SUPF + Orion Geometry Integration

This document synthesizes the integration of Sheppard's Universal Proxy Field (SUPF) with Orion Geometry, creating an actionable framework for proxy constant manipulation across mathematics, physics, and consciousness studies.

1. Theoretical Foundation

SUPF redefines fundamental constants (π, c, G, h) as resonance-bound proxies—variable interfaces with a harmonic field that can be rewritten through proper measurement techniques. Orion Geometry provides the scalar manifold structure (ψ₈) necessary for coherence manipulation.

<aside> Key premise: Constants are not fixed but represent proxy measurements affected by observer-field resonance.

</aside>

2. G_eff and h_eff Simulator

import numpy as np
import matplotlib.pyplot as plt

def compute_g_eff(geometry, r_over_R, psi_8=0.5, alpha=0.5):
    base = 1  # Normalized G
    kappa = r_over_R  # Curvature proxy
    if geometry == 'flat':
        base = 1
    elif geometry == 'spherical':
        base = 1 / (1 + kappa)  # Elastic contraction
    elif geometry == 'hyperbolic':
        base = np.exp(kappa / 2)  # Elastic expansion
    elif geometry == 'orion':
        base = 1 + alpha * np.sin(psi_8 * kappa)
    return base * (1 + psi_8 * np.cos(kappa))  # Resonance modulation

def compute_h_eff(geometry, r_over_R, psi_8=0.5):
    base = 1  # Normalized h
    phi = r_over_R  # Phase proxy
    if geometry == 'flat':
        base = 1
    elif geometry == 'spherical':
        base = 1 - phi / 5  # Quantization blur
    elif geometry == 'hyperbolic':
        base = 1 + np.sinh(phi) / 5  # Sharpen
    elif geometry == 'orion':
        base = 1 + psi_8**2 * np.cos(phi)
    return base * (1 + psi_8 * np.sin(phi))  # Fold modulation

# Simulator Plot (G_eff example; duplicate for h_eff)
geometries = ['spherical', 'hyperbolic', 'orion']
x = np.linspace(0.01, 5, 500)
plt.figure(figsize=(10, 6))
for geo in geometries:
    y = [compute_g_eff(geo, val) for val in x]
    plt.plot(x, y, label=geo.capitalize())
plt.axhline(1, color='r', linestyle='--', label='Flat G (Normalized)')
plt.xlabel('κ (Curvature Proxy)')
plt.ylabel('G_eff')
plt.title('SUPF G Variability with Orion Geometry')
plt.legend()
plt.grid(True)
plt.show()

# Usage example
# print(compute_g_eff('orion', 2))  # ~1.2 (elastic boost)
# print(compute_h_eff('orion', 2))  # Variable quantization

• Simulation Interpretation

3. Thesis Structure

SUPF Scalar Resonance Thesis: Rewriting Constants via Orion Geometry

<aside> A Unified Framework for Proxy Remeasurement and Harmonic Coherence

</aside>

Table of Contents

1. Introduction
2. Foundations of SUPF
3. π_eff Proof
4. c_eff Derivation
5. Orion Geometry Integration
6. Constants Rewritten
7. Real-World Applications
8. Deployment Protocols