An independent exact recheck of the classification of bistable two-species mass-action networks (a recheck of a result by others)

B. Peng (arXiv:2610.32739, 23 Oct 2026, unrefereed) classifies the bistable networks among small two-species bimolecular mass-action networks with at most three directed reactions: 681 orbits under species exchange, 27 of them bistable (two positive sinks), with rational witnesses and 654 exclusions (JAC 245, DIV 216, ROOT 179, FLUX 14). This is an independent recheck of a result by others. We claim nothing new. Pure mathematical dynamical systems; no biological or medical claim. What was rechecked (Tier C: exact rational and symbolic arithmetic, certified ball arithmetic). The enumeration (1351 labelled edge sets, 681 orbits of sizes 1/10/100/570); all 27 Table 2 witnesses (each has exactly 3 positive equilibria: 2 sinks and 1 saddle), by a producer (Groebner/Sturm/rational intervals) and independently by an auditor (certified root isolation, 400-bit Arb); the exclusion certificates JAC 245 and DIV 216 (both) and ROOT 179 and FLUX 14 (auditor), all conditional on the paper's Lemma 3, which was read but not machine-checked. The producer's own fixed-degree reading of ROOT gave only 105; the gap comes from that reading, not from the paper. Random searches (Tier X; 85.1M producer samples, 4.4M auditor samples) found no bistable network among the excluded ones. Audit. A separate AI agent instance (not a human) reproduced the results with its own code (ACCEPT_WITH_CORRECTIONS; five corrections applied). Outcome: PARTIAL. Limitations. Lemma 3, its Sard step, the JAC midpoint identity, Theorem 2 and B_E = B_F beyond counts were not verified; the author's code and catalogue were not used; the preregistration is self-attested; the prior-art search was limited; no Lean; no human audit. The paper's full text is third-party and is not redistributed.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-01
DOI
https://doi.org/10.5281/zenodo.23867826
Primary Topic
Advanced Differential Equations and Dynamical Systems
Type
preprint
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preprint

An independent exact recheck of the classification of bistable two-species mass-action networks (a recheck of a result by others)

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

An independent exact recheck of the classification of bistable two-species mass-action networks (a recheck of a result by others)

Xavier Callens
preprint en

Abstract

B. Peng (arXiv:2610.32739, 23 Oct 2026, unrefereed) classifies the bistable networks among small two-species bimolecular mass-action networks with at most three directed reactions: 681 orbits under species exchange, 27 of them bistable (two positive sinks), with rational witnesses and 654 exclusions (JAC 245, DIV 216, ROOT 179, FLUX 14). This is an independent recheck of a result by others. We claim nothing new. Pure mathematical dynamical systems; no biological or medical claim. What was rechecked (Tier C: exact rational and symbolic arithmetic, certified ball arithmetic). The enumeration (1351 labelled edge sets, 681 orbits of sizes 1/10/100/570); all 27 Table 2 witnesses (each has exactly 3 positive equilibria: 2 sinks and 1 saddle), by a producer (Groebner/Sturm/rational intervals) and independently by an auditor (certified root isolation, 400-bit Arb); the exclusion certificates JAC 245 and DIV 216 (both) and ROOT 179 and FLUX 14 (auditor), all conditional on the paper's Lemma 3, which was read but not machine-checked. The producer's own fixed-degree reading of ROOT gave only 105; the gap comes from that reading, not from the paper. Random searches (Tier X; 85.1M producer samples, 4.4M auditor samples) found no bistable network among the excluded ones. Audit. A separate AI agent instance (not a human) reproduced the results with its own code (ACCEPT_WITH_CORRECTIONS; five corrections applied). Outcome: PARTIAL. Limitations. Lemma 3, its Sard step, the JAC midpoint identity, Theorem 2 and B_E = B_F beyond counts were not verified; the author's code and catalogue were not used; the preregistration is self-attested; the prior-art search was limited; no Lean; no human audit. The paper's full text is third-party and is not redistributed.

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