{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HUYSTN7VUHEFSBVQKRMTCJTLV7","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":"c42a40e6e3896def617c07b5268f2c0386a66eeca2cf8de5fec5c6b331dc5add","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2011-10-27T11:15:12Z","title_canon_sha256":"df841649ce3c19cfba266bd0ed26cc6fc1703a5ee4963423010b1e9590977f0e"},"schema_version":"1.0","source":{"id":"1110.6051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6051","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6051v1","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6051","created_at":"2026-05-18T04:10:09Z"},{"alias_kind":"pith_short_12","alias_value":"HUYSTN7VUHEF","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HUYSTN7VUHEFSBVQ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HUYSTN7V","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:61b5143a73c40e795916356f8dc287c4488d9d58ffa86fd194a8eccedd370df5","target":"graph","created_at":"2026-05-18T04:10:09Z","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":"Background: A classical problem in metabolic design is to maximize the production of desired compound in a given chemical reaction network by appropriately directing the mass flow through the network. Computationally, this problem is addressed as a linear optimization problem over the \"flux cone\". The prior construction of the flux cone is computationally expensive and no polynomial-time algorithms are known.\nResults: Here we show that the output maximization problem in chemical reaction networks is NP-complete. This statement remains true even if all reactions are monomolecular or bimolecular","authors_text":"Christoph Flamm, Daniel Merkle, Jakob L. Andersen, Peter F. Stadler","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2011-10-27T11:15:12Z","title":"Maximizing Output and Recognizing Autocatalysis in Chemical Reaction Networks is NP-Complete"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6051","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":"sha256:578dfe03a74071002838fa21159943eb3b7bf91ce6f3c869547f6ce69507a736","target":"record","created_at":"2026-05-18T04:10:09Z","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":"c42a40e6e3896def617c07b5268f2c0386a66eeca2cf8de5fec5c6b331dc5add","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2011-10-27T11:15:12Z","title_canon_sha256":"df841649ce3c19cfba266bd0ed26cc6fc1703a5ee4963423010b1e9590977f0e"},"schema_version":"1.0","source":{"id":"1110.6051","kind":"arxiv","version":1}},"canonical_sha256":"3d3129b7f5a1c85906b0545931266bafc703debefc5a5350ae9fa274586fd48f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d3129b7f5a1c85906b0545931266bafc703debefc5a5350ae9fa274586fd48f","first_computed_at":"2026-05-18T04:10:09.821785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:09.821785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6MWE/fZF7MhTjExYLPRMZcTnP1iG745Yrvj6I1xLdazE1vga27cLpBrxpUZQ3z/VtN1Jo/NAWq2gOb7kaBskCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:09.822223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:578dfe03a74071002838fa21159943eb3b7bf91ce6f3c869547f6ce69507a736","sha256:61b5143a73c40e795916356f8dc287c4488d9d58ffa86fd194a8eccedd370df5"],"state_sha256":"55318deb5b86744a53b607ee50f3eb30725c33c6a6eeb3d1ea864bb95e48f291"}