{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PX7TK5HZ5MHMAF5UQYDJWGG2NZ","short_pith_number":"pith:PX7TK5HZ","schema_version":"1.0","canonical_sha256":"7dff3574f9eb0ec017b486069b18da6e44a7867bbd9018c21f2463055a7cd12d","source":{"kind":"arxiv","id":"1108.2974","version":2},"attestation_state":"computed","paper":{"title":"Bifurcations in Boolean Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chris J. Kuhlman, David Murrugarra, Henning S. Mortveit, V.S.Anil Kumar","submitted_at":"2011-08-15T11:43:43Z","abstract_excerpt":"This paper characterizes the attractor structure of synchronous and asynchronous Boolean networks induced by bi-threshold functions. Bi-threshold functions are generalizations of classical threshold functions and have separate threshold values for the transitions 0 -> 1 (up-threshold) and 1 -> 0 (down-threshold). We show that synchronous bi-threshold systems may, just like standard threshold systems, only have fixed points and 2-cycles as attractors. Asynchronous bi-threshold systems (fixed permutation update sequence), on the other hand, undergo a bifurcation: when the difference \\Delta of th"},"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":"1108.2974","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-15T11:43:43Z","cross_cats_sorted":[],"title_canon_sha256":"bf81bd1d3b8aa3e0a003c0d20840678e9d491b0c8f5c42655608c3d12d561d50","abstract_canon_sha256":"5cf2ff1d96b2c306e1986088fe42c798fc345c415f76e89aec429e7197660723"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:16.209515Z","signature_b64":"yNIiv/yRzZT8MmkVfymsRbmb/iNES1QdA/lbWXBKnc7Jsp1KqXvPUkUxit2OqNn+4Do3GIgEJht9k+DbFjMwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dff3574f9eb0ec017b486069b18da6e44a7867bbd9018c21f2463055a7cd12d","last_reissued_at":"2026-05-18T03:36:16.209037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:16.209037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bifurcations in Boolean Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chris J. Kuhlman, David Murrugarra, Henning S. Mortveit, V.S.Anil Kumar","submitted_at":"2011-08-15T11:43:43Z","abstract_excerpt":"This paper characterizes the attractor structure of synchronous and asynchronous Boolean networks induced by bi-threshold functions. Bi-threshold functions are generalizations of classical threshold functions and have separate threshold values for the transitions 0 -> 1 (up-threshold) and 1 -> 0 (down-threshold). We show that synchronous bi-threshold systems may, just like standard threshold systems, only have fixed points and 2-cycles as attractors. Asynchronous bi-threshold systems (fixed permutation update sequence), on the other hand, undergo a bifurcation: when the difference \\Delta of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2974","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":"1108.2974","created_at":"2026-05-18T03:36:16.209103+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.2974v2","created_at":"2026-05-18T03:36:16.209103+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2974","created_at":"2026-05-18T03:36:16.209103+00:00"},{"alias_kind":"pith_short_12","alias_value":"PX7TK5HZ5MHM","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PX7TK5HZ5MHMAF5U","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PX7TK5HZ","created_at":"2026-05-18T12:26:39.201973+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/PX7TK5HZ5MHMAF5UQYDJWGG2NZ","json":"https://pith.science/pith/PX7TK5HZ5MHMAF5UQYDJWGG2NZ.json","graph_json":"https://pith.science/api/pith-number/PX7TK5HZ5MHMAF5UQYDJWGG2NZ/graph.json","events_json":"https://pith.science/api/pith-number/PX7TK5HZ5MHMAF5UQYDJWGG2NZ/events.json","paper":"https://pith.science/paper/PX7TK5HZ"},"agent_actions":{"view_html":"https://pith.science/pith/PX7TK5HZ5MHMAF5UQYDJWGG2NZ","download_json":"https://pith.science/pith/PX7TK5HZ5MHMAF5UQYDJWGG2NZ.json","view_paper":"https://pith.science/paper/PX7TK5HZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.2974&json=true","fetch_graph":"https://pith.science/api/pith-number/PX7TK5HZ5MHMAF5UQYDJWGG2NZ/graph.json","fetch_events":"https://pith.science/api/pith-number/PX7TK5HZ5MHMAF5UQYDJWGG2NZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PX7TK5HZ5MHMAF5UQYDJWGG2NZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PX7TK5HZ5MHMAF5UQYDJWGG2NZ/action/storage_attestation","attest_author":"https://pith.science/pith/PX7TK5HZ5MHMAF5UQYDJWGG2NZ/action/author_attestation","sign_citation":"https://pith.science/pith/PX7TK5HZ5MHMAF5UQYDJWGG2NZ/action/citation_signature","submit_replication":"https://pith.science/pith/PX7TK5HZ5MHMAF5UQYDJWGG2NZ/action/replication_record"}},"created_at":"2026-05-18T03:36:16.209103+00:00","updated_at":"2026-05-18T03:36:16.209103+00:00"}