{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AEDQZ3QIIWSVBDNTWZQTPN3CC6","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":"010eae98dfcd58a83d9899d317e11733dc54e8edcc53c6fb7a3e109fac3fc619","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-09-11T05:40:24Z","title_canon_sha256":"fc86dbf1409b52e489e6979c09958ed8507bcdeded70e3e5a9115ee26d18d84f"},"schema_version":"1.0","source":{"id":"1009.2137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2137","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2137v1","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2137","created_at":"2026-05-18T04:41:04Z"},{"alias_kind":"pith_short_12","alias_value":"AEDQZ3QIIWSV","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AEDQZ3QIIWSVBDNT","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AEDQZ3QI","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:2139b6e8fff098fc3927ca74583b019a5900a98cd08a67ec8bb023f741ead757","target":"graph","created_at":"2026-05-18T04:41:04Z","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 address the question of optimization of the biomass long term productivity in the framework of microalgal biomass production in photobioreactors under the influence of day/night cycles. For that, we propose a simple bioreactor model accounting for light attenuation in the reactor due to biomass density and obtain the control law that optimizes productivity over a single day through the application of Pontryagin's maximum principle, with the dilution rate being the control. An important constraint on the obtained solution is that the biomass in the reactor should be at the same level at the ","authors_text":"Andrei R. Akhmetzhanov (INRIA Sophia Antipolis), Fr\\'ed\\'eric Grognard (INRIA Sophia Antipolis), LAPHAP), Masci Pierre (INRIA Sophia Antipolis), Olivier Bernard (INRIA Sophia Antipolis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-09-11T05:40:24Z","title":"Optimization of a photobioreactor biomass production using natural light"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2137","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":"sha256:7929cda0be7ea82632f87abf83b741024fcedc089990e559d052cbbf73726a2b","target":"record","created_at":"2026-05-18T04:41:04Z","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":"010eae98dfcd58a83d9899d317e11733dc54e8edcc53c6fb7a3e109fac3fc619","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-09-11T05:40:24Z","title_canon_sha256":"fc86dbf1409b52e489e6979c09958ed8507bcdeded70e3e5a9115ee26d18d84f"},"schema_version":"1.0","source":{"id":"1009.2137","kind":"arxiv","version":1}},"canonical_sha256":"01070cee0845a5508db3b66137b762178d665bb5f52836c0b89f58fe84c40c7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01070cee0845a5508db3b66137b762178d665bb5f52836c0b89f58fe84c40c7c","first_computed_at":"2026-05-18T04:41:04.718286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:04.718286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fm1SOJiilXYMpUJybkB8mbukRlQjfUC/H6MODEq3yhppjAiBVy8LBbLLmJ8gzgNTw/VaXqpPxWOKDQXvTxzcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:04.718706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7929cda0be7ea82632f87abf83b741024fcedc089990e559d052cbbf73726a2b","sha256:2139b6e8fff098fc3927ca74583b019a5900a98cd08a67ec8bb023f741ead757"],"state_sha256":"49fed0c6db508d6d30034d2e3b49037e45fdf11991f132bd4f79ca4726b20f4b"}