{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:J7D2AFK6DPBFKSZIUCWQ26SSPC","short_pith_number":"pith:J7D2AFK6","schema_version":"1.0","canonical_sha256":"4fc7a0155e1bc2554b28a0ad0d7a52788d209e6ba1a2d39ffffe281f4141d74e","source":{"kind":"arxiv","id":"q-bio/0611028","version":1},"attestation_state":"computed","paper":{"title":"Periodic solutions of piecewise affine gene network models: the case of a negative feedback loop","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"q-bio.QM","authors_text":"Etienne Farcot (INRIA Sophia Antipolis), Jean-Luc Gouz\\'e (INRIA Sophia Antipolis)","submitted_at":"2006-11-08T11:16:54Z","abstract_excerpt":"In this paper the existence and unicity of a stable periodic orbit is proven, for a class of piecewise affine differential equations in dimension 3 or more, provided their interaction structure is a negative feedback loop. It is also shown that the same systems converge toward a unique stable equilibrium point in dimension 2. This extends a theorem of Snoussi, which showed the existence of these orbits only. The considered class of equations is usually studied as a model of gene regulatory networks. It is not assumed that all decay rates are identical, which is biologically irrelevant, but has"},"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":"q-bio/0611028","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-bio.QM","submitted_at":"2006-11-08T11:16:54Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"d9540743c8f205284a1b3ef7ebd97d4731645c3c5172b4b200ccf16d5a5dbaab","abstract_canon_sha256":"d3b587f693247267b6f90b7d339a8351800f22de826099a57d61f237acea2ae8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:45.997052Z","signature_b64":"MLOcpOM4jA+EWDwhvcYNX/TobCatsdPN0vbSH30IJRse7oDJTIh9ayOibdL53wbQy6AlBu4aJQXbo1KvKk3WCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fc7a0155e1bc2554b28a0ad0d7a52788d209e6ba1a2d39ffffe281f4141d74e","last_reissued_at":"2026-05-18T01:08:45.996701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:45.996701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Periodic solutions of piecewise affine gene network models: the case of a negative feedback loop","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"q-bio.QM","authors_text":"Etienne Farcot (INRIA Sophia Antipolis), Jean-Luc Gouz\\'e (INRIA Sophia Antipolis)","submitted_at":"2006-11-08T11:16:54Z","abstract_excerpt":"In this paper the existence and unicity of a stable periodic orbit is proven, for a class of piecewise affine differential equations in dimension 3 or more, provided their interaction structure is a negative feedback loop. It is also shown that the same systems converge toward a unique stable equilibrium point in dimension 2. This extends a theorem of Snoussi, which showed the existence of these orbits only. The considered class of equations is usually studied as a model of gene regulatory networks. It is not assumed that all decay rates are identical, which is biologically irrelevant, but has"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-bio/0611028","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":"q-bio/0611028","created_at":"2026-05-18T01:08:45.996756+00:00"},{"alias_kind":"arxiv_version","alias_value":"q-bio/0611028v1","created_at":"2026-05-18T01:08:45.996756+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-bio/0611028","created_at":"2026-05-18T01:08:45.996756+00:00"},{"alias_kind":"pith_short_12","alias_value":"J7D2AFK6DPBF","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"J7D2AFK6DPBFKSZI","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"J7D2AFK6","created_at":"2026-05-18T12:25:54.717736+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/J7D2AFK6DPBFKSZIUCWQ26SSPC","json":"https://pith.science/pith/J7D2AFK6DPBFKSZIUCWQ26SSPC.json","graph_json":"https://pith.science/api/pith-number/J7D2AFK6DPBFKSZIUCWQ26SSPC/graph.json","events_json":"https://pith.science/api/pith-number/J7D2AFK6DPBFKSZIUCWQ26SSPC/events.json","paper":"https://pith.science/paper/J7D2AFK6"},"agent_actions":{"view_html":"https://pith.science/pith/J7D2AFK6DPBFKSZIUCWQ26SSPC","download_json":"https://pith.science/pith/J7D2AFK6DPBFKSZIUCWQ26SSPC.json","view_paper":"https://pith.science/paper/J7D2AFK6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=q-bio/0611028&json=true","fetch_graph":"https://pith.science/api/pith-number/J7D2AFK6DPBFKSZIUCWQ26SSPC/graph.json","fetch_events":"https://pith.science/api/pith-number/J7D2AFK6DPBFKSZIUCWQ26SSPC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J7D2AFK6DPBFKSZIUCWQ26SSPC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J7D2AFK6DPBFKSZIUCWQ26SSPC/action/storage_attestation","attest_author":"https://pith.science/pith/J7D2AFK6DPBFKSZIUCWQ26SSPC/action/author_attestation","sign_citation":"https://pith.science/pith/J7D2AFK6DPBFKSZIUCWQ26SSPC/action/citation_signature","submit_replication":"https://pith.science/pith/J7D2AFK6DPBFKSZIUCWQ26SSPC/action/replication_record"}},"created_at":"2026-05-18T01:08:45.996756+00:00","updated_at":"2026-05-18T01:08:45.996756+00:00"}