Use double scalars for bounded native depth steering

tools/android/exercise-playground.ps1

@@ -175,7 +175,7 @@ function ApproachDepth([string]$Name,$Source){
             $sourcePoint=@($friends|Sort-Object {[Math]::Pow($_.x-$pointer[0],2)+[Math]::Pow($_.y-$pointer[1],2)})[0]
             $targetPoint=@($friends|Where-Object {$_-ne$sourcePoint})[0]
             $dx=$targetPoint.x-$sourcePoint.x;$dy=$targetPoint.y-$sourcePoint.y;$length=[Math]::Sqrt($dx*$dx+$dy*$dy)
-            if($length-lt2){break};$scale=[Math]::Min(1,12/$length)
+            if($length-lt2){break};$scale=[Math]::Min(1.0,12.0/$length)
             $next=@([int][Math]::Round($pointer[0]+$dx*$scale),[int][Math]::Round($pointer[1]+$dy*$scale))
             if(!(WorldSafe $next)){throw 'Live depth approach leaves UI-safe input region'}
             $pointer=$next;NativeTouch @($pointer[0],$pointer[1],73,1024)

tools/android/test-playground-contracts.ps1

@@ -167,6 +167,54 @@ exit ([int]$env:PLAYGROUND_CONTROL_TOUCH_EXIT)
         $point=@([int]1096,[int]609);$pointer=$null;$pointerError=$null
         try{. ([scriptblock]::Create($pointerAssignment.Extent.Text))}catch{$pointerError=$_.Exception.Message}
         Probe 'actual-deep-contact-pointer-exact-native-point' ($null-eq$pointerError-and$pointer-is[array]-and$pointer.Count-eq2-and$pointer[0]-is[int]-and$pointer[1]-is[int]-and$pointer[0]-eq1116-and$pointer[1]-eq609) @{statement=$pointerAssignment.Extent.Text;actualPoint=$point;pointer=$pointer;error=$pointerError;scope='Actual ApproachDepth assignment with observed native first-hit point; no native input'}
+        $commonAst=[Management.Automation.Language.Parser]::ParseFile((Join-Path $PSScriptRoot 'final-common.ps1'),[ref]$null,[ref]$null)
+        $worldSafe=$commonAst.Find({param($node)$node-is[Management.Automation.Language.FunctionDefinitionAst]-and$node.Name-eq'WorldSafe'},$true)
+        function RunApproachControl($Case,[string]$Mutation='valid'){
+            & {
+                param($Definition,$SafeDefinition,$Source,$Case,$Mutation)
+                . ([scriptblock]::Create($Definition));. ([scriptblock]::Create($SafeDefinition))
+                $commands=[Collections.Generic.List[object]]::new();$contactLog=[Collections.Generic.List[object]]::new();$vision=@{calls=0}
+                $fixtures=@{stages=@(@{stage=1;min=@{x=-8;y=0;z=-6};max=@{x=8;y=6;z=6}})}
+                function FixtureState($Board,[string]$Type,[int]$Stage){$state=Clone $floatProduction;$state.latestFreePlay=Clone $Board;return $state}
+                function LoadFixture([string]$Name,$State,[string]$Type,[int]$Stage){return Clone $State}
+                function BallPoint($Board,[string]$Id){return @(1096,609)}
+                function NativeTouch([int[]]$Contacts){$contactLog.Add([object]$Contacts)}
+                function Start-Sleep([int]$Milliseconds){}
+                function Step([string]$Name,[string[]]$Arguments=@(),[int]$Delay=500){}
+                function BlueFriends([string]$Path){$vision.calls++;if($vision.calls-eq1){return @(@{x=$Case.sourceX;y=$Case.sourceY},@{x=$Case.targetX;y=$Case.targetY})};return @()}
+                $controlAfter=FixtureState $Source 'free' 1
+                $controlAfter.latestFreePlay.balls[0].position=[pscustomobject]@{x=0;y=3;z=0};$controlAfter.latestFreePlay.balls[1].position=[pscustomobject]@{x=1;y=3;z=0}
