docs: a walkthrough that runs, and a front page whose output is not typed

[sotashimozono]

Measured before writing anything: docs/src had 32 fenced ```julia blocks whose output was typed
by hand, against one @example and one `jldoctest`. Two of those 32 had already been caught
producing output the code cannot produce (#26) — a report in the wrong order, and a frame count
written from a simplified trace.

Worse, the single most important output in the documentation — the exit summary, the thing the
front page exists to sell — was a ```console block reading … your output …. It could not be an
`@example`: the summary fires at exit, and a documentation build does not exit between blocks. That
is precisely why it was typed.

One source, three consumers

examples/walkthrough.jl is a Literate source:

consumer	what it gets
Literate at docs-build time	docs/src/walkthrough.md — gitignored, so no second drifting copy is committed
a reader	julia --project=examples examples/walkthrough.jl runs standalone
test/test_examples.jl	runs it and asserts what the page claims

It walks one small package through the whole arc — mark, entered, @entered, record, reach,
audit, compare/isbreaking — and every step carries its control, because a claim without
one is worth little here:

• a marked definition the run never touched is absent, not reported as zero
• a caller with nothing unvalidated behind it gives an empty record, not a small one
• the same removal is breaking or not depending on whether the notice was in the source

The exit summary, actually run

The page runs examples/sweep.jl as its own process and prints what came back. That made a
property visible that was nowhere in the documentation:

the summary goes to stderr, the result to stdout — so julia sweep.jl > result.dat keeps
the data clean and still puts the notice in front of whoever ran it. The test asserts it, and fails
if the summary ever changes streams.

Two things the page says because they were measured

• :clean is version-sensitive. A lengths that called tanh was :clean on 1.12.2 and
  :unknown on 1.14.0-DEV — resolving tanh reaches Base internals that moved. The walkthrough
  uses a formulation that is :clean on both and states the sensitivity, since that is one of
  the reasons reach is itself declared @experimental.
• Pinax is not the subject. It has zero marks today, so it could demonstrate audit but not
  the headline, and depending on it would put a [sources] rev in the docs environment. Its real
  audited numbers stay in the prose of adopting.md.

🤖 Generated with Claude Code

[github-actions]

📚 Docs preview: https://codes.sota-shimozono.com/ExperimentalAPI.jl/previews/PR32/

(updates on each push to this PR)

[codecov]

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