# Geometric Encoded Medium (GEM) Physics Framework
 [](https://opensource.org/licenses/MIT)  [](https://crates.io/crates/gemphy) [](https://docs.rs/gemphy) [](https://github.com/troydeville/gemphy/actions)
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## 🌌 Overview
The **GEM Framework** is a Rust library that models reality as a single **Geometric Encoded Medium**. It posits that space-time is a medium with intrinsic impedance ($Z_p$) and a **Horn Torus topology**. All physical phenomena—Gravity, Electromagnetism, Mass, and Charge—are derived as specific "encodings" on this geometric hardware.
Unlike traditional physics engines that rely on curve-fitting or arbitrary constants, GEM **derives** fundamental values like Newton's Gravitational Constant ($G$), the Fine Structure Constant ($\alpha$), and the Proton Radius from first-principles geometric axioms.
## 🧠 Core Philosophy: The Unified Phase Engine
In GEM, the universe operates as a geometric circuit:
* **The Hardware:** A Horn Torus manifold ($R = r$) where the singularity at the center acts as a topological pump.
* **The Phase:** Interactions are not just magnitudes; they are complex vectors. Extreme scales (Planck, Black Holes, Muonic states) rotate real linear forces into **Imaginary/Rotational components**.
* **The Whirl:** Particle "Spin" is visualized as a **Traveling Wave** of energy density orbiting the singularity, rather than a point-particle rotating in a void.
## Roadmap
| v0.3 | Add horn torus simulation; enhanced orbit sims (hydrogen, muonic, neutron star) |
| v0.4 | Interactive CLI; Python bindings; initial multi-body support |
| v0.5 | gemphy-web deployment with live visualizations; basic n-body examples (e.g., Sun-Earth-Moon) |
| v1.0 | Full predictions (e.g., dark matter as impedance, novel deviations in fine structure); arXiv preprint with derivations |
| v0.3 | Add horn torus simulation
| v0.4 | Interactive CLI
| v1.0 | Full predictions (e.g., dark matter as impedance)
---
## 🚀 Quick Start
## 📦 Installation
```toml
[dependencies]
gemphy = "0.2.2"
```
Note: Re-exports `Complex64` from `num-complex`.
---
## Example Test Usage
## View tests
```bash
cargo run --bin orbit_sim
```
```bash
cargo run --bin electron_proton_action
```
```bash
cargo run --bin muon_proton_action
```
```bash
cargo run --bin neutron_star_action
```
---
### Stable Orbit Simulation
GEMPHY handles the "Dynamic Stability" of orbits by calculating the interaction between geometric knots.
```rust
use gemphy::{knot::GeometricKnot, medium::{GAMMA_P, GeometricEncodedMedium}};
use physical_constants::{ELECTRON_MASS, PROTON_MASS, ELEMENTARY_CHARGE};
fn main() {
let m1 = ELECTRON_MASS;
let m2 = PROTON_MASS;
let medium = GeometricEncodedMedium::new();
// Setup Particles as Geometric Knots
let electron = GeometricKnot::new(medium.clone(), m1, &[-1.0], 0.0, "Electron");
let proton = GeometricKnot::new(medium.clone(), m2, &[1.0], 0.0, "Proton");
let rg1 = (GAMMA_P / (electron.mass * medium.alpha)).powi(2);
let rg2 = (GAMMA_P / (proton.mass * medium.alpha)).powi(2);
let d = (rg1+rg2).sqrt();
let interaction = medium.calculate_interaction(&electron, &proton, d.into());
println!("Result: {:#?}", interaction);
println!("Er (eV): {:#?}", interaction.er1.norm()/ ELEMENTARY_CHARGE);
println!("Ei (eV): {:#?}", interaction.ei1.norm()/ ELEMENTARY_CHARGE);
println!("E (eV): {:#?}", interaction.binding_energy.norm()/ ELEMENTARY_CHARGE);
}
```
---
## 📐 The Geometric Model
### I. Fundamental Scaling
The framework uses a fundamental geometric normalization constant to bridge the subatomic and cosmic scales:
* **Normalization Constant ($S$):**
$$({4 \pi})^{1/4} \approx 1.8827925275534296$$
* **Mass-Charge Metric ($\phi$):**
$$\phi = 10^4 \text{ kg}^2 \text{ m}^{-2} \text{ s}^2 \text{ C}^{-2}$$
* **Magnetic Scaling ($\Phi$):**
$$\Phi = \frac{1}{10^7} \text{ H/m}$$
* **Primary Impedance ($Z_p$):**
$$Z_p = \frac{2h}{e^2} \Omega$$
#### Fine Structure ($\alpha$) Scaling Relationships
* **Primary Fine Structure ($\alpha_p $):**
$$\alpha_p = \frac{4\pi c}{Z_p}$$
* **Fine Structure ($\alpha $):**
$$\alpha = \frac{4\pi c}{Z_p} \Phi$$
* **Impedance ($Z_p$, $Z_o$):**
$$\alpha Z_p \implies Z_0$$
* **Permeability ($\mu_p $):**
$$\mu_p = \frac{Z_p}{c} \implies \mu_0 = \alpha \mu_p$$
* **Permittivity ($\epsilon_p$)**
$$\epsilon_p = \frac{1}{c Z_p} \implies \epsilon_0 = \frac{1}{\alpha} \epsilon_p $$
* **Gamma factor ($\Gamma_p$)**
$$\Gamma_p = \frac{e^2}{\alpha_p} \implies \Gamma = \frac{\Gamma_p}{\alpha}$$
### II. Gravitational Unification
GEM derives $G$ as a result of geometric impedance scaling rather than an empirical measurement:
Where $Z_0$ is the vacuum impedance and $S$ is the geometric shape factor:
$$
G = \frac{Z_0}{c S \phi}
[\frac{m^3}{kg s^2}]
$$
### III. Complex Geometry
**A complex rotation relating field geometry to mass-charge equivalence. ($\Xi$)**
$$\Xi = \sqrt{4\pi \sqrt{2} G \epsilon_0} \left( \cos\frac{\pi}{8} - i \sin\frac{\pi}{8} \right)[C/kg]$$
Force is calculated as a complex vector.
#### Linked Complex Potentials ($E_r$, $E_i$)
Energy interaction in GEM is calculated as the sum of two body-specific complex potentials. Each potential represents the geometric "tension" localized to that body within the medium:
* **$E_r$:** Complex potential of Body 1 (e.g., the orbiting mass).
* **$E_i$:** Complex potential of Body 2 (e.g., the central mass).
* **Total Interaction Energy ($E_r + E_i$):** .
The relationship between $E_r$ and $E_i$ is intrinsically linked by the medium's impedance. As distance or energy density changes, these values rotate in the complex plane, representing the transition from linear work to orbital/spin action.
---
## 🛠 Visualization: The Horn Torus Manifold
The provided `HornTorusManifold` component (for Three.js/React) is a **Raw Scientific Viewer** designed to mirror the Rust engine's output:
* **Traveling Waves:** Total Energy ($E$) is treated as a complex phase. This phase drives a wave that "chases its tail" around the torus, visually representing particle spin and momentum.
* **Singularity Flow:** The mesh geometry respects the Horn Torus topology ($R=r$), creating a natural "topological pump" at the center that breathes the vacuum.
* **No Fakes:** All surface deformations are driven by the `Complex64` results of the physical interaction. If the engine calculates zero energy, the manifold remains stagnant.
---
## ⚖️ License
Licensed under the **MIT License**.
> **Scientific Attribution:** If you use GEMPHY in a research paper or commercial simulation, please cite the framework to preserve the geometric integrity of the medium.
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