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output/vmix_summary.txt

@@ -60,10 +60,31 @@ Spacings < 0.3: 2105 (2.1050%)
 Top 10 smallest: [0.021778217770792023, 0.02849899040877336, 0.03108647742323653, 0.03753749176803932, 0.040620459319434]
 
 
+Mertens Extremal Analysis (up to 5,000,000)
+==================================================
+Max |M(x)|: 773
+Max |M(x)|/√x: 1.0000
+Within 2024 bound (0.6482): False
+Sign changes: 12,032 (rate: 0.0024)
+Variance M(x)/√x: 0.008394
+RH predicted variance (1/π²): 0.101321
+Variance ratio: 0.0828
+Gaussian test: Shapiro p=0.0000 → FAIL
+
+
+Cross-Module Analysis
+==================================================
+Transfer learning MAE: 4.92 (baseline: 4.85)
+Improvement: -1.6%
+Best feature index: 5
+Conjecture: Higher spectral rigidity → smaller prime gaps
+Correlation: 0.9998 → SUPPORTED
+
+
 Transformer Prime Gap Predictor
 ==================================================
-MAE: 7.02 (baseline: 6.57)
-Improvement vs mean baseline: -6.8%
+MAE: 6.87 (baseline: 6.57)
+Improvement vs mean baseline: -4.6%
 
 
 TDA Zero Analyzer (Persistent Homology)
@@ -80,3 +101,5 @@ Window sizes: [100, 500, 1000, 5000, 10000, 50000, 100000]
 Entropies: [3.18, 2.971, 2.85, 2.593, 2.496, 2.302, 2.225]
 Trend: decreasing
 Final normalized entropy: 0.5688
+
+