A certified three-equilibrium bound for 375 fixed quadratic zero-one reaction networks

Article v1 and exact certificates for at most three distinct positive equilibria, including degenerate equilibria, at all positive rate constants in the fixed 375-network list of Tang and Zhang. Includes 375 Cramer reductions, a second resultant route checked with explicit Sylvester determinants, a post-selected finite structural observation, and one seven-reaction family with a rational witness. The original enumeration, 373/2 classification, exceptional identifiers and Lemma 3 are Tang–Zhang results; the original enumeration and the 373-network stability classification are not reverified here. Upstream raw data are not bundled; their pinned input is fetched and hashed. No priority, proof-assistant assurance or human peer review is claimed. Original prose and derived certificates: CC BY 4.0. Code: Apache 2.0. The related two-network collection is available as version 1.0.0, DOI 10.5281/zenodo.23659209 (all versions: 10.5281/zenodo.23659208). Publication identifiers for this 375-network package are pending.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-28
DOI
https://doi.org/10.5281/zenodo.23715810
Primary Topic
Advanced Differential Equations and Dynamical Systems
Type
preprint
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preprint

A certified three-equilibrium bound for 375 fixed quadratic zero-one reaction networks

竜彦 滝本
2 links
Zenodo (CERN European Organization for Nuclear Research)
Advanced Differential Equations and Dynamical Systems
preprint

A certified three-equilibrium bound for 375 fixed quadratic zero-one reaction networks

竜彦 滝本
preprint en

Abstract

Article v1 and exact certificates for at most three distinct positive equilibria, including degenerate equilibria, at all positive rate constants in the fixed 375-network list of Tang and Zhang. Includes 375 Cramer reductions, a second resultant route checked with explicit Sylvester determinants, a post-selected finite structural observation, and one seven-reaction family with a rational witness. The original enumeration, 373/2 classification, exceptional identifiers and Lemma 3 are Tang–Zhang results; the original enumeration and the 373-network stability classification are not reverified here. Upstream raw data are not bundled; their pinned input is fetched and hashed. No priority, proof-assistant assurance or human peer review is claimed. Original prose and derived certificates: CC BY 4.0. Code: Apache 2.0. The related two-network collection is available as version 1.0.0, DOI 10.5281/zenodo.23659209 (all versions: 10.5281/zenodo.23659208). Publication identifiers for this 375-network package are pending.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Differential Equations and Dynamical Systems
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