chain line: the logic is the connective — LaTeX ∧ and ⟹ via KaTeX (owner ruling)

'A → B → C' misread as chained implication when A and B are
CO-premises. The honest shape (owner, 2026-09-30): premises join
with the LaTeX LAND (∧), the conclusion separates by the LaTeX
IMPLICATION (⟹) — A ∧ B ⟹ C.

The glyphs are REAL KaTeX renders — components/latex-glyph.tsx wraps
katex.renderToString (cached per command; the app's math engine, the
stylesheet already rides app-wide from app/layout.tsx). No SVGs, no
font-dependent unicode. PROMINENT in the theme foreground (white in
the dark theme) per the owner's same-round ruling — the logic is the
payload, not the old dim gray. A lonely chip carries no glyph (it
reads as a standalone proposition); the plain-text '→' survives only
in the row's aria-label (formatChainLine, the screen-reader form).

components/latex-glyph.tsx

@@ -0,0 +1,53 @@
+import katex from "katex";
+
+/**
+ * THE LaTeX glyph seam (owner ruling, 2026-09-30): UI connectors that
+ * want math symbols render the REAL LaTeX glyphs through KaTeX — the
+ * app's math engine, already shipped (app/layout.tsx carries the
+ * katex stylesheet) — never hand-rolled SVGs or font-dependent
+ * unicode. Born for the chain table's logical connectives: premises
+ * join with \land (∧), the conclusion separates with \implies (⟹) —
+ * `A ∧ B ⟹ C`, not the misleading `A → B → C`.
+ *
+ * Prominent by the same ruling: the connectives render in the
+ * theme's FOREGROUND (white in the dark theme) — the chain line's
+ * logic is the payload, not decoration. Callers pass the class.
+ */
+
+/** Cached katex HTML per command — the glyph set is tiny and
+ *  renderToString is pure; one render per command per process. */
+const cache = new Map<string, string>();
+
+/** The raw katex HTML for a LaTeX command (pure, sync — SSR-safe). */
+export function latexGlyphHtml(cmd: string): string {
+	let html = cache.get(cmd);
+	if (html === undefined) {
+		html = katex.renderToString(cmd, { throwOnError: false, output: "html" });
+		cache.set(cmd, html);
+	}
+	return html;
+}
+
+/** One rendered LaTeX glyph. `cmd` is the LaTeX command ("\land",
+ *  "\implies"); the output is aria-hidden — callers carry the textual
+ *  aria-label (formatChainLine keeps the plain-text form). */
+export function LatexGlyph({
+	cmd,
+	testid,
+	className,
+}: {
+	cmd: string;
+	testid?: string;
+	className?: string;
+}) {
+	return (
+		<span
+			data-testid={testid}
+			aria-hidden="true"
+			className={className}
+			// katex.renderToString is the library's own trusted output
+			// (the same thing rehype-katex injects for markdown math).
+			dangerouslySetInnerHTML={{ __html: latexGlyphHtml(cmd) }}
+		/>
+	);
+}