{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:DJTM6AHLNIKJ2NFPBRN6JEZDUI","short_pith_number":"pith:DJTM6AHL","schema_version":"1.0","canonical_sha256":"1a66cf00eb6a149d34af0c5be49323a22f632a8ddf1c4cb18ed919deca226d58","source":{"kind":"arxiv","id":"math/0509141","version":2},"attestation_state":"computed","paper":{"title":"Dynamical complexity of discrete time regulatory networks","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Edgardo Ugalde, Ricardo Lima","submitted_at":"2005-09-07T06:55:52Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0509141","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2005-09-07T06:55:52Z","cross_cats_sorted":[],"title_canon_sha256":"b1d4c57bf30636cfafef7aa0d4d943d33b033c745b5fbc05e9c6e0155bc2a7c3","abstract_canon_sha256":"75eb10e504fc5e996b9aecc562e17050e8cde2b1e2fc044f803b944a2e60ee65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:24.870500Z","signature_b64":"6KY8B+L+Qw6y8Kw+Xe6YI4tcAF6lK2YzL0pXnYNXehIGNZXVNVq6hHIb1XZmTp3w6KMfXrvY0PqMhm7I8N9JCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a66cf00eb6a149d34af0c5be49323a22f632a8ddf1c4cb18ed919deca226d58","last_reissued_at":"2026-05-18T01:38:24.869669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:24.869669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamical complexity of discrete time regulatory networks","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Edgardo Ugalde, Ricardo Lima","submitted_at":"2005-09-07T06:55:52Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509141","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0509141","created_at":"2026-05-18T01:38:24.869806+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0509141v2","created_at":"2026-05-18T01:38:24.869806+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0509141","created_at":"2026-05-18T01:38:24.869806+00:00"},{"alias_kind":"pith_short_12","alias_value":"DJTM6AHLNIKJ","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"DJTM6AHLNIKJ2NFP","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"DJTM6AHL","created_at":"2026-05-18T12:25:53.335082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DJTM6AHLNIKJ2NFPBRN6JEZDUI","json":"https://pith.science/pith/DJTM6AHLNIKJ2NFPBRN6JEZDUI.json","graph_json":"https://pith.science/api/pith-number/DJTM6AHLNIKJ2NFPBRN6JEZDUI/graph.json","events_json":"https://pith.science/api/pith-number/DJTM6AHLNIKJ2NFPBRN6JEZDUI/events.json","paper":"https://pith.science/paper/DJTM6AHL"},"agent_actions":{"view_html":"https://pith.science/pith/DJTM6AHLNIKJ2NFPBRN6JEZDUI","download_json":"https://pith.science/pith/DJTM6AHLNIKJ2NFPBRN6JEZDUI.json","view_paper":"https://pith.science/paper/DJTM6AHL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0509141&json=true","fetch_graph":"https://pith.science/api/pith-number/DJTM6AHLNIKJ2NFPBRN6JEZDUI/graph.json","fetch_events":"https://pith.science/api/pith-number/DJTM6AHLNIKJ2NFPBRN6JEZDUI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DJTM6AHLNIKJ2NFPBRN6JEZDUI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DJTM6AHLNIKJ2NFPBRN6JEZDUI/action/storage_attestation","attest_author":"https://pith.science/pith/DJTM6AHLNIKJ2NFPBRN6JEZDUI/action/author_attestation","sign_citation":"https://pith.science/pith/DJTM6AHLNIKJ2NFPBRN6JEZDUI/action/citation_signature","submit_replication":"https://pith.science/pith/DJTM6AHLNIKJ2NFPBRN6JEZDUI/action/replication_record"}},"created_at":"2026-05-18T01:38:24.869806+00:00","updated_at":"2026-05-18T01:38:24.869806+00:00"}