{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:EM2PMMH3CIEE33QKLVEQJ2Z3KZ","short_pith_number":"pith:EM2PMMH3","schema_version":"1.0","canonical_sha256":"2334f630fb12084dee0a5d4904eb3b5659209bffa9e64c634140d7ee1d2da508","source":{"kind":"arxiv","id":"2606.04709","version":1},"attestation_state":"computed","paper":{"title":"A Bias-Corrected Weighted Logistic Model for Gene Regulatory Networks: Functional Equivalence with the Product-of-Logistics and Comparison with Weighted-Sum Formulations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ismail Belgacem","submitted_at":"2026-06-03T10:39:18Z","abstract_excerpt":"We introduce a bias-corrected weighted-logistic (bcw) formulation for ODE models of gene regulatory networks. Each gene's regulatory function is a single sigmoid $\\sigma(\\lambda S_i+\\lambda b_i)$ of the signed weighted regulator sum $S_i$, with a combinatorial bias $b_i=-\\lambda^{-1}\\log(2^{m_i}-1)$ depending only on the in-degree $m_i$ and the steepness $\\lambda$. We prove this is the unique single-sigmoid correction recovering the critical-point value $1/2^{m_i}$ of the product-of-logistics model and sharing its canonical equilibrium $x_i^*=\\kappa_i/(\\gamma_i 2^{m_i})$ under self-consistency"},"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":"2606.04709","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2026-06-03T10:39:18Z","cross_cats_sorted":[],"title_canon_sha256":"74cf6145ed1f009982ba53ff89e5e54af287d4ce7d86874144377bc3a1f6ffb0","abstract_canon_sha256":"60846d2ac36c8534f17163890bd814d7c428721133f643f4a25a9b8275cbedb6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:26.052727Z","signature_b64":"7+TVPr+qbqZzAC1cHu+Rw4AIYmnSoO7cK6LJh6XkOtgkRdLiBRnNoiOOuw6qDt/987C6CVpZVsKij3CwQrvVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2334f630fb12084dee0a5d4904eb3b5659209bffa9e64c634140d7ee1d2da508","last_reissued_at":"2026-06-04T01:09:26.051979Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:26.051979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Bias-Corrected Weighted Logistic Model for Gene Regulatory Networks: Functional Equivalence with the Product-of-Logistics and Comparison with Weighted-Sum Formulations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ismail Belgacem","submitted_at":"2026-06-03T10:39:18Z","abstract_excerpt":"We introduce a bias-corrected weighted-logistic (bcw) formulation for ODE models of gene regulatory networks. Each gene's regulatory function is a single sigmoid $\\sigma(\\lambda S_i+\\lambda b_i)$ of the signed weighted regulator sum $S_i$, with a combinatorial bias $b_i=-\\lambda^{-1}\\log(2^{m_i}-1)$ depending only on the in-degree $m_i$ and the steepness $\\lambda$. We prove this is the unique single-sigmoid correction recovering the critical-point value $1/2^{m_i}$ of the product-of-logistics model and sharing its canonical equilibrium $x_i^*=\\kappa_i/(\\gamma_i 2^{m_i})$ under self-consistency"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04709","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04709/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.04709","created_at":"2026-06-04T01:09:26.052104+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.04709v1","created_at":"2026-06-04T01:09:26.052104+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04709","created_at":"2026-06-04T01:09:26.052104+00:00"},{"alias_kind":"pith_short_12","alias_value":"EM2PMMH3CIEE","created_at":"2026-06-04T01:09:26.052104+00:00"},{"alias_kind":"pith_short_16","alias_value":"EM2PMMH3CIEE33QK","created_at":"2026-06-04T01:09:26.052104+00:00"},{"alias_kind":"pith_short_8","alias_value":"EM2PMMH3","created_at":"2026-06-04T01:09:26.052104+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/EM2PMMH3CIEE33QKLVEQJ2Z3KZ","json":"https://pith.science/pith/EM2PMMH3CIEE33QKLVEQJ2Z3KZ.json","graph_json":"https://pith.science/api/pith-number/EM2PMMH3CIEE33QKLVEQJ2Z3KZ/graph.json","events_json":"https://pith.science/api/pith-number/EM2PMMH3CIEE33QKLVEQJ2Z3KZ/events.json","paper":"https://pith.science/paper/EM2PMMH3"},"agent_actions":{"view_html":"https://pith.science/pith/EM2PMMH3CIEE33QKLVEQJ2Z3KZ","download_json":"https://pith.science/pith/EM2PMMH3CIEE33QKLVEQJ2Z3KZ.json","view_paper":"https://pith.science/paper/EM2PMMH3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.04709&json=true","fetch_graph":"https://pith.science/api/pith-number/EM2PMMH3CIEE33QKLVEQJ2Z3KZ/graph.json","fetch_events":"https://pith.science/api/pith-number/EM2PMMH3CIEE33QKLVEQJ2Z3KZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EM2PMMH3CIEE33QKLVEQJ2Z3KZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EM2PMMH3CIEE33QKLVEQJ2Z3KZ/action/storage_attestation","attest_author":"https://pith.science/pith/EM2PMMH3CIEE33QKLVEQJ2Z3KZ/action/author_attestation","sign_citation":"https://pith.science/pith/EM2PMMH3CIEE33QKLVEQJ2Z3KZ/action/citation_signature","submit_replication":"https://pith.science/pith/EM2PMMH3CIEE33QKLVEQJ2Z3KZ/action/replication_record"}},"created_at":"2026-06-04T01:09:26.052104+00:00","updated_at":"2026-06-04T01:09:26.052104+00:00"}