Reproduction code — A circulation bound on the frenetic component of branch selection

Reproduction code for the manuscript “A circulation bound on the frenetic component of branch selection” by Shigeo Kaneko. The deposited scripts reproduce the manuscript’s numerical and computational results, regenerate all fourteen figures, and provide consistency checks for the central circulation bound. The analytical proof is contained in the manuscript. The paper establishes |ΔC| ≤ ½ Σ_cyc, where ΔC is the reversal-even frenetic or traffic asymmetry between the dominant forward and backward escape tubes, and Σ_cyc ≥ 0 is the entropy production around the transition cycle closed by those tubes. The proof uses tube minimality, reversal parity, and closure of the comparison class under time reversal. The dimensionless frenetic polarization index η = 2ΔC / Σ_cyc ∈ [−1,1] quantifies the imbalance between the two reciprocal optimality gaps. It approaches saturation along nondegenerate branchwise approaches to the route-handover locus where the forward tube and the time-reversed backward tube become co-optimal. Detailed balance forces ΔC = 0, so circulation around the selected transition cycle is necessary, though not sufficient, for frenetic branch selection. The bound is a structural consistency relation of the minimum-action description, not a thermodynamic variational principle or conversion-efficiency law. The code examines the bound in finite-state networks, Schnakenberg and Hill matrix-tree constructions, chemical-reaction-network count lattices, continuous Langevin systems, and spatial field models. It also shows that the pairwise tube bound does not extend directly to arbitrary arborescence comparisons, confirming that reversal closure is essential. The sfef/ directory contains the Freidlin–Wentzell diffusion benchmarks, including the two-channel route-handover example reaching η ≈ 0.97, the single-channel envelope remaining at |η| ≲ 0.37, and the window-closing trajectory experiment. Further scripts reproduce the contact-weight correction, rotational Maier–Stein example, coarse-graining results, Schüttler–Jack–Cates instanton, spatial-field instanton, and trajectory-level mechanism diagnostic. Every numerical entry in Tables I–IV is associated with a deposited verification script. The aggregate runner checks reported numerical values rather than relying on exit codes alone. See README.md for the claim-to-script map and expected_outputs.txt for reference outputs. V5 changes: 1. Replaced “efficiency |η|” with “frenetic polarization |η|” in the terminology and in Figs. 1 and 9. 2. Added calibration_locus.py to test calibration dependence of the route-handover locus and distinguish symmetry-pinned η = 0 from accidental cancellation. 3. Updated the aggregate runner, documentation, and deposited figures. 4. No numerical result reported in V4 was changed. Licences: source code (*.py, *.sh), MIT; generated data, figures, and documentation, CC BY 4.0. The Mendeley Data record-level licence is CC BY 4.0.