pages/method.md

Method, environment, and deviations

Source and implementation

Paper v4 was retrieved 2026-08-01 with an explicit browser User-Agent. HTML SHA-256 is 62cc33fa20ebd0d07a64a0386b96318a3ae6341880c031689c139d6c8ffe409a; source archive SHA-256 is 5237b9fec2f128b23266771acbc8e44837619d5309cd32840ce537071b64c47f. The implementation was reconstructed independently from the equations and audited against author code commit 22f40289 where useful.

The fixed command for every experiment node is:

uv sync --frozen --all-extras && uv run --frozen python -m reproduction.run_all

One repository .venv, Python 3.11, pyproject.toml, and uv.lock are reused. All scientific compute ran on Hugging Face cpu-upgrade; estimated and selected core count was 8, actual cgroup quota was 8 CPUs, RAM contract 32 GB, and no GPU was present. Git SHA, seeds, runtime, allocation, complete outputs, checker output, and controls are in raw JSON.

Non-circularity

Claim 3's 1% equivalence margin, 4-SE diagonal limit, and off-diagonal 5-SE/1% control were committed before sampling. Claim 4 compares fresh samples against immutable PDF-extracted curves and rejects an infinite-width substitution. Claim 5 uses the analytical critical slope as a prediction, while low/high controls must fail for their intended exponential reason. No sample size or prediction was fit to the reproduction output.

Deviations

• Claim 4 uses four representative Figure 2 widths rather than every plotted width, but retains the paper's 100,000 samples at every tested width.
• Claim 3 includes both the proof-level symbolic reconstruction and a finite source-scale experiment; the experiment alone would only corroborate the theorem.
• Trace averages use two unbiased Rademacher Hutchinson probes per network, as independently calibrated against exact Jacobians.