Supplementary material

"Preservation versus Selection in Koide's Charged-Lepton Mass Relation"

Author: CosmicThinker25 (independent researcher). Technical and computational assistance: Claude (Anthropic).

Scripts (run in this order)

1. koide_sweep.py — S3-invariant gradient-flow sweep on S^2_+; geometric null; per-trajectory and per-potential Koide-band frequencies across four windows. Writes sweep_data.npz. The full run takes several minutes; use --fast for a smoke test.

2. koide_running.py — one-loop SM running of K(mu) from MS-bar lepton masses at M_Z (Sec. 5 table).

3. make_figures.py — reads sweep_data.npz and writes the three figures (fig1_sphere.pdf, fig2_hist.pdf, fig3_null.pdf). Requires matplotlib.

python koide_sweep.py            # full run -> paper tables (Sec. 8) + sweep_data.npz
python koide_sweep.py --fast     # quick smoke test
python koide_running.py          # running table (Sec. 5)
python make_figures.py           # figures (needs sweep_data.npz from step 1)

Reproducibility

Seeds are fixed and explicit (no hash()); sweep results are byte-identical across runs and machines, independent of PYTHONHASHSEED.

Fixed seeds: null=20240628, gaussian=20240728, uniform=20240829.

Environment

Tested with: Python 3.12.3, NumPy 2.4.4, SciPy 1.17.1, Matplotlib 3.10.8.

NumPy is used for the sweep, SciPy for the running calculation, and Matplotlib for the figures.

Scope

Negative, bounded methodological note. The sweep is exploratory within a low-order polynomial ansatz in the invariants (e2,e3); it is not an impossibility theorem.

The boundary is handled by reflection (x_i -> |x_i|), which biases the vertex rate but not the relative under-population of the Koide band. An internal-coordinate integrator is left for future work.