SMONAD hydrogen: optional mathematical verification

From the uploaded website root, run:

    node tools/hydrogen/verify-math.mjs

Expected result: 32 numerical test groups passed.

This is an optional command-line check for maintainers. The website does not
load this script, and it does not need Node.js to serve any hydrogen page.
The command does not write files, access the network, or require npm packages.
It imports the shipped calculations from assets/hydrogen/math.js.

Use Node.js 22.7 or newer, which detects ES-module syntax in the browser's .js
module without adding a package.json. Verification here used Node.js 24.19.0.
No build step or Node process is required for normal website operation.

The checks cover CODATA-scale consistency, reduced-mass limits, energy and
wavelength relations, independently integrated 1s/2s/2p normalization and
moments, CDF derivatives and quantiles, known nodes and radial maxima,
parameter sensitivities, two-body RMS speeds, shared-level shift cycles,
common-offset cancellation, and identifiability of coincident contact terms.

These checks verify the stated effective models and numerical implementation.
They do not establish a source-level SMM/DTT derivation or a precision
spectroscopic prediction including all radiative and nuclear corrections.

Exit status 0 means all tests passed. A failed assertion exits nonzero and
identifies the calculation to inspect. Keep this directory and
assets/hydrogen/math.js in their supplied locations when running the command.
