Initial attempt

src/display-buffer.coffee

@@ -841,7 +841,7 @@ class DisplayBuffer extends Model
     if screenLine.isSoftWrapped() and column >= maxScreenColumn
       if wrapAtSoftNewlines
         row++
-        column = 0
+        column = @screenLines[row].tokens[0].value.length # TODO: call screenLine.clipScreenColumn
       else
         column = screenLine.clipScreenColumn(maxScreenColumn - 1)
     else if wrapBeyondNewlines and column > maxScreenColumn and row < @getLastRow()

src/token.coffee

@@ -144,6 +144,14 @@ class Token
       isHardTab: isHardTab
     )
 
+  buildPhantomToken: (length) ->
+    new Token(
+      value: _.multiplyString(" ", length),
+      scopes: @scopes,
+      bufferDelta: 0,
+      isAtomic: true
+    )
+
   isOnlyWhitespace: ->
     not WhitespaceRegex.test(@value)
 

src/tokenized-line.coffee

@@ -97,19 +97,23 @@ class TokenizedLine
       leftTextLength += nextToken.value.length
       leftTokens.push nextToken
 
+    tab = leftTokens[0].buildPhantomToken(@indentLevel * 2)
+
     leftFragment = new TokenizedLine(
       tokens: leftTokens
       startBufferColumn: @startBufferColumn
       ruleStack: @ruleStack
       invisibles: @invisibles
-      lineEnding: null
+      lineEnding: null,
+      indentLevel: @indentLevel
     )
     rightFragment = new TokenizedLine(
-      tokens: rightTokens
+      tokens: [tab].concat(rightTokens)
       startBufferColumn: @bufferColumnForScreenColumn(column)
       ruleStack: @ruleStack
       invisibles: @invisibles
-      lineEnding: @lineEnding
+      lineEnding: @lineEnding,
+      indentLevel: @indentLevel
     )
     [leftFragment, rightFragment]