{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XHDQRUZCPXCKGR3XYA2CORWLF3","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":"aa14abadb2f38a9ce4d8b3cc8972bd5970cd6e66632c972a5df28178a239de0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-11-24T04:37:20Z","title_canon_sha256":"f9a19415d68596b4b23f21454010b3efb30b5ee2a882e39ceb3a7f03a9bac9b7"},"schema_version":"1.0","source":{"id":"1211.5646","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.5646","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"arxiv_version","alias_value":"1211.5646v4","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5646","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"pith_short_12","alias_value":"XHDQRUZCPXCK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XHDQRUZCPXCKGR3X","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XHDQRUZC","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:106a350843a7697c6963591237e2a7bdf11aee443cbf4b4360ff9860fe60c944","target":"graph","created_at":"2026-05-18T02:30:01Z","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":"Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here develop a quasispecies theory for the dynamics of modularity in populations of these systems. We show how the steady-state fitness in a randomly changing environment can be computed. We derive a fluctuation dissipation relation for the rate of change of modularity and use it to derive a relationship between rate of environmental changes and rate of growth of modu","authors_text":"Jeong-Man Park, Liang Ren Niestemski, Michael W. Deem","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-11-24T04:37:20Z","title":"Quasispecies Theory for Evolution of Modularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5646","kind":"arxiv","version":4},"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:c040acd853df74af2c785937a59ead62334a8c59cea4a7524d9264c0029edbee","target":"record","created_at":"2026-05-18T02:30:01Z","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":"aa14abadb2f38a9ce4d8b3cc8972bd5970cd6e66632c972a5df28178a239de0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-11-24T04:37:20Z","title_canon_sha256":"f9a19415d68596b4b23f21454010b3efb30b5ee2a882e39ceb3a7f03a9bac9b7"},"schema_version":"1.0","source":{"id":"1211.5646","kind":"arxiv","version":4}},"canonical_sha256":"b9c708d3227dc4a34777c0342746cb2ee698d806a9744327df1bdd5734ee30ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9c708d3227dc4a34777c0342746cb2ee698d806a9744327df1bdd5734ee30ad","first_computed_at":"2026-05-18T02:30:01.398122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:01.398122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"heFic7KfpOgS5FDZthprQ+dkCmDpvNQnm+8AFYlWgzy6+j4h9woE2rvpHRohou6CrT646YJU+/GeN5G5hvBUCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:01.398586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.5646","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c040acd853df74af2c785937a59ead62334a8c59cea4a7524d9264c0029edbee","sha256:106a350843a7697c6963591237e2a7bdf11aee443cbf4b4360ff9860fe60c944"],"state_sha256":"52ff42e564b2b9429d59f96428a0616f12f9b806be5a3ae5ddcebe068411b3a1"}