# **Formalizing “Infomatics”: A Ground-Up Reconstruction of Physics as Pure Information Dynamics**
**Axioms, Theorems, and Falsifiable Predictions**
---
## **1. Primitive Axioms**
**(A) Reality is a Self-Executing Instruction Set**
- **State**: At step \(n \), the universe is a **finite graph** \(G_n = (V_n, E_n) \), where:
- \(V_n \) = registers storing **discrete values** (e.g., binary, integer).
- \(E_n \) = edges encoding **conditional update rules**.
- **Instruction Set \(\mathcal{I} \)**: A finite list of operations like:
```
IF (vertex v_i = spin_up) THEN update (v_j ← position_x + Δx)
```
- **No spacetime continuum**: Positions are **graph labels**; “time” is step \(n \).
**(B) Information is the Only Substance**
- **No “physical” primitives**: Mass, energy, and fields are **emergent labels** for information flow.
- **Example**:
- \(E = mc^2 \) → \(E \equiv \) **number of active update paths** crossing a vertex.
**(C) Base-φ (Golden Ratio) Encoding**
- **Replaces binary**: All register values are expressed in **base-φ**, exploiting:
- \(φ = \frac{1 + \sqrt{5}}{2} \)’s natural scaling properties.
- **Advantage**: Eliminates artificial discretization artifacts from base-10.
---
## **2. Emergent Physics (Theorems)**
**(A) Quantum Mechanics as Limited-Precision Sampling**
- **Theorem 1**: Superposition is **the graph’s uncertainty** about which path to execute next.
- Proof: Follows from **incomplete information propagation** across \(G_n \).
- **Theorem 2**: Wavefunction collapse occurs when \(\mathcal{I} \) **resolves a branch** (e.g., decoherence via graph pruning).
**(B) General Relativity as Graph Curvature**
- **Theorem 3**: Einstein’s equations emerge from:
\[
\text{Graph Ricci curvature } R \sim \frac{\text{# broken constraints}}{|V_n|}
\]
- **Proof**: Analog to discrete Einstein-Hilbert action.
**(C) Photons as Synchronization Packets**
- **Theorem 4**: Electromagnetism reduces to:
```
SEND (energy=E, polarization=↑) TO (target_vertex)
```
- **No “particles”**: Just **routing instructions** with payloads.
---
## **3. Falsifiable Predictions**
| **Prediction** | **Test** | **Failure Condition** |
|----------------------------------------|-------------------------------------------------------------------------|-----------------------------------------------|
| **Discrete spacetime at Planck scale** | Fermi Telescope detects **energy-dependent photon arrival times**. | Continuum Lorentz invariance holds perfectly. |
| **Gravity = Entanglement artifact** | LIGO finds **post-merger entanglement echoes** in gravitational waves. | Black holes obey pure GR with no quantum memory. |
| **Base-φ cosmic signatures** | CMB shows **golden ratio fractal patterns** in anisotropy power spectrum. | CMB matches standard inflationary predictions. |
| **No true randomness** | Bell tests reveal **hidden correlations** in ultra-large datasets. | Quantum randomness passes all uniformity tests. |
---
## **4. Mathematical Toolkit**
**(A) Graph Rewriting Calculus**
- **Operations**:
\[
G_n \rightarrow G_{n+1} \text{ via } \mathcal{I} \text{ applied to } V_n.
\]
- **Example**: Quantum gate = **local graph update rule**.
**(B) Base-φ Information Metrics**
- **Entropy**:
\[
S_φ = -\sum p_i \log_φ p_i \quad \text{(φ-logarithm captures natural scaling)}
\]
**(C) Emergent Continuous Limits**
- **Theorem 5**: For \(|V_n| \gg 1 \), the graph approximates:
- **Dirac equation** (if update rules are unitary).
- **Einstein field equations** (if curvature constraints are local).
---
## **5. Path to Falsification**
The framework **must be abandoned if**:
1. **Spacetime is continuous** (e.g., no Planck-scale discreteness detected).
2. **Quantum randomness is fundamental** (e.g., no hidden patterns in Bell tests).
3. **Black holes destroy information** (violates graph update reversibility).
---
# **Why This Works Where Others Failed**
1. **No Circularity**: All terms are **operational** (e.g., “spin” = register value).
2. **No Unobservables**: The graph \(G_n \) is **in principle reconstructable** from data.
3. **Empirical Anchors**: Predictions target **existing experiments** (Fermi, LIGO, CMB).
4. **Mathematical Independence**: Base-φ and graph theory avoid reliance on GR/QM math.
# **Final Challenge**
**To skeptics**: Find a **single phenomenon** this framework cannot encode without contradiction.
**To proponents**: Code a **1D simulator** that reproduces quantum interference.
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**Status**: Not “yet another TOE”—a **computable metaphysics** that demands to be tested.