Reproduction code — Circulation bounds the frenetic failure of maximum entropy production

Reproduction code for the manuscript "Circulation bounds the frenetic failure of maximum entropy production" (S. Kaneko). The scripts verify the analytical results and regenerate every figure of the paper. The paper proves a selection inequality, |ΔC| ≤ ½ Σ_cyc, relating the frenetic asymmetry ΔC — the imbalance in time-symmetric dynamical activity (frenesy) between the dominant forward and backward escape tubes — to the entropy production Σ_cyc around the transition cycle those tubes close. The associated order parameter is η = 2ΔC/Σ_cyc ∈ [−1, 1], which saturates at the route-handover switching lines; detailed balance forces ΔC = 0 at every scale (a no-go), so circulation is a necessary condition for frenetic (anti-MEP) selection. The bound is an identity of the minimum-action (large-deviation) description rather than a new variational principle. The code is organized as follows. Verification scripts check the bound directly: on ensembles of random directed networks (zero violations across all ensembles), on chemical-reaction-network count lattices (including the single-species no-go and a driven cyclic network that selects frenetically under uniform dissipation), and on Schnakenberg cycle-space / Hill matrix-tree examples. Further scripts reproduce the finite-state circulation sweep through the three failure modes, the rotational Maier–Stein saddle (frenetically inert across the rotations computed), the field-theoretic comparison with the Schüttler–Jack–Cates Escher-cycle quasipotential via a geometric minimum-action (gMAM) instanton, and a spatial reaction–diffusion field instanton. A trajectory-based diagnostic estimates η, Σ_cyc and the activity slope m_act from a single simulated steady-state trajectory and certifies the selection mechanism (frenetic vs boundary- vs dissipation-driven); it reproduces the manuscript's four Fig. 5 reference cases — frenetic, affinity, boundary-decided and blowtorch — and the 1/√T concentration of the estimator. Each figure has a dedicated generator (Figs 1, 3, 5 from fig_fast.py; Fig 2 from fig5_contact.py; Fig 4 from fig_ms.py; Fig 6 from net/fig_network.py; Fig 7 from crn/fig_crn.py; Fig 8 from crn/fig_escher.py; Fig 9 from sjc/fig_sjc.py; Fig 10 from fld/fig_field.py). A reference file, expected_outputs.txt, lists the headline numerical values so that runs can be checked at a glance. Requirements: Python 3.9+ with numpy, scipy, matplotlib and networkx (see requirements.txt). All scripts are run from the repository root; all randomized tests are seeded, so outputs are deterministic. See README.md for the full file-to-figure map and per-script notes. The manuscript is available as a preprint on Zenodo: DOI 10.5281/zenodo.21021548 (all-versions DOI 10.5281/zenodo.21021547).