feat: implement authentic adjacent bead spacing for realistic abacus appearance

This commit perfects the visual authenticity of the soroban abacus by implementing
proper spacing between beads that matches how a real abacus behaves.

Key improvements:
1. Adjacent Bead Spacing System:
   - Adjacent beads of same type (active-to-active, inactive-to-inactive): 0.5pt spacing (nearly touching)
   - Transition gaps (active-to-inactive): 8pt spacing (clear visual separation)
   - Bar-to-bead gaps: 1pt (active) or 8pt (inactive) as appropriate

2. Physical Abacus Authenticity:
   - Active beads cluster together near the reckoning bar
   - Inactive beads cluster together away from active beads
   - Clear visual distinction between active and inactive states
   - Matches the tactile grouping behavior of real soroban beads

3. Enhanced Visual Impact:
   - Numbers like 2,3,4: Active earth beads touch each other
   - Numbers like 6,7,8,9: Both active and inactive groups clearly defined
   - Number 0: All inactive beads form cohesive groups
   - Number 5: Clean separation between active heaven and inactive earth

Technical Implementation:
- New adjacent-spacing parameter (0.5pt) for same-type bead pairs
- Updated positioning calculations throughout earth bead logic
- Maintained rod bounds calculation compatibility
- Preserved all existing gap logic for different-type transitions

The result is a much more authentic and visually appealing representation that
accurately reflects how beads behave on a physical soroban abacus.

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

templates/flashcards.typ

@@ -32,7 +32,8 @@
   // Drawing parameters scaled by base-size
   let rod-width = 3pt * base-size
   let bead-size = 12pt * base-size
-  let bead-spacing = 4pt * base-size
+  let bead-spacing = 4pt * base-size  // Original spacing (will be overridden for adjacent same-type beads)
+  let adjacent-spacing = 0.5pt * base-size  // Minimal spacing for adjacent beads of same type
   let column-spacing = 25pt * base-size
   let heaven-earth-gap = 30pt * base-size
   let bar-thickness = 2pt * base-size
@@ -143,15 +144,15 @@
         #let furthest-earth-y = if earth-active > 0 {
           // Position of the last inactive earth bead (or last active if all are active)
           if earth-active == 4 {
-            // All earth beads are active - furthest is the 4th active bead
-            heaven-earth-gap + bar-thickness + active-gap + bead-size / 2 + 3 * (bead-size + bead-spacing)
+            // All earth beads are active - furthest is the 4th active bead (using adjacent spacing)
+            heaven-earth-gap + bar-thickness + active-gap + bead-size / 2 + 3 * (bead-size + adjacent-spacing)
           } else {
             // Some inactive beads - furthest is the last inactive bead
-            heaven-earth-gap + bar-thickness + active-gap + bead-size / 2 + earth-active * (bead-size + bead-spacing) + inactive-gap + (4 - 1 - earth-active) * (bead-size + bead-spacing)
+            heaven-earth-gap + bar-thickness + active-gap + bead-size / 2 + (earth-active - 1) * (bead-size + adjacent-spacing) + bead-size / 2 + inactive-gap + bead-size / 2 + (4 - 1 - earth-active) * (bead-size + adjacent-spacing)
           }
         } else {
-          // No active beads: furthest is the last inactive bead
-          heaven-earth-gap + bar-thickness + inactive-gap + bead-size / 2 + 3 * (bead-size + bead-spacing)
+          // No active beads: furthest is the last inactive bead (using adjacent spacing)
+          heaven-earth-gap + bar-thickness + inactive-gap + bead-size / 2 + 3 * (bead-size + adjacent-spacing)
         }
         
         // Calculate rod bounds (from outermost visible bead to outermost visible bead)
@@ -207,16 +208,16 @@
         #for i in range(4) [
           #let is-active = i < earth-active
           #let earth-y = if is-active {
-            // Active beads: positioned near reckoning bar with better spacing, in sequence
-            heaven-earth-gap + bar-thickness + active-gap + bead-size / 2 + i * (bead-size + bead-spacing)
+            // Active beads: positioned near reckoning bar, adjacent beads touch
+            heaven-earth-gap + bar-thickness + active-gap + bead-size / 2 + i * (bead-size + adjacent-spacing)
           } else {
             // Inactive beads: positioned after the active beads + gap, or after reckoning bar + gap if no active beads
             if earth-active > 0 {
-              // Position after the last active bead + gap
-              heaven-earth-gap + bar-thickness + active-gap + bead-size / 2 + earth-active * (bead-size + bead-spacing) + inactive-gap + (i - earth-active) * (bead-size + bead-spacing)
+              // Position after the last active bead + gap, then adjacent inactive beads touch
+              heaven-earth-gap + bar-thickness + active-gap + bead-size / 2 + (earth-active - 1) * (bead-size + adjacent-spacing) + bead-size / 2 + inactive-gap + bead-size / 2 + (i - earth-active) * (bead-size + adjacent-spacing)
             } else {
-              // No active beads: position after reckoning bar + gap
-              heaven-earth-gap + bar-thickness + inactive-gap + bead-size / 2 + i * (bead-size + bead-spacing)
+              // No active beads: position after reckoning bar + gap, adjacent inactive beads touch
+              heaven-earth-gap + bar-thickness + inactive-gap + bead-size / 2 + i * (bead-size + adjacent-spacing)
             }
           }