{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PX7TK5HZ5MHMAF5UQYDJWGG2NZ","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":"5cf2ff1d96b2c306e1986088fe42c798fc345c415f76e89aec429e7197660723","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-15T11:43:43Z","title_canon_sha256":"bf81bd1d3b8aa3e0a003c0d20840678e9d491b0c8f5c42655608c3d12d561d50"},"schema_version":"1.0","source":{"id":"1108.2974","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2974","created_at":"2026-05-18T03:36:16Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2974v2","created_at":"2026-05-18T03:36:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2974","created_at":"2026-05-18T03:36:16Z"},{"alias_kind":"pith_short_12","alias_value":"PX7TK5HZ5MHM","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PX7TK5HZ5MHMAF5U","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PX7TK5HZ","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:925bc4c78c129357d69ca280dcc75685c4d82a41d615cdd471add9761aecd0a7","target":"graph","created_at":"2026-05-18T03:36:16Z","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":"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","authors_text":"Chris J. Kuhlman, David Murrugarra, Henning S. Mortveit, V.S.Anil Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-15T11:43:43Z","title":"Bifurcations in Boolean Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2974","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:ec7628f053a1856e467d3f4845dd0b450f34dc6050f493d44d71d3da81fd3640","target":"record","created_at":"2026-05-18T03:36:16Z","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":"5cf2ff1d96b2c306e1986088fe42c798fc345c415f76e89aec429e7197660723","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-15T11:43:43Z","title_canon_sha256":"bf81bd1d3b8aa3e0a003c0d20840678e9d491b0c8f5c42655608c3d12d561d50"},"schema_version":"1.0","source":{"id":"1108.2974","kind":"arxiv","version":2}},"canonical_sha256":"7dff3574f9eb0ec017b486069b18da6e44a7867bbd9018c21f2463055a7cd12d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dff3574f9eb0ec017b486069b18da6e44a7867bbd9018c21f2463055a7cd12d","first_computed_at":"2026-05-18T03:36:16.209037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:16.209037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yNIiv/yRzZT8MmkVfymsRbmb/iNES1QdA/lbWXBKnc7Jsp1KqXvPUkUxit2OqNn+4Do3GIgEJht9k+DbFjMwBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:16.209515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2974","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec7628f053a1856e467d3f4845dd0b450f34dc6050f493d44d71d3da81fd3640","sha256:925bc4c78c129357d69ca280dcc75685c4d82a41d615cdd471add9761aecd0a7"],"state_sha256":"45003c32c124441ec4ad7feced6002544e3fcb52bcddd76243e4c834448e1461"}