SSZ-Lensing

Radial Scaling Gauge Validation Suite

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Paper: Radial Scaling Gauge for Maxwell Fields

Authors: Carmen N. Wrede & Lino P. Casu

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Overview

Comprehensive validation suite for the Radial Scaling Gauge framework from the SSZ (Segmented Spacetime) theory. This repository tests gravitational lensing, Shapiro delay, and redshift predictions against experimental data.

Key Result: 28/28 tests pass (100%) - NO FITTING

Core Physics

The Radial Scaling Gauge

Gravitational effects are described by a single scaling function:

s(r) = 1 + Xi(r) = 1 + r_s/(2r)

Where:

• Xi(r) = Segment density (gravitational potential proxy)
• r_s = 2GM/c² = Schwarzschild radius
• s(r) = Physical distance scaling factor

Key Formulas

Observable	Formula	Test
Time Dilation	D(r) = 1/(1 + Xi)	GPS, Pound-Rebka
Shapiro Delay	dt = (r_s/c) * ln(4*r1*r2/r_min²)	Cassini 2003
Light Deflection	delta = (1+gamma)*r_s/b	1919 Eclipse
Redshift	z = Xi(r1) - Xi(r2)	Tokyo Skytree

Test Results Summary

Section	Tests	Status
Section 2: Radial Scaling	8	PASS
Section 3: EM Phase	7	PASS
Appendix A.1: Shapiro Delay	3	PASS
Appendix A.2: Lensing	3	PASS
Appendix B: WKB Phase	2	PASS
Frame Consistency	2	PASS
Experimental Validation	3	PASS
TOTAL	28	100%

Experimental Validation

Shapiro Delay (Cassini 2003)

• Measured: gamma = 1.000021 ± 2.3e-5
• Our prediction: Matches GR (gamma = 1)
• Delay: ~265 microseconds

Light Deflection (Solar Limb)

• 1919 Eclipse: 1.75 arcseconds
• Our prediction: 1.75 arcseconds
• Agreement: < 1%

Gravitational Redshift

• Pound-Rebka (22.5m): 2.46e-15 ✓
• GPS (20,200 km): 45.7 us/day ✓
• Tokyo Skytree (450m): 4.9e-14 ✓

Project Structure

ssz-lensing/
├── tests/
│   └── test_radial_scaling_gauge.py   # 28 comprehensive tests
├── plots/
│   ├── generate_plots.py              # Visualization generator
│   └── *.png                          # 7 plots
├── notebooks/
│   └── radial_scaling_gauge_colab.ipynb  # Interactive notebook
├── test-reports/
│   ├── RADIAL_SCALING_GAUGE_REPORT.md
│   └── radial_scaling_gauge_results.json
├── LICENSE.md                         # ACSL v1.4
└── README.md

Quick Start

Run Tests

cd tests
python test_radial_scaling_gauge.py

Generate Plots

cd plots
python generate_plots.py

Open in Colab

Click the Colab badge above or visit: Open Notebook

Requirements

pip install numpy matplotlib

Key Insight: No Fitting Required

All experimental predictions emerge directly from:

Xi(r) = r_s / (2r)

This single formula, derived from SSZ principles, reproduces:

• Shapiro delay measurements
• Gravitational lensing angles
• Clock comparison experiments
• GPS relativistic corrections

No free parameters. No curve fitting. Pure physics.

License

Anti-Capitalist Software License v1.4

See LICENSE.md for details.

Authors

• Carmen N. Wrede
• Lino P. Casu

Repository

https://github.com/error-wtf/ssz-lensing