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>This content has not been peer reviewed.
# Simulating the Ledger
A Reality Engine that does something never achieved before moves away from **Simulating Objects** (like current game engines) and **Simulates the Ledger**.
- **Traditional engine:** *"Here is a ball, it has gravity, move it."*
- **This engine:** *"Here is a set of relations, I have 100 bits of power, find the cheapest way to keep them from disappearing."*
Physics (gravity, MOND, decay, dimension) emerges as a **side-effect of resource management**. The implementation exposes five **unprecedented functions** and a **master loop** that use the ledger as the single source of truth.
---
## 1. `calculate_relational_friction(path_complexity)` — A5
**Difference:** Distance is not a coordinate; it is a **workload tax**. Current engines use Euclidean distance $\sqrt{x^2+y^2}$; this one uses **A5 (Relational Distance)**.
**Function:** Returns the multiplier by which path cost scales. The number of substrate updates required to connect two nodes depends on path complexity; if the path is complex (e.g. fractal, or many hops), the distance "stretches."
**Unprecedented result:** Gravity (curvature) emerges: "heavy" objects create path-congestion, making the distance around them cost more bits to traverse.
**Code:** `rst_engine.ledger.calculate_relational_friction(path_complexity)` → float. Used in path cost: `effective_cost = base_cost * friction`.
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## 2