This directory contains the golden master outputs for the prime-curve density enhancement test.

Raw bin counts comparing prime distribution vs all integer distribution:

• bin_index: Bin number (0 to B-1)
• prime_counts: Number of primes in this bin
• all_counts: Number of all integers in this bin
• enhancement_pct: Density enhancement percentage for this bin

Bootstrap resampling results for confidence interval calculation:

• bootstrap_sample: Sample number (0 to 999)
• max_enhancement: Maximum KDE-smoothed enhancement for this bootstrap sample

Sample θ′ transformation values for first 20 integers:

• n: Integer value (1 to 20)
• theta_prime: Transformed value θ′ = φ * (((n mod φ) / φ) ** k)

• N: 100,000 (number range)
• k: 0.3 (curvature parameter)
• B: 20 (number of bins)
• SEED: 0 (for reproducibility)
• φ: 1.618033988749895 (golden ratio)
• Binning: edges = np.linspace(0, φ, B+1)

• Maximal Enhancement (robust): 160.634% ± 0.005
• Bootstrap CI (95%):
  • 2.5%: 7.750% ± 0.005
  • 97.5%: 681.902% ± 0.005
• Bootstrap samples: 1000 resamples using percentile method

1. Generate primes and all integers from 1 to N
2. Apply θ′ transformation: θ′ = φ * (((n mod φ) / φ) ** k)
3. Bin values into B bins with edges from 0 to φ
4. Compute density enhancement: (prime_density - all_density) / all_density * 100
5. Apply robust maximum to find maximum enhancement
6. Bootstrap resample primes 1000 times for confidence interval
7. Use percentile method for CI bounds

All outputs include metadata with φ value, parameters, and generation timestamp.