Browser app for JAXSR at /jaxsr/app

[jkitchin]

Adds a zero-install front end published alongside the docs on GitHub Pages, at
https://kitchingroup.cheme.cmu.edu/jaxsr/app/: upload a spreadsheet, assign column
roles, pick which function families the search may draw from, and get a ranked table of
candidate equations with diagnostics and exports. Everything runs client-side through
Pyodide, so no data leaves the browser and there is no server to operate.

How it runs without JAX

jaxlib is a compiled XLA wheel with no Emscripten build, so JAX cannot run under
Pyodide. JAXSR barely needs it: roughly 1300 jnp.* calls that NumPy also provides,
plus a short tail of genuinely JAX-specific API (jit, grad, lax.erf, .at[]
index updates, random).

webapp/py/jax_shim.py supplies that tail on top of NumPy and registers itself in
sys.modules before import jaxsr, so the library itself is unmodified. That
substitution is only trustworthy if JAXSR behaves the same on top of it, so the whole
test suite runs through the shim as a new CI job (numpy-backend). A library change
that only breaks the browser path is caught at PR time.

Measured in real Pyodide: ~6 s to boot, 9-26 ms per fit, SymPy lazy-loaded in
377 ms and only when someone asks for LaTeX.

Three pre-existing bugs this surfaced

None of these are shim artifacts. All three reproduce on real JAX with
jax_enable_x64, which docs/guides/performance.md actively recommends.

• basis.py — _safe_exp clipped to a hardcoded ±500. At float32 that overflows
  to inf and the non-finite column filter drops the term; at float64 it yields a
  finite ~1e217 that survives selection and overflows Phi.T @ Phi. On real JAX in x64
  this silently returned a garbage 2-term model instead of recovering exp(x0*x1). The
  bound is now derived from np.finfo(dtype), and only the upper side is clipped —
  large negative arguments underflowing to zero is a legitimate result, not an
  out-of-domain one.

• metrics.py — every information criterion returned +inf for mse <= 0, scoring
  a perfect fit as the worst possible model. Exact zeros are routine in float64
  because selection.py computes MSE by a closed form that cancels, so the correct
  model was being rejected outright. MSE is now floored so the log-likelihood stays
  finite and fewer parameters still wins ties.

• metrics.py — the IC functions did scalar math with jnp, so every AIC/BIC in
  jaxsr was computed in float32. Switched to math: exact, and dtype-independent.

One API addition

SymbolicRegressor.selection_path_, a public accessor for the candidates the search
evaluated, so the app does not have to reach into _selection_path. Its docstring
records a subtlety worth knowing independently of this PR: the path predates the
pruning and constraint refitting in fit(), so path.best can carry terms the
returned model does not.

Verification

• 656 tests pass on both backends — real JAX and the NumPy shim.
• New tests/test_metrics.py closes a gap listed in CLAUDE.md; new
  tests/test_numpy_shim.py covers the JAX contract and checks a fit through the shim
  agrees with the same fit on real JAX.
• Driven end-to-end in headless Chromium: uploads a real multi-sheet .xlsx with an ID
  column, a text column and failed runs, fits, and checks the rendered output. No
  console errors.
• The bundled example workbook is generated from equations recorded on its own answer
  key. It includes stir_rpm, a variable drawn independently of the response — the
  winning model correctly excludes it, all four true coefficients land inside their 95%
  intervals, and the intercept is selected but flagged not significant, which is right
  since the data has no constant term.

Worth knowing

• Deployment only takes effect on merge. docs.yml uploads the Pages artifact on
  pushes to main only; this PR exercises the doc build and both test backends but does
  not publish.
• Browser verification used headless Chromium via Playwright, not a real interactive
  browser session. Worth a manual look before merging.
• jupyter and nbconvert are declared runtime dependencies of jaxsr but are imported
  nowhere in src/. They are why micropip tried to pull in tornado and pyzmq. Harmless
  here since the app installs with deps=False, but they make every pip install jaxsr
  heavier than it needs to be. Not addressed in this PR.
• The CLAUDE.md change also carries a pre-existing Crucible block that was already
  uncommitted in the working tree.

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