docs(0.S): the doc fences migrated by ludic migrate state; LANGUAGE.md's state section says what the tool and the checker do now; no module-level var left in the docs

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/language/math/math-abs.md

@@ -18,8 +18,8 @@ Parameters:
 
 ```ludic
 program ChaseDistance {
-  var target: int = 40
-  var here: int = 12
+  let target: int = 40
+  let here: int = 12
 
   handler Report phase Update {
     let gap = Math.abs(target - here)   # 28, regardless of which is larger

docs/language/math/math-ceil.md

@@ -20,7 +20,7 @@ Parameters:
 program RowsNeeded {
   const ROW_HEIGHT: fixed = 12.0
 
-  var content_height: fixed = 30.0
+  let content_height: fixed = 30.0
 
   handler Layout phase Update {
     let rows = Math.ceil(content_height / ROW_HEIGHT)   # 3

docs/language/math/math-clamp.md

@@ -22,10 +22,12 @@ Parameters:
 program CameraBounds {
   const WORLD_WIDTH: int = 320
 
-  var camera_x: int = 0
+  state CameraBoundsState {
+    camera_x: int = 0
+  }
 
-  handler Follow phase Update {
-    camera_x = Math.clamp(camera_x, 0, WORLD_WIDTH - 1)
+  handler Follow(camera_bounds_st: mut CameraBoundsState) phase Update {
+    camera_bounds_st.camera_x = Math.clamp(camera_bounds_st.camera_x, 0, WORLD_WIDTH - 1)
   }
 }
 ```

docs/language/math/math-floor.md

@@ -20,7 +20,7 @@ Parameters:
 program TileIndex {
   const TILE_SIZE: fixed = 16.0
 
-  var world_x: fixed = 40.5
+  let world_x: fixed = 40.5
 
   handler Locate phase Update {
     let column = Math.floor(world_x / TILE_SIZE)   # 2

docs/language/math/math-inverse_lerp.md

@@ -22,7 +22,7 @@ Parameters:
 program HealthFraction {
   const MAX_HP: fixed = 200.0
 
-  var hp: fixed = 150.0
+  let hp: fixed = 150.0
 
   handler Draw phase Render {
     let fraction = Math.inverse_lerp(0.0, MAX_HP, hp)   # 0.75

docs/language/math/math-lerp.md

@@ -20,11 +20,13 @@ Parameters:
 
 ```ludic
 program EaseCamera {
-  var camera_x: fixed = 0.0
-  var target_x: fixed = 100.0
+  state EaseCameraState {
+    camera_x: fixed = 0.0
+  }
+  let target_x: fixed = 100.0
 
-  handler Follow phase Update {
-    camera_x = Math.lerp(camera_x, target_x, 0.1)   # glides a tenth of the way each frame
+  handler Follow(ease_camera_st: mut EaseCameraState) phase Update {
+    ease_camera_st.camera_x = Math.lerp(ease_camera_st.camera_x, target_x, 0.1)   # glides a tenth of the way each frame
   }
 }
 ```

docs/language/math/math-max.md

@@ -19,10 +19,12 @@ Parameters:
 
 ```ludic
 program Countdown {
-  var timer: int = 60
+  state CountdownState {
+    timer: int = 60
+  }
 
-  handler Tick phase Update {
-    timer = Math.max(timer - 1, 0)   # stops at 0, never negative
+  handler Tick(countdown_st: mut CountdownState) phase Update {
+    countdown_st.timer = Math.max(countdown_st.timer - 1, 0)   # stops at 0, never negative
   }
 }
 ```

docs/language/math/math-min.md

@@ -19,10 +19,12 @@ Parameters:
 
 ```ludic
 program ClampScore {
-  var score: int = 0
+  state ClampScoreState {
+    score: int = 0
+  }
 
-  handler AddPoint phase Update {
-    score = Math.min(score + 1, 100)   # never climbs past 100
+  handler AddPoint(clamp_score_st: mut ClampScoreState) phase Update {
+    clamp_score_st.score = Math.min(clamp_score_st.score + 1, 100)   # never climbs past 100
   }
 }
 ```

docs/language/math/math-remap.md

@@ -25,7 +25,7 @@ program HealthBar {
   const MAX_HP: fixed = 200.0
   const BAR_WIDTH: fixed = 64.0
 
-  var hp: fixed = 150.0
+  let hp: fixed = 150.0
 
   handler Draw phase Render {
     let width = Math.remap(hp, 0.0, MAX_HP, 0.0, BAR_WIDTH)   # 48.0

docs/language/math/math-round.md

@@ -18,7 +18,7 @@ Parameters:
 
 ```ludic
 program SnapToPixel {
-  var smooth_x: fixed = 10.5
+  let smooth_x: fixed = 10.5
 
   handler Draw phase Render {
     let px = Math.round(smooth_x)   # 11

docs/language/math/math-sign.md

@@ -18,11 +18,13 @@ Parameters:
 
 ```ludic
 program FaceTarget {
-  var x: int = 8
-  var target: int = 20
+  state FaceTargetState {
+    x: int = 8
+  }
+  let target: int = 20
 
-  handler StepToward phase Update {
-    x = x + Math.sign(target - x)   # +1 while target is to the right
+  handler StepToward(face_target_st: mut FaceTargetState) phase Update {
+    face_target_st.x = face_target_st.x + Math.sign(target - face_target_st.x)   # +1 while target is to the right
   }
 }
 ```