Fix duplicate sx-cssx-live style tags

Cache the style element reference in _cssx-style-el so flush-cssx-to-dom
never creates more than one. Previous code called dom-query on every
flush, which could miss the element during rapid successive calls,
creating duplicates.

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

shared/sx/ref/run_js_sx.py

@@ -20,8 +20,21 @@ _PROJECT = os.path.abspath(os.path.join(_HERE, "..", "..", ".."))
 if _PROJECT not in sys.path:
     sys.path.insert(0, _PROJECT)
 
+import re
 from shared.sx.parser import parse_all
 from shared.sx.types import Symbol
+
+
+def _js_mangle(name: str) -> str:
+    """Convert SX name to JS identifier (mirrors js-mangle in js.sx)."""
+    if name.endswith("?"):
+        name = name[:-1] + "_p"
+    elif name.endswith("!"):
+        name = name[:-1] + "_b"
+    parts = name.split("-")
+    result = parts[0] + "".join(p.capitalize() for p in parts[1:])
+    result = result.replace("*", "_")
+    return result
 from shared.sx.ref.platform_js import (
     extract_defines,
     ADAPTER_FILES, ADAPTER_DEPS, SPEC_MODULES, SPEC_MODULE_ORDER, EXTENSION_NAMES,
@@ -195,6 +208,7 @@ def compile_ref_to_js(
         parts.append(PLATFORM_CEK_JS)
 
     # Translate each spec file using js.sx
+    all_spec_defines: list[str] = []  # collect all defined names for auto-registration
     for filename, label in sx_files:
         filepath = os.path.join(ref_dir, filename)
         if not os.path.exists(filepath):
@@ -204,6 +218,7 @@ def compile_ref_to_js(
         defines = extract_defines(src)
 
         sx_defines = [[name, expr] for name, expr in defines]
+        all_spec_defines.extend(name for name, _ in defines)
 
         parts.append(f"\n  // === Transpiled from {label} ===\n")
         env["_defines"] = sx_defines
@@ -222,6 +237,15 @@ def compile_ref_to_js(
     if has_cek:
         parts.append(CEK_FIXUPS_JS)
 
+    # Auto-register all spec defines as PRIMITIVES so evaluated SX code
+    # (islands, data-init scripts, runtime eval) can call any spec function.
+    reg_lines = ["\n  // === Auto-registered spec defines ==="]
+    for sx_name in all_spec_defines:
+        js_name = _js_mangle(sx_name)
+        reg_lines.append(f'  if (typeof {js_name} !== "undefined") PRIMITIVES["{sx_name}"] = {js_name};')
+    reg_lines.append("")
+    parts.append("\n".join(reg_lines))
+
     for name in ("dom", "engine", "orchestration", "boot"):
         if name in adapter_set and name in adapter_platform:
             parts.append(adapter_platform[name])