+                $controlAfter.latestFreePlay.groups=@([pscustomobject]@{id='steering-control-merged';ballIds=@($Source.balls.id)})
+                switch($Mutation){
+                    'wrong-id'{$controlAfter.latestFreePlay.balls[0].id='wrong-id'}
+                    'wrong-membership'{$controlAfter.latestFreePlay.groups[0].ballIds=@($Source.balls[0].id)}
+                    'camera-one-ulp'{$controlAfter.latestFreePlay.camera.distance=[double][MathF]::BitIncrement([single]$controlAfter.latestFreePlay.camera.distance)}
+                    'outside-bounds'{$controlAfter.latestFreePlay.balls[0].position.x=100;$controlAfter.latestFreePlay.balls[1].position.x=101}
+                    'wrong-contact'{$controlAfter.latestFreePlay.balls[1].position.x=2}
+                }
+                function Save([string]$Name){return Clone $controlAfter}
+                $accepted=$false;$message=$null;try{ApproachDepth 'steering-control' $Source;$accepted=$true}catch{$message=$_.Exception.Message}
+                return @{accepted=$accepted;contacts=$contactLog.ToArray();observations=$vision.calls;error=$message}
+            } $approach.Extent.Text $worldSafe.Extent.Text $producer $Case $Mutation
+        }
+        $steeringCases=@(
+            @{name='actual-native-far';sourceX=1143.320388349515;sourceY=609.5533980582524;targetX=1384.984126984127;targetY=609.6190476190476;expected=@(1128,609)},
+            @{name='mid-right';sourceX=1116;sourceY=609;targetX=1140;targetY=609;expected=@(1128,609)},
+            @{name='far-left';sourceX=1116;sourceY=609;targetX=996;targetY=609;expected=@(1104,609)},
+            @{name='far-up';sourceX=1116;sourceY=609;targetX=1116;targetY=489;expected=@(1116,597)},
+            @{name='mid-down';sourceX=1116;sourceY=609;targetX=1116;targetY=633;expected=@(1116,621)},
+            @{name='near-left';sourceX=1116;sourceY=609;targetX=1111;targetY=609;expected=@(1111,609)},
+            @{name='near-diagonal';sourceX=1116;sourceY=609;targetX=1119;targetY=613;expected=@(1119,613)}
+        )
+        foreach($case in $steeringCases){
+            $run=RunApproachControl $case;$moves=@($run.contacts|Where-Object {$_[3]-eq1024});$next=if($moves.Count-eq3){$moves[2]}else{$null}
+            $correct=$run.accepted-and$run.observations-eq2-and$moves.Count-eq3-and$next[0]-eq$case.expected[0]-and$next[1]-eq$case.expected[1]-and([Math]::Pow($next[0]-1116,2)+[Math]::Pow($next[1]-609,2)-le144)
+            Probe "actual-approach-depth-steering-$($case.name)" $correct @{case=$case;run=$run;scope='Actual full ApproachDepth AST with PNG/touch/save transport doubles; expected exact direction and maximum12px step, no native verdict'}
+        }
+        foreach($mutation in @('wrong-id','wrong-membership','camera-one-ulp','outside-bounds','wrong-contact')){
+            $run=RunApproachControl $steeringCases[0] $mutation
+            Probe "actual-approach-depth-contact-rejects-$mutation" (!$run.accepted-and$run.error-like'*actual-id-contact-merge*') @{run=$run;scope='Actual full ApproachDepth real3D contact Check rejects invalid saved result; transport replay only'}
+        }
         $reentry=$gestureAst.Find({param($node)$node-is[Management.Automation.Language.FunctionDefinitionAst]-and$node.Name-eq'SameProgress'},$true)
         if($reentry){. ([scriptblock]::Create($reentry.Extent.Text))}
         Probe 'actual-reentry-comparator-present' ($null-ne$reentry) 'Only outer puzzleStates order may be canonicalized; Same remains strict'