Persist home stepper state to localStorage via freeze scope

- freeze-scope "home-stepper" captures step-idx signal
- Each step/back saves to localStorage via freeze-to-sx
- On mount, restores from localStorage via thaw-from-sx
- Invalid state resets to default (step 9)
- Clear preview lake before replay to prevent duplicates
- Register local-storage-get/set/remove as primitives
- Arrows 3x bigger

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

shared/static/scripts/sx-browser.js

@@ -14,7 +14,7 @@
   // =========================================================================
 
   var NIL = Object.freeze({ _nil: true, toString: function() { return "nil"; } });
-  var SX_VERSION = "2026-03-14T22:48:39Z";
+  var SX_VERSION = "2026-03-15T00:04:32Z";
 
   function isNil(x) { return x === NIL || x === null || x === undefined; }
   function isSxTruthy(x) { return x !== false && !isNil(x); }
@@ -5757,6 +5757,20 @@ PRIMITIVES["resource"] = resource;
   PRIMITIVES["is-html-tag?"] = function(n) { return HTML_TAGS.indexOf(n) >= 0; };
   PRIMITIVES["make-env"] = function() { return merge(componentEnv, PRIMITIVES); };
 
+  // localStorage — defined here (before boot) so islands can use at hydration
+  PRIMITIVES["local-storage-get"] = function(key) {
+    try { var v = localStorage.getItem(key); return v === null ? NIL : v; }
+    catch (e) { return NIL; }
+  };
+  PRIMITIVES["local-storage-set"] = function(key, val) {
+    try { localStorage.setItem(key, val); } catch (e) {}
+    return NIL;
+  };
+  PRIMITIVES["local-storage-remove"] = function(key) {
+    try { localStorage.removeItem(key); } catch (e) {}
+    return NIL;
+  };
+
 
   // =========================================================================
   // Platform interface — DOM adapter (browser-only)
@@ -7019,6 +7033,7 @@ PRIMITIVES["resource"] = resource;
   function localStorageRemove(key) {
     try { localStorage.removeItem(key); } catch (e) {}
   }
+  // localStorage primitives registered in CEK_FIXUPS_JS for ordering
 
   // --- Cookies ---
 

shared/sx/ref/platform_js.py

@@ -1531,6 +1531,20 @@ CEK_FIXUPS_JS = '''
   PRIMITIVES["make-symbol"] = function(n) { return new Symbol(n); };
   PRIMITIVES["is-html-tag?"] = function(n) { return HTML_TAGS.indexOf(n) >= 0; };
   PRIMITIVES["make-env"] = function() { return merge(componentEnv, PRIMITIVES); };
+
+  // localStorage — defined here (before boot) so islands can use at hydration
+  PRIMITIVES["local-storage-get"] = function(key) {
+    try { var v = localStorage.getItem(key); return v === null ? NIL : v; }
+    catch (e) { return NIL; }
+  };
+  PRIMITIVES["local-storage-set"] = function(key, val) {
+    try { localStorage.setItem(key, val); } catch (e) {}
+    return NIL;
+  };
+  PRIMITIVES["local-storage-remove"] = function(key) {
+    try { localStorage.removeItem(key); } catch (e) {}
+    return NIL;
+  };
 '''
 
 
@@ -2912,6 +2926,7 @@ PLATFORM_BOOT_JS = """
   function localStorageRemove(key) {
     try { localStorage.removeItem(key); } catch (e) {}
   }
+  // localStorage primitives registered in CEK_FIXUPS_JS for ordering
 
   // --- Cookies ---