{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:DJTM6AHLNIKJ2NFPBRN6JEZDUI","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":"75eb10e504fc5e996b9aecc562e17050e8cde2b1e2fc044f803b944a2e60ee65","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2005-09-07T06:55:52Z","title_canon_sha256":"b1d4c57bf30636cfafef7aa0d4d943d33b033c745b5fbc05e9c6e0155bc2a7c3"},"schema_version":"1.0","source":{"id":"math/0509141","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0509141","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0509141v2","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509141","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"DJTM6AHLNIKJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DJTM6AHLNIKJ2NFP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DJTM6AHL","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:beb04e1bc387c8f90ab25112562773f4c7640c5ff782bbb4c4a30adad929d2f0","target":"graph","created_at":"2026-05-18T01:38:24Z","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":"Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks which present both discrete and continuous aspects. Our models consist of a network of units, whose states are quantified by a continuous real variable. The state of each unit in the network evolves according to a contractive transformation chosen from a finite collection of possible transformations, according to a rule which depends on the state of the neighbo","authors_text":"Edgardo Ugalde, Ricardo Lima","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2005-09-07T06:55:52Z","title":"Dynamical complexity of discrete time regulatory networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509141","kind":"arxiv","version":2},"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":"sha256:8f0aed0f0c1bc3bc852b0de8894bf56fb3149a62b33c5c62efbab95bfb9e1b7e","target":"record","created_at":"2026-05-18T01:38:24Z","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":"75eb10e504fc5e996b9aecc562e17050e8cde2b1e2fc044f803b944a2e60ee65","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2005-09-07T06:55:52Z","title_canon_sha256":"b1d4c57bf30636cfafef7aa0d4d943d33b033c745b5fbc05e9c6e0155bc2a7c3"},"schema_version":"1.0","source":{"id":"math/0509141","kind":"arxiv","version":2}},"canonical_sha256":"1a66cf00eb6a149d34af0c5be49323a22f632a8ddf1c4cb18ed919deca226d58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a66cf00eb6a149d34af0c5be49323a22f632a8ddf1c4cb18ed919deca226d58","first_computed_at":"2026-05-18T01:38:24.869669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:24.869669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6KY8B+L+Qw6y8Kw+Xe6YI4tcAF6lK2YzL0pXnYNXehIGNZXVNVq6hHIb1XZmTp3w6KMfXrvY0PqMhm7I8N9JCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:24.870500Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0509141","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f0aed0f0c1bc3bc852b0de8894bf56fb3149a62b33c5c62efbab95bfb9e1b7e","sha256:beb04e1bc387c8f90ab25112562773f4c7640c5ff782bbb4c4a30adad929d2f0"],"state_sha256":"d981139fd1f6d09a3cd23403817c79350ba7cfbc2d3c9b41c5dc0d6eb61e0ba0"}