iOS 1.0 RC 1: battery and heat work, version label, web player redraw tweaks

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

ios/Stemify/Engine/StemEngine.swift

@@ -201,7 +201,11 @@ final class StemEngine: @unchecked Sendable {
     static let ringSeconds = 3
     /// Frames each stem must have before (re)starting output.
     static let prefill = 8192
+    /// Mixed audio kept ahead of the speaker. Short while someone's looking, so faders and EQ
+    /// answer quickly; deep when nobody is, so the engine wakes a few times a second instead of
+    /// hundreds and the CPU can sleep between bursts.
     static let bufferMs = 120
+    static let backgroundBufferMs = 600
 
     /// Where playback is; position = frame + (now - nanos) while [running].
     struct Snapshot {
@@ -446,7 +450,8 @@ final class StemEngine: @unchecked Sendable {
         guard let s = session, wantPlay else {
             setFlags(false, false)
             publish()
-            idle(100)
+            // Nothing moves while paused; a command wakes the loop.
+            idle(2000)
             return
         }
         if let e = s.error() {
@@ -483,9 +488,13 @@ final class StemEngine: @unchecked Sendable {
         setFlags(true, false)
 
         guard let tap else { return }
-        if tap.ring.freeFrames < Self.chunk {
+        let target = min(trackRate * (AppActivity.isActive ? Self.bufferMs : Self.backgroundBufferMs) / 1000, tap.ring.capacityFrames)
+        let buffered = tap.ring.availableFrames
+        if buffered + Self.chunk > target {
             publish()
-            idle(5)
+            // Sleep until the buffer is half drained, then top it up in one burst.
+            let ms = Double(buffered - target / 2) * 1000 / Double(max(1, trackRate)) / speed
+            idle(max(5, Int(ms)))
             return
         }
         let n = mixChunk(s)
@@ -620,7 +629,7 @@ final class StemEngine: @unchecked Sendable {
         #if os(iOS)
         try? AVAudioSession.sharedInstance().setPreferredSampleRate(Double(rate))
         #endif
-        let t = OutputTap(rate: rate, frames: max(4096, rate * Self.bufferMs / 1000))
+        let t = OutputTap(rate: rate, frames: max(4096, rate * Self.backgroundBufferMs / 1000))
         t.setLatency(Self.outputLatency())
         t.speed = speed
         guard let fmt = AVAudioFormat(standardFormatWithSampleRate: Double(rate), channels: 2) else {