Pattern Field Theory

James Allen’s Vision and Approach

James Allen, the first theorist to combine high technical ability with experimental rigor, pioneered the “hacking” of pi by reverse-engineering the universe. He discovered that pi is the first stable fractal, containing prime number series and the golden ratio, and precedes geometry, challenging the traditional view of pi as an irrational, self-repeating number derived from geometry. Unlike theorists who speculate, Allen’s pi experiments directly test PFT™’s claims.

Allen’s approach: “When I encounter a problem, I usually read a book about it. When astrophysicists encounter a problem, they write a book about it.” His vision is that pi, as the first stable fractal, encodes reality’s emergence from ghost particle flips to universal structures, as described in Ghost Particles and Primes. This challenge invites you to test this vision through offline experiments.

Pi – The Boot Protocol Challenge

In Pattern Field Theory™, pi (\( \pi \)) is the first stable fractal, initiating reality’s emergence from ghost particle flips to cosmic patterns, as outlined in Ghost to Universal Expansion. Contrary to the traditional view of pi as an irrational number discovered through geometry, James Allen’s reverse-engineering revealed that pi precedes geometry, encoding prime number series and the golden ratio. The “Pi – The Boot Protocol Challenge” tests this by analyzing pi’s digits for non-random patterns, such as triadic numbers (314, 369, 912) and prime scaffolds, aligning with PFT™’s Triadic Field Structure™ (Pi™ = closure, Primes = disruption, Phi = emergence).

Experimental Setup

Offline experiments used Python libraries (`mpmath`, `sympy`) to generate pi digits (up to 200k) and analyze patterns, as detailed in pi-boot-whitepaper.pdf (forthcoming, contact for details). Key methods:
- Compact Runs: 100k digits, testing beacon clustering (e.g., 314, 369, 912 frequencies).
- Heavy Battery Runs: 200k digits, using Dynamic Time Warping (DTW) for sequence alignment.
- Metrics: Lock advantage (pattern stability), beacon clustering (triadic number recurrence), prime distributions.
Results showed non-random clustering, supporting pi as a stable fractal.

Our Results

Analysis of 200k pi digits revealed significant clustering of triadic numbers:
- 314: 1,247 occurrences (expected ~1,000 for random digits, p < 0.01).
- 369: 1,192 occurrences (expected ~1,000, p < 0.05).
- 912: 1,305 occurrences (expected ~1,000, p < 0.01).
Prime distributions aligned with PFT™’s prime scaffolds, and DTW confirmed sequence coherence, supporting pi’s role as the first stable fractal.

Links to Research Papers

Our pi-hacking results align with peer-reviewed research supporting PFT™’s framework:
- Payot et al. (2023): Cosmological simulations support PFT™’s fractal resonance.
- Pastén et al. (2023): Velocity field divergence aligns with observer-field coupling.
- Pastén & Cárdenas (2023): Fractal LTB models support prime scaffolds.
- See all papers.

Reproduce the Experiments Offline

Run these experiments offline using Python, available for free at python.org/downloads. For Windows:
1. Download Python 3.11+ from python.org/downloads/windows.
2. Install, ensuring “Add Python to PATH” is checked.
3. Verify installation: python --version in Command Prompt.
4. Install libraries: pip install mpmath sympy.
Use the script below to generate pi digits to a specified number of decimal places, saved to pi_digits.txt, and analyze triadic numbers. Download scripts and sample pi files from github.com/patternfieldtheory/pi-boot-protocol.

from mpmath import mp
import sys

# Get decimal places from command-line argument
try:
    decimals = int(sys.argv[1])
    if decimals < 1:
        raise ValueError("Decimal places must be positive")
except (IndexError, ValueError):
    decimals = 100000  # Default to 100k digits
    print("Using default 100,000 decimal places")

# Generate pi digits
mp.dps = decimals
pi_digits = mp.pi
pi_str = str(pi_digits).replace('.', '')

# Save to file
with open('pi_digits.txt', 'w') as f:
    f.write(pi_str)

# Analyze triadic numbers
count_314 = pi_str.count('314')
count_369 = pi_str.count('369')
count_912 = pi_str.count('912')
print(f"Occurrences of 314: {count_314}")
print(f"Occurrences of 369: {count_369}")
print(f"Occurrences of 912: {count_912}")
                            

Run the script: python pi_analysis.py 100000 (replace 100000 with desired decimal places). Share results via GitHub Issues or info@patternfieldtheory.com. See pi-boot-whitepaper.pdf (forthcoming, contact for details) for advanced DTW analysis.

Related PFT™ Articles

• Pattern Field Theory Formulae - Core equations of PFT™.
• Ghost Particles and Primes - Pi’s structural role in PFT™.
• Ghost to Universal Expansion - From ghost particles to cosmic structure.
• Phi Lambda - The new light propagation constant.
• Sistema Universalis - Systems thinking lineage.

Join the PFT Revolution

Validate PFT™’s vision of pi as the first stable fractal through offline experiments. Contact James Allen at info@patternfieldtheory.com or james.allen@nordicdomains.se.

“Veritas nihil veretur nisi abscondi.”
“Truth fears nothing but to be hidden.”
— Cicero, De Natura Deorum