{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:HFE572CC4A4E2CJICHIWSJLPNM","short_pith_number":"pith:HFE572CC","schema_version":"1.0","canonical_sha256":"3949dfe842e0384d092811d169256f6b38b89faa120c3873b68a9ea429024d83","source":{"kind":"arxiv","id":"1905.03407","version":1},"attestation_state":"computed","paper":{"title":"Chaos in a continuous-time Boolean network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"math.DS","authors_text":"Roderick Edwards","submitted_at":"2019-05-09T01:55:51Z","abstract_excerpt":"Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range of behaviors but are mathematically more tractable. The form of an underlying discrete (fractional-linear) map encodes information on existence, stability and exact periods of periodic orbits. In richly connected structures with four or more variables, aperiodic behaviour can occur. We investigate a simple 4-dimensional example with Boolean interaction terms "},"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":"1905.03407","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-09T01:55:51Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"4f256654ae5e1648b6ecbaea1b1443f4b5ef29ed136222859c6e2ece791925cc","abstract_canon_sha256":"3e5b3d81c70aaec406ef0a4b0bfc828df3e05a78d1039b81bff7ccdb3e90932e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:40.040774Z","signature_b64":"eZn1rJ9ZJqug3qD+HLP4NKM2ZiB+mAyACH5521fl5PgFV5PrKSk589cquy5gTkO3FKlf9LDfZVraR+GMBeBOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3949dfe842e0384d092811d169256f6b38b89faa120c3873b68a9ea429024d83","last_reissued_at":"2026-05-17T23:46:40.039984Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:40.039984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chaos in a continuous-time Boolean network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"math.DS","authors_text":"Roderick Edwards","submitted_at":"2019-05-09T01:55:51Z","abstract_excerpt":"Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range of behaviors but are mathematically more tractable. The form of an underlying discrete (fractional-linear) map encodes information on existence, stability and exact periods of periodic orbits. In richly connected structures with four or more variables, aperiodic behaviour can occur. We investigate a simple 4-dimensional example with Boolean interaction terms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03407","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.03407","created_at":"2026-05-17T23:46:40.040116+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.03407v1","created_at":"2026-05-17T23:46:40.040116+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03407","created_at":"2026-05-17T23:46:40.040116+00:00"},{"alias_kind":"pith_short_12","alias_value":"HFE572CC4A4E","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"HFE572CC4A4E2CJI","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"HFE572CC","created_at":"2026-05-18T12:33:18.533446+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/HFE572CC4A4E2CJICHIWSJLPNM","json":"https://pith.science/pith/HFE572CC4A4E2CJICHIWSJLPNM.json","graph_json":"https://pith.science/api/pith-number/HFE572CC4A4E2CJICHIWSJLPNM/graph.json","events_json":"https://pith.science/api/pith-number/HFE572CC4A4E2CJICHIWSJLPNM/events.json","paper":"https://pith.science/paper/HFE572CC"},"agent_actions":{"view_html":"https://pith.science/pith/HFE572CC4A4E2CJICHIWSJLPNM","download_json":"https://pith.science/pith/HFE572CC4A4E2CJICHIWSJLPNM.json","view_paper":"https://pith.science/paper/HFE572CC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.03407&json=true","fetch_graph":"https://pith.science/api/pith-number/HFE572CC4A4E2CJICHIWSJLPNM/graph.json","fetch_events":"https://pith.science/api/pith-number/HFE572CC4A4E2CJICHIWSJLPNM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HFE572CC4A4E2CJICHIWSJLPNM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HFE572CC4A4E2CJICHIWSJLPNM/action/storage_attestation","attest_author":"https://pith.science/pith/HFE572CC4A4E2CJICHIWSJLPNM/action/author_attestation","sign_citation":"https://pith.science/pith/HFE572CC4A4E2CJICHIWSJLPNM/action/citation_signature","submit_replication":"https://pith.science/pith/HFE572CC4A4E2CJICHIWSJLPNM/action/replication_record"}},"created_at":"2026-05-17T23:46:40.040116+00:00","updated_at":"2026-05-17T23:46:40.040116+00:00"}