refactor: Improve mobile UI, dependency management, and docs

- Update README.md and CONTRIBUTE.md with correct file paths
- Replace CDN links with npm dependencies for KaTeX and Plausible
- Set Schrödinger equation as default
- Refactor mobile layout:
  - Add mobile header with toggle buttons
  - Convert sidebar and editor to full-screen overlays
  - Optimize equation display spacing (dynamic margin based on size)
  - Improve responsiveness for small screens

Author: stared

src/components/CentralPanel.vue

@@ -116,7 +116,7 @@ h1 {
   font-family: var(--font-ui);
   font-size: 1rem;
   color: var(--text-secondary);
-  margin-bottom: 2.5rem;
+  margin-bottom: 1.5rem;
   text-align: center;
   opacity: 0.8;
 }
@@ -128,7 +128,7 @@ h1 {
 
   .subtitle {
     font-size: 0.875rem;
-    margin-bottom: 1.5rem;
+    margin-bottom: 1rem;
   }
 }
 </style>

src/components/equation/EquationDisplay.vue

@@ -174,8 +174,9 @@ onUnmounted(() => resizeObserver?.disconnect());
 
 <style scoped>
 #equation-container {
-  padding: 3rem 2rem;
-  margin-bottom: 2.5rem;
+  padding: 0.25rem 1rem;
+  min-height: 150px; /* Ensure smaller formulas have some breathing room */
+  margin-bottom: 1.5rem;
   display: flex;
   justify-content: center;
   align-items: center;
@@ -184,6 +185,10 @@ onUnmounted(() => resizeObserver?.disconnect());
   background: var(--bg-primary);
 }
 
+#equation-container :deep(.katex-display) {
+  margin: 0;
+}
+
 .selection-overlay {
   position: absolute;
   top: 0;
@@ -219,7 +224,7 @@ onUnmounted(() => resizeObserver?.disconnect());
 
 @media (max-width: 768px) {
   #equation-container {
-    padding: 1.5rem 1rem;
+    padding: 0.5rem 1rem;
     overflow-x: auto;
     justify-content: flex-start;
     /* Ensure container can scroll */