Add the initial example corpus and its verification script

[DerekCorniello]

The initial example corpus for mux-examples, plus the CI that verifies it.

Implements muxlang/mux-context#26, and depends on the decision recorded for
muxlang/mux-context#44: the compiler's test corpus and the published examples
are separate artifacts, so nothing here moves out of mux-compiler/test_scripts.

What is here

12 examples, each a directory with the program, a README saying what it
teaches, and an expected_output.txt that CI diffs against.

Language essentials: hello, collections, classes_and_interfaces,
enums_and_match, optional_and_result, generics_and_closures

Programs that do a job: csv_to_json, inventory_report, event_timeline,
route_finder, dice_simulation, http_server

Every one is deterministic and offline - no clock, no network, no unseeded
randomness, no file it did not write itself. That is the constraint that makes a
recorded output a usable assertion, and it is written into AGENTS.md so the
next example follows it.

scripts/run-examples.sh compiles and runs each example and diffs its
output. It is the shared contract, and it takes nothing but a mux binary:

MUX_BIN=/path/to/mux ./scripts/run-examples.sh            # check
MUX_BIN=/path/to/mux ./scripts/run-examples.sh --update   # re-record

.github/workflows/examples.yml builds mux-compiler main and runs it.
Deliberately NOT path-filtered: it is a required check, and a required check
skipped by a paths filter never reports, so the PR would wait on it forever.

Why CI builds main rather than a release

An example is authored here before the compiler change it depends on has
shipped. Pinning to a release would deadlock: the fix for a compiler-caused
failure could not merge until the release shipped, and the release should not
ship with a broken example. The guarantee that examples work against a real
RELEASE comes from the release jobs in mux-compiler and mux-runtime running this
same script - that part is not built yet and is the obvious follow-up.

Authoring this found nine defects

Writing programs against a real compiler is what turned them up, which is most
of the argument for the repo existing. All are now fixed and merged:

• mux-runtime#50 - next_range returned only the lower half of its range
• mux-runtime#51 - string.length() counted bytes, not characters
• mux-runtime#52 - JSON integers became floats; values past 2^53 changed
• mux-runtime#53 - JSON object keys were re-ordered alphabetically
• mux-compiler#394 - ICE writing a captured variable from inside a match arm
• mux-compiler#395 - expressions could not span lines; no trailing comma in calls
• mux-compiler#397 - a match arm's pattern binding leaked into later arms
• mux-compiler#391 - importing a type whose interface was not in scope was an ICE
• plus a nested function reading an enclosing local, also an ICE

The last commit retires the workarounds those fixes made unnecessary:
dice_simulation uses random.next_range again and rolls a uniform 1-6 rather
than never exceeding 3, and http_server reads status 201 rather than 201.0.

Still worked around, deliberately

Two notes remain in the examples because the underlying issues are open, and
both say so in the code:

• http_server compares a quoted path ("\"/echo\""), because Json has
  only stringify and a string field arrives JSON-encoded with no way to strip
  the quotes (mux-compiler#392, #389).
• route_finder imports Collection by hand. That is now a clean diagnostic
  rather than an ICE, but importing a type still does not pull in the interfaces
  it implements (mux-compiler#391).

Verification

12/12, run twice for determinism, against mux-compiler main at 9b32db3 - the
merge of #396 - with the runtime its lockfile resolves.

[greptile-apps]

Greptile Summary

The PR adds twelve deterministic Mux examples and a shared verification runner, along with CI that builds the compiler and checks recorded output.

• Adds language-focused and end-to-end example programs with documentation and expected output.
• Adds update and verification modes for recorded baselines.
• Adds GitHub Actions coverage against mux-compiler main.

Confidence Score: 5/5

The PR appears safe to merge.

No blocking failure remains.

Important Files Changed

Filename	Overview
scripts/run-examples.sh	Adds example discovery, compilation, output comparison, baseline updates, portable timeout handling, and correct failure propagation.
.github/workflows/examples.yml	Adds CI that builds the compiler and runtime before running the shared example verifier.
README.md	Documents the example corpus, verification workflow, authoring requirements, and the planned status of release integration.
examples/csv_to_json/main.mux	Adds a self-contained CSV-to-JSON example with safe handling for ragged rows.
examples/http_server/main.mux	Adds a deterministic loopback HTTP client/server example with coordinated output after thread completion.

_{Reviews (4): Last reviewed commit: "Fail --update when a baseline cannot be ..." | Re-trigger Greptile}