perf(analysis): reuse sorted spectral percentile windows

Reuse sorted windows for related percentiles and reject unsuitable edges before computing expensive tail statistics. Preserve cutoff results with 31 regression fixtures and 400 exact old/new comparisons.

lib/widgets/audio_analysis_widget.dart

@@ -430,18 +430,9 @@ double? estimateEffectiveSpectralCutoffHz({
 
   final centralStart = math.max(0, (height * 0.05).floor());
   final centralEnd = math.min(height, (height * 0.95).ceil());
-  final lowLevel = _spectralPercentile(
-    smoothed,
-    centralStart,
-    centralEnd,
-    0.10,
-  );
-  final highLevel = _spectralPercentile(
-    smoothed,
-    centralStart,
-    centralEnd,
-    0.95,
-  );
+  final central = _sortedSpectralWindow(smoothed, centralStart, centralEnd);
+  final lowLevel = _sortedSpectralPercentile(central, 0.10);
+  final highLevel = _sortedSpectralPercentile(central, 0.95);
   final dynamicSpan = highLevel - lowLevel;
   if (highLevel < 24) return null;
   if (dynamicSpan < 1) return maxFrequencyHz;
@@ -485,16 +476,19 @@ double? estimateEffectiveSpectralCutoffHz({
     if (belowEnd > belowStart && aboveEnd > aboveStart) {
       final belowLevel = _spectralMedian(smoothed, belowStart, belowEnd);
       final aboveLevel = _spectralMedian(smoothed, aboveStart, aboveEnd);
-      final tailLevel = _spectralMedian(smoothed, aboveStart, height);
+      if (belowLevel - aboveLevel < minimumDrop) continue;
+      // All tail statistics share one sorted window. Rejected local edges do
+      // not need to copy and sort the rest of the spectrum at all.
+      final tail = _sortedSpectralWindow(smoothed, aboveStart, height);
+      final tailLevel = _sortedSpectralPercentile(tail, 0.50);
+      if (belowLevel - tailLevel < minimumDrop) continue;
       final tailSpread =
-          _spectralPercentile(smoothed, aboveStart, height, 0.80) -
-          _spectralPercentile(smoothed, aboveStart, height, 0.20);
+          _sortedSpectralPercentile(tail, 0.80) -
+          _sortedSpectralPercentile(tail, 0.20);
+      if (tailSpread > stableTailSpread) continue;
       final baseStart = math.max(0, edgeIndex - (3000 / hzPerRow).ceil());
       final baseLevel = _spectralMedian(smoothed, baseStart, belowEnd);
-      if (belowLevel - aboveLevel >= minimumDrop &&
-          belowLevel - tailLevel >= minimumDrop &&
-          baseLevel - tailLevel >= minimumDrop &&
-          tailSpread <= stableTailSpread) {
+      if (baseLevel - tailLevel >= minimumDrop) {
         final cutoff = (edgeIndex + 0.5) * hzPerRow;
         return cutoff.clamp(0.0, maxFrequencyHz).toDouble();
       }
@@ -523,12 +517,13 @@ double? estimateEffectiveSpectralCutoffHz({
     if (belowEnd <= belowStart || aboveStart >= height) continue;
     final belowLevel = _spectralMedian(smoothed, belowStart, belowEnd);
     if (belowLevel < activeThreshold) continue;
-    final tailLevel = _spectralMedian(smoothed, aboveStart, height);
+    final tail = _sortedSpectralWindow(smoothed, aboveStart, height);
+    final tailLevel = _sortedSpectralPercentile(tail, 0.50);
+    if (belowLevel - tailLevel < activeMargin) continue;
     final tailSpread =
-        _spectralPercentile(smoothed, aboveStart, height, 0.80) -
-        _spectralPercentile(smoothed, aboveStart, height, 0.20);
-    if (belowLevel - tailLevel >= activeMargin &&
-        tailSpread <= stableTailSpread) {
+        _sortedSpectralPercentile(tail, 0.80) -
+        _sortedSpectralPercentile(tail, 0.20);
+    if (tailSpread <= stableTailSpread) {
       final cutoffIndex = edgeIndex - supportRows / 2;
       final cutoff = (cutoffIndex + 0.5) * hzPerRow;
       return cutoff.clamp(0.0, maxFrequencyHz).toDouble();
@@ -571,19 +566,20 @@ double? estimateEffectiveSpectralCutoffHz({
 }
 
 double _spectralMedian(Float64List values, int start, int end) {
-  return _spectralPercentile(values, start, end, 0.50);
+  return _sortedSpectralPercentile(
+    _sortedSpectralWindow(values, start, end),
+    0.50,
+  );
 }
 
-double _spectralPercentile(
-  Float64List values,
-  int start,
-  int end,
-  double percentile,
-) {
+Float64List _sortedSpectralWindow(Float64List values, int start, int end) {
   final safeStart = start.clamp(0, values.length).toInt();
   final safeEnd = end.clamp(safeStart, values.length).toInt();
-  if (safeEnd <= safeStart) return 0;
-  final sorted = values.sublist(safeStart, safeEnd)..sort();
+  return values.sublist(safeStart, safeEnd)..sort();
+}
+
+double _sortedSpectralPercentile(Float64List sorted, double percentile) {
+  if (sorted.isEmpty) return 0;
   final index = ((sorted.length - 1) * percentile)
       .round()
       .clamp(0, sorted.length - 1)