Typography round 2 (owner): lh-input (caret at the font-metric floor) + 14px session titles

- lh-input: lh-prose's 1.5 reading leading made typing carets tower
  (~25px box on 16.5px text, ~2.1× the glyphs — the caret fills the line
  box in Chromium). Inputs are not paragraphs: 1.25 leading drops the
  caret to ~21px, the font-metric floor (as close to the glyphs as
  Chromium will draw). Swapped on every typing surface — composer
  (chat + home), the thinking field, answer + editable-Other inputs, the
  model search; rendered prose (message.tsx container, option
  descriptions, chat.tsx pre-wrap) keeps lh-prose 1.5. Same family and
  size as prose; only leading differs.
- Session titles: 14px (text-base) — Source Sans at 12.5px read as
  small as the 11px mono meta under them; the title now holds its rank.
  Live: title "Source Sans 3" 14px vs meta "JetBrains Mono" 11px, row
  52px; composer line box 20.625px (was 24.75px).

Gates: typecheck, lint, 469/469.

app/globals.css

@@ -164,6 +164,19 @@ body {
 	color: var(--lh-ink-italic);
 }
 
+/* lh-input (owner, typography round 2): lh-prose's 1.5 READING leading
+   makes typing carets tower over the glyphs — the caret fills the line
+   box (24.75px at 16.5px text, ~2.1× the glyph height). Inputs are not
+   paragraphs: a tighter 1.25 leading brings the caret to the font-metric
+   floor (~21px, as close to the glyphs as Chromium will draw it) while
+   wrapped lines in growing textareas still read fine. Rendered prose keeps
+   1.5 — the two share family and size, they differ only in leading. */
+.lh-input {
+	font-family: var(--font-prose);
+	font-size: var(--lh-prose-size);
+	line-height: 1.25;
+}
+
 /* Thin dark native scrollbar (app-wide): dark thumb, transparent track. */
 * {
 	scrollbar-width: thin;

components/composer.tsx

@@ -59,7 +59,7 @@ export function Composer({
 				placeholder="Ask, answer, or steer the lesson…"
 				autoFocus={autoFocus}
 				rows={1}
-				className="field-sizing-content lh-prose max-h-48 min-h-10 flex-1 resize-none bg-transparent px-2.5 py-2 outline-none placeholder:text-muted-foreground"
+				className="field-sizing-content lh-input max-h-48 min-h-10 flex-1 resize-none bg-transparent px-2.5 py-2 outline-none placeholder:text-muted-foreground"
 			/>
 			{verdict && !busy ? (
 				// The plan verdict (docs/probe-teach-split.md §4): accept

components/home.tsx

@@ -91,7 +91,7 @@ export function Home() {
 						placeholder="What do you want to learn?"
 						autoFocus
 						rows={1}
-						className="field-sizing-content lh-prose max-h-48 min-h-10 flex-1 resize-none bg-transparent px-2.5 py-2 outline-none placeholder:text-muted-foreground"
+						className="field-sizing-content lh-input max-h-48 min-h-10 flex-1 resize-none bg-transparent px-2.5 py-2 outline-none placeholder:text-muted-foreground"
 					/>
 					<button
 						type="submit"

components/model-picker.tsx

@@ -222,7 +222,7 @@ export function ModelControl({
 						value={query}
 						onChange={(e) => setQuery(e.target.value)}
 						placeholder="Search models…"
-						className="lh-prose mb-1.5 w-full rounded-lg border bg-background px-2 py-1.5 text-foreground outline-none focus:ring-1 focus:ring-ring"
+						className="lh-input mb-1.5 w-full rounded-lg border bg-background px-2 py-1.5 text-foreground outline-none focus:ring-1 focus:ring-ring"
 					/>
 					{error && <div className="mb-1.5 text-destructive">{error}</div>}
 					{!catalog && (

components/question-dock.tsx

@@ -387,7 +387,7 @@ function QuestionDockForm({
 										setSel((prev) => (prev.otherSelected ? prev : toggleOther(selectMode, prev)));
 									}}
 									placeholder="Type your own answer…"
-									className="lh-prose w-full min-w-0 flex-1 bg-transparent outline-none placeholder:text-muted-foreground"
+									className="lh-input w-full min-w-0 flex-1 bg-transparent outline-none placeholder:text-muted-foreground"
 									onClick={(e) => e.stopPropagation()}
 								/>
 							</div>
@@ -429,7 +429,7 @@ function QuestionDockForm({
 							}}
 							placeholder="Type your answer…"
 							rows={1}
-							className="field-sizing-content lh-prose max-h-48 min-h-10 w-full resize-none bg-transparent px-2.5 py-2 outline-none placeholder:text-muted-foreground"
+							className="field-sizing-content lh-input max-h-48 min-h-10 w-full resize-none bg-transparent px-2.5 py-2 outline-none placeholder:text-muted-foreground"
 						/>
 					) : (
 						<textarea
@@ -446,7 +446,7 @@ function QuestionDockForm({
 							placeholder="Why this answer? What are you unsure about? Say as much as you like — the teacher reads all of this."
 							rows={1}
 							className={cn(
-								"field-sizing-content lh-prose max-h-48 w-full resize-none bg-transparent px-2.5 py-2 outline-none placeholder:text-muted-foreground/70",
+								"field-sizing-content lh-input max-h-48 w-full resize-none bg-transparent px-2.5 py-2 outline-none placeholder:text-muted-foreground/70",
 								// Phase-scaled prominence: teaching invites depth,
 								// probing stays quick.
 								phase === "teach" ? "min-h-[4.5rem]" : "min-h-10",

components/sidebar.tsx

@@ -138,7 +138,7 @@ export function SessionRow({
 				    the meta line below stays JetBrains Mono (machine data). One
 				    rule, finally applied to the picker too (owner, typography
 				    round): mono = chrome, Source Sans = human words. */}
-				<span className="block truncate font-prose">{chat.title}</span>
+				<span className="block truncate font-prose text-base">{chat.title}</span>
 				<span className="block text-xs text-muted-foreground">{sessionMeta(chat)}</span>
 			</span>
 		</button>