65HHG3OWYHEQS.json","view_paper":"https://pith.science/paper/2TWCXUND","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.01347&json=true","fetch_graph":"https://pith.science/api/pith-number/2TWCXUNDMKSVF65HHG3OWYHEQS/graph.json","fetch_events":"https://pith.science/api/pith-number/2TWCXUNDMKSVF65HHG3OWYHEQS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2TWCXUNDMKSVF65HHG3OWYHEQS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2TWCXUNDMKSVF65HHG3OWYHEQS/action/storage_attestation","attest_author":"https://pith.science/pith/2TWCXUNDMKSVF65HHG3OWYHEQS/action/author_attestation","sign_citation":"https://pith.science/pith/2TWCXUNDMKSVF65HHG3OWYHEQS/action/citation_signature","submit_replication":"https://pith.science/pith/2TWCXUNDMKSVF65HHG3OWYHEQS/action/replication_record"}},"created_at":"2026-07-03T00:16:58.012786+00:00","updated_at":"2026-07-03T00:16:58.012786+00:00"}