diff --git a/frontend/src/components/ui/Button.dom.test.tsx b/frontend/src/components/ui/Button.dom.test.tsx
index dc20d45a..77bd7c2e 100644
--- a/frontend/src/components/ui/Button.dom.test.tsx
+++ b/frontend/src/components/ui/Button.dom.test.tsx
@@ -98,6 +98,18 @@ describe("Button primitive (S5)", () => {
     }
   });
 
+  it("carries the coarse-pointer minimum target, except on a link", () => {
+    // The 1024x768 comfort contract: the minimum lives in the primitive, so no call site can opt
+    // out of it by accident. A link is text in a sentence and is excluded by design.
+    const { unmount } = render(<Button>Tap</Button>);
+    expect(screen.getByRole("button", { name: "Tap" }).className).toContain("touch-target");
+    unmount();
+    render(<Button variant="link">Read more</Button>);
+    expect(screen.getByRole("button", { name: "Read more" }).className).not.toContain(
+      "touch-target",
+    );
+  });
+
   it("fullWidth adds the w-full utility", () => {
     render(<Button fullWidth>Wide</Button>);
     expect(screen.getByRole("button", { name: "Wide" }).className).toContain("w-full");
diff --git a/frontend/src/components/ui/Button.tsx b/frontend/src/components/ui/Button.tsx
index e7b47d7a..15b2bc79 100644
--- a/frontend/src/components/ui/Button.tsx
+++ b/frontend/src/components/ui/Button.tsx
@@ -60,6 +60,11 @@ const VARIANTS: Record<ButtonVariant, string> = {
   link: "font-semibold text-accent hover:underline",
 };
 
+// The geometry ladder, and the whole of it — a call site picks a rung, it does not invent one. The
+// rungs were derived from what the app actually used (counted during E10 S1b): `px-3 py-2 text-sm`
+// (22 sites), `px-2 py-1 text-xs` (12), `px-3 py-1.5 text-sm` (11). Every value is rem-derived, so
+// the Settings text-size slider (--font-scale, applied to the root font-size) scales the padding and
+// the box with the label instead of leaving a shrunken button around bigger text.
 const SIZES: Record<ButtonSize, string> = {
   xs: "px-2 py-1 text-xs rounded-md gap-1",
   sm: "px-3 py-1.5 text-sm rounded-lg gap-1.5",
@@ -113,6 +118,11 @@ export const Button = forwardRef<HTMLButtonElement, ButtonProps>(function Button
   // here rather than by asking every call site to pass `size="none"` alongside `variant="link"` —
   // a pairing everyone would eventually forget, which is how a "link" grows a button's box.
   const resolvedSize: ButtonSize = size ?? (variant === "link" ? "none" : "md");
+  // The 1024x768 comfort contract lives HERE, not in the call sites: on a coarse pointer every
+  // button-shaped control gets at least a 2.75rem box (see .touch-target in index.css). `link` is
+  // excluded on purpose — it is a run of text inside a sentence, and a 44px-tall inline link would
+  // wreck the paragraph it sits in rather than make anything easier to hit.
+  const touchTarget = variant !== "link";
   const leading = loading ? <Loader2 className="w-4 h-4 animate-spin" /> : icon;
   return (
     <button
@@ -129,6 +139,7 @@ export const Button = forwardRef<HTMLButtonElement, ButtonProps>(function Button
         BASE,
         VARIANTS[variant],
         SIZES[resolvedSize],
+        touchTarget && "touch-target",
         fullWidth && "w-full",
         className,
       )}
diff --git a/frontend/src/components/ui/README.md b/frontend/src/components/ui/README.md
index 86cfa80d..e9d04615 100644
--- a/frontend/src/components/ui/README.md
+++ b/frontend/src/components/ui/README.md
@@ -37,6 +37,27 @@ domain-free.
 | page & panel structure | `PageShell`, `PageScroller`, `PanelGroup`, `PanelGroups`, `Tabs`, `BackToTop`                                                                         |
 | state & messaging      | `QueryState`, `Banner`, `InlineNotice`                                                                                                                |
 
+## The size contract (E10 S1c)
+
+The app optimises for **1024x768 (tablet landscape) as the floor**; below it we owe an honest
+message, above it correct rendering all the way up. That contract lives in these components, not in
+the ~160 call sites, because a rule repeated in 160 places is a rule that is already broken
+somewhere:
+
+- **Geometry is a ladder, not a free choice.** `Button`'s `SIZES` are the rungs, derived from what
+  the app actually used. Pick a rung; do not hand-roll padding on a primitive.
+- **Everything is rem-derived**, so the Settings text-size slider (`--font-scale` on the root
+  font-size) scales boxes and padding with the label. A `text-[Npx]` font size is an eslint error for
+  exactly this reason.
+- **Minimum target: 2.75rem, on coarse pointers only** (`.touch-target`, index.css). A 32px icon
+  button is fine with a mouse and not with a thumb, so the box grows where there is no precise
+  pointer. It grows the real box rather than painting an invisible hit area: two expanded hit areas
+  on neighbouring icon buttons would overlap, and an overlap fires the _wrong_ button.
+- `link` is excluded from the minimum: it is text inside a sentence.
+
+Controls outside this directory (chips, list rows, the player's overlay buttons) are **not** covered
+yet -- they are the next thing to bring under the contract, not evidence that there isn't one.
+
 ## Adding one
 
 Move a component in when a second module needs it and it is domain-free — not on speculation. Adding
diff --git a/frontend/src/index.css b/frontend/src/index.css
index 8a5efe72..ab0c0e60 100644
--- a/frontend/src/index.css
+++ b/frontend/src/index.css
@@ -539,6 +539,26 @@ body {
   .btn-warn:hover:not(:disabled) {
     opacity: 0.9;
   }
+
+  /* ===== E10 S1c · the minimum-target half of the 1024x768 comfort contract =====
+     A 32px icon button is fine with a mouse (a precise pointer plus hover to confirm the aim) and
+     not fine with a thumb. So the minimum grows ONLY where there is no precise pointer, which on
+     this app's real second device — a tablet — is exactly where it is needed.
+
+     min-* rather than width/height so it can only ever grow a control, never shrink one, and so a
+     `w-8 h-8` utility on the same element still loses to it (min-width beats width in CSS).
+     Growing the BOX rather than painting an invisible ::after hit area is deliberate: an expanded
+     hit area on two icon buttons sitting 4px apart would overlap, and the overlap fires the WRONG
+     button — a worse failure than a small target. Real space cannot overlap.
+
+     2.75rem, not 44px: the whole app is rem-derived off `--font-scale`, so a target defined in px
+     would be the one control that ignores the user's text-size setting. */
+  @media (pointer: coarse) {
+    .touch-target {
+      min-width: 2.75rem;
+      min-height: 2.75rem;
+    }
+  }
 }
 .glass-hover:hover {
   border-color: color-mix(in srgb, var(--accent) 55%, transparent);