{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VRF3TNLJT2JUO7NSPUE4QTVSR6","short_pith_number":"pith:VRF3TNLJ","canonical_record":{"source":{"id":"1704.02189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-07T11:22:45Z","cross_cats_sorted":["q-bio.MN"],"title_canon_sha256":"ab07f038aa35482d13d7ebbbe390c6ac03630022d81355df0a2f548caa7b7160","abstract_canon_sha256":"887737878e29f684c27e416eb4da949d2f50bab6ba4f777448ff2b4c52d81f01"},"schema_version":"1.0"},"canonical_sha256":"ac4bb9b5699e93477db27d09c84eb28fbe083485ebce12a9ee61b1aba8657849","source":{"kind":"arxiv","id":"1704.02189","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02189","created_at":"2026-05-18T00:46:50Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02189v1","created_at":"2026-05-18T00:46:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02189","created_at":"2026-05-18T00:46:50Z"},{"alias_kind":"pith_short_12","alias_value":"VRF3TNLJT2JU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VRF3TNLJT2JUO7NS","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VRF3TNLJ","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VRF3TNLJT2JUO7NSPUE4QTVSR6","target":"record","payload":{"canonical_record":{"source":{"id":"1704.02189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-07T11:22:45Z","cross_cats_sorted":["q-bio.MN"],"title_canon_sha256":"ab07f038aa35482d13d7ebbbe390c6ac03630022d81355df0a2f548caa7b7160","abstract_canon_sha256":"887737878e29f684c27e416eb4da949d2f50bab6ba4f777448ff2b4c52d81f01"},"schema_version":"1.0"},"canonical_sha256":"ac4bb9b5699e93477db27d09c84eb28fbe083485ebce12a9ee61b1aba8657849","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:50.478362Z","signature_b64":"O9f/ExxDXXB1omr9erQwew/H0QYmmx04uaY6ZGxKx37uadbHaJwEeY5N3uQ11WQVVoZykHADVr4z4DKSpKJWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac4bb9b5699e93477db27d09c84eb28fbe083485ebce12a9ee61b1aba8657849","last_reissued_at":"2026-05-18T00:46:50.477814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:50.477814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.02189","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":"2026-05-18T00:46:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YCRJoyUybP7GUXeLgo7S3Ffp/pUvAfup3IU6wr10eNRBFMOmHmooJQ3hYtRt3hEBYx0b0D5QMGaRM7jFLUE9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:16:49.317109Z"},"content_sha256":"c7f7f032c21ab9502e2f49cb80ec6d77c03132a3d5a9c6cc40ca60d1fc0fee7e","schema_version":"1.0","event_id":"sha256:c7f7f032c21ab9502e2f49cb80ec6d77c03132a3d5a9c6cc40ca60d1fc0fee7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VRF3TNLJT2JUO7NSPUE4QTVSR6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimality in cellular storage via the Pontryagin Maximum Principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.MN"],"primary_cat":"math.OC","authors_text":"Henning Lindhorst, Steffen Waldherr","submitted_at":"2017-04-07T11:22:45Z","abstract_excerpt":"We study an optimal control problem arising from a resource allocation problem in cellular metabolism. A minimalistic model that describes the production of enzymatic vs. non-enzymatic biomass components from a single nutrient source is introduced. The basic growth modes with this model are linear growth, where only the non-enzymatic component is produced, and exponential growth with only enzymatic components being produced. Using Pontryagin's maximum principle, we derive the optimal growth trajectory depending on the model's parameters. It turns out that depending on the parameters, either a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02189","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":"2026-05-18T00:46:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VIi+iPQ/Y4VMIWvVuVs7J4GCVeE8ibLEZzBJe0egL2cQ18I3vhsG3m8nMCuFoPfDVkWI5DE6hES3n0DQP+hDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:16:49.317786Z"},"content_sha256":"390d7b5668354cc6c3308385610742de0b22b255a94ebceeec26531b726585b1","schema_version":"1.0","event_id":"sha256:390d7b5668354cc6c3308385610742de0b22b255a94ebceeec26531b726585b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRF3TNLJT2JUO7NSPUE4QTVSR6/bundle.json","state_url":"https://pith.science/pith/VRF3TNLJT2JUO7NSPUE4QTVSR6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRF3TNLJT2JUO7NSPUE4QTVSR6/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":"2026-05-26T03:16:49Z","links":{"resolver":"https://pith.science/pith/VRF3TNLJT2JUO7NSPUE4QTVSR6","bundle":"https://pith.science/pith/VRF3TNLJT2JUO7NSPUE4QTVSR6/bundle.json","state":"https://pith.science/pith/VRF3TNLJT2JUO7NSPUE4QTVSR6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRF3TNLJT2JUO7NSPUE4QTVSR6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VRF3TNLJT2JUO7NSPUE4QTVSR6","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":"887737878e29f684c27e416eb4da949d2f50bab6ba4f777448ff2b4c52d81f01","cross_cats_sorted":["q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-07T11:22:45Z","title_canon_sha256":"ab07f038aa35482d13d7ebbbe390c6ac03630022d81355df0a2f548caa7b7160"},"schema_version":"1.0","source":{"id":"1704.02189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02189","created_at":"2026-05-18T00:46:50Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02189v1","created_at":"2026-05-18T00:46:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02189","created_at":"2026-05-18T00:46:50Z"},{"alias_kind":"pith_short_12","alias_value":"VRF3TNLJT2JU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VRF3TNLJT2JUO7NS","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VRF3TNLJ","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:390d7b5668354cc6c3308385610742de0b22b255a94ebceeec26531b726585b1","target":"graph","created_at":"2026-05-18T00:46:50Z","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 study an optimal control problem arising from a resource allocation problem in cellular metabolism. A minimalistic model that describes the production of enzymatic vs. non-enzymatic biomass components from a single nutrient source is introduced. The basic growth modes with this model are linear growth, where only the non-enzymatic component is produced, and exponential growth with only enzymatic components being produced. Using Pontryagin's maximum principle, we derive the optimal growth trajectory depending on the model's parameters. It turns out that depending on the parameters, either a ","authors_text":"Henning Lindhorst, Steffen Waldherr","cross_cats":["q-bio.MN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-07T11:22:45Z","title":"Optimality in cellular storage via the Pontryagin Maximum Principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02189","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:c7f7f032c21ab9502e2f49cb80ec6d77c03132a3d5a9c6cc40ca60d1fc0fee7e","target":"record","created_at":"2026-05-18T00:46:50Z","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":"887737878e29f684c27e416eb4da949d2f50bab6ba4f777448ff2b4c52d81f01","cross_cats_sorted":["q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-07T11:22:45Z","title_canon_sha256":"ab07f038aa35482d13d7ebbbe390c6ac03630022d81355df0a2f548caa7b7160"},"schema_version":"1.0","source":{"id":"1704.02189","kind":"arxiv","version":1}},"canonical_sha256":"ac4bb9b5699e93477db27d09c84eb28fbe083485ebce12a9ee61b1aba8657849","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac4bb9b5699e93477db27d09c84eb28fbe083485ebce12a9ee61b1aba8657849","first_computed_at":"2026-05-18T00:46:50.477814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:50.477814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O9f/ExxDXXB1omr9erQwew/H0QYmmx04uaY6ZGxKx37uadbHaJwEeY5N3uQ11WQVVoZykHADVr4z4DKSpKJWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:50.478362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7f7f032c21ab9502e2f49cb80ec6d77c03132a3d5a9c6cc40ca60d1fc0fee7e","sha256:390d7b5668354cc6c3308385610742de0b22b255a94ebceeec26531b726585b1"],"state_sha256":"0c873a098573960377f5a045317c119a4ca48a64cc84552efad30553aacc080e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nfg+utudtsF/Y8Nz4TthC6BijN5y+HAj9R+oi3J3I2RFQeIMe6vKgqQlPxt8kaqA3VHtfScxOt71qTYBx+zQDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:16:49.320915Z","bundle_sha256":"9b21a13a8f6ff088a4c2eeabc9d428928e35ac6c6089d211e470d35a9ae8e19b"}}