fix(analysis): detect full-band spectral cutoff

lib/widgets/audio_analysis_info_card.dart

@@ -171,13 +171,16 @@ class _AudioInfoCard extends StatelessWidget {
                   value: _formatClipping(context, data.clippingSamples),
                   cs: cs,
                 ),
-                if (data.spectralCutoffHz != null)
-                  _MetricChip(
-                    icon: Icons.filter_alt_outlined,
-                    label: context.l10n.audioAnalysisSpectralCutoff,
-                    value: _formatFrequency(data.spectralCutoffHz!),
-                    cs: cs,
+                _MetricChip(
+                  icon: Icons.filter_alt_outlined,
+                  label: context.l10n.audioAnalysisSpectralCutoff,
+                  value: formatAudioAnalysisSpectralCutoff(
+                    data.spectralCutoffHz,
+                    notDetectedLabel:
+                        context.l10n.audioAnalysisCutoffNotDetected,
                   ),
+                  cs: cs,
+                ),
                 _MetricChip(
                   icon: Icons.numbers,
                   label: context.l10n.audioAnalysisSamples,
@@ -228,11 +231,6 @@ class _AudioInfoCard extends StatelessWidget {
     return data.channels > 0 ? '${data.channels}' : 'N/A';
   }
 
-  String _formatFrequency(double hz) {
-    if (hz >= 1000) return '${(hz / 1000).toStringAsFixed(1)} kHz';
-    return '${hz.round()} Hz';
-  }
-
   String _formatBitrate(int bitsPerSecond) {
     if (bitsPerSecond >= 1000000) {
       return '${(bitsPerSecond / 1000000).toStringAsFixed(2)} Mbps';

lib/widgets/audio_analysis_models.dart

@@ -3,7 +3,7 @@ part of 'audio_analysis_widget.dart';
 // Analysis result models and per-run parameter records.
 
 class AudioAnalysisData {
-  static const cacheVersion = 7;
+  static const cacheVersion = 8;
 
   final String filePath;
   final int fileSize;

lib/widgets/audio_analysis_widget.dart

@@ -24,6 +24,19 @@ const int audioSpectrogramHeight = 800;
 const int audioSpectralAnalysisWidth = 400;
 const double audioSpectrogramDynamicRangeDb = 120;
 
+String formatAudioAnalysisSpectralCutoff(
+  double? cutoffHz, {
+  required String notDetectedLabel,
+}) {
+  if (cutoffHz == null || !cutoffHz.isFinite || cutoffHz <= 0) {
+    return notDetectedLabel;
+  }
+  if (cutoffHz >= 1000) {
+    return '${(cutoffHz / 1000).toStringAsFixed(1)} kHz';
+  }
+  return '${cutoffHz.round()} Hz';
+}
+
 String _buildShowspectrumOptions({required int width, required String color}) {
   return 'showspectrumpic='
       's=${width}x$audioSpectrogramHeight:'
@@ -385,8 +398,10 @@ double? estimateEffectiveSpectralCutoffHz({
   }
 
   // A genuinely broadband signal with no internal falling edge reaches the
-  // analysis ceiling. Report Nyquist only when both its baseband and top band
-  // are populated; silence or an isolated high-frequency line returns null.
+  // analysis ceiling. Natural music has a pronounced spectral tilt, so the
+  // top band does not need to be almost as loud as the baseband. It must still
+  // sit clearly above the measured low-level floor; silence or an isolated
+  // high-frequency line therefore continues to return null.
   final basebandLevel = _spectralMedian(
     smoothed,
     (height * 0.05).floor(),
@@ -397,7 +412,8 @@ double? estimateEffectiveSpectralCutoffHz({
     (height * 0.90).floor(),
     math.max(1, (height * 0.98).floor()),
   );
-  if (basebandLevel >= 24 && topBandLevel >= basebandLevel - minimumDrop) {
+  final populatedTopFloor = math.max(24.0, lowLevel * 0.60);
+  if (basebandLevel >= 24 && topBandLevel >= populatedTopFloor) {
     return maxFrequencyHz;
   }
   return null;