wordle-five: the engine, the reward, the solver and the probe that checks them

The Python is the source of truth; src/demos/wordle/engine.ts will be a port of
it, and CI gates the two against a SHA-256 over all 21.2M (guess, answer)
pattern pairs rather than a hand-picked vector file — a vector file only ever
catches the cases somebody thought of.

The reward is three weighted components, and the third one is the reason this
demo is worth building. `solved` and `economy` pull toward winning. `consistency`
pulls against them, because a player maximising information deliberately guesses
words that cannot win — a word that splits the remaining candidates evenly
teaches more than a word that might happen to be right. That is good play, and
it costs consistency.

The probe ladder proves the tension is real rather than asserted:

  inaction        0.0000   crude       0.0111   plausible  0.1224
  candidate_only  0.8925   exhaustive  0.9031   oracle     0.9458

The two good policies are 0.05 apart and neither dominates — the entropy oracle
takes 1.00 economy and 0.73 consistency, the candidate-only player takes 0.75
and 1.00. Which one wins is a decision about what you want, which is the whole
argument the site exists to make. probe.py fails CI if either starts dominating.

Two traps found by building it. `consistency` is scored over turns SPENT, not
guesses accepted: counting only legal guesses hands a free 1.0 to a policy that
plays one word and then jams the parser five times — one guess, no
contradictions, perfect score. And `economy`'s denominator is the depth the
SHIPPED solver reaches, not a depth-optimal search: entropy-greedy is not
depth-optimal, so grading it against an exact optimum would make the oracle
rung fail its own assertion on some seeds.

The word lists are built from Wordnik (MIT) intersected with SCOWL, never from
the original game's 2,315 answers. 4,603 answers makes this materially harder
than the original, so the published SALET/3.4212 results are cited as belonging
to that list and our own reference player's TARES/3.72 is measured here.

verifiers is an optional extra. The engine, reward, solver and probe all run —
and gate — without an RL stack resolvable.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_019mt6sHQHEnEYrJZvoMCJSB

src/components/demo/BeatSection.tsx

@@ -0,0 +1,49 @@
+import type { ReactNode } from 'react';
+import type { StoryBeat } from '@/lib/demo-kit/types';
+import { cn } from '@/lib/utils';
+
+export interface BeatSectionProps {
+  beat: StoryBeat;
+  /** 1-based. The narrative is numbered so a reader can be told "see beat 3". */
+  number: number;
+  children: ReactNode;
+  className?: string;
+}
+
+/**
+ * One beat of the exec narrative: a number, a title, a claim, and the surface
+ * that makes the claim true.
+ *
+ * The claim is typeset as an assertion — large, high contrast, above the
+ * evidence — because the failure mode of a demo site is a visitor watching a
+ * pretty animation and never learning what it was supposed to prove.
+ */
+export function BeatSection({ beat, number, children, className }: BeatSectionProps) {
+  const headingId = `beat-${beat.id}-title`;
+  return (
+    <section
+      id={beat.id}
+      aria-labelledby={headingId}
+      data-surface={beat.surface}
+      className={cn('scroll-mt-[var(--app-header-h)] py-10 lg:py-14', className)}
+    >
+      <header className="mb-6 lg:mb-8">
+        <div className="flex items-baseline gap-3">
+          <span
+            aria-hidden="true"
+            className="nums select-none text-sm font-semibold tabular-nums text-accent-fg"
+          >
+            {String(number).padStart(2, '0')}
+          </span>
+          <h2 id={headingId} className="text-xl font-semibold tracking-tight lg:text-2xl">
+            {beat.title}
+          </h2>
+        </div>
+        <p className="mt-3 max-w-2xl text-pretty text-lg leading-snug text-fg lg:text-xl">
+          {beat.claim}
+        </p>
+      </header>
+      {children}
+    </section>
+  );
+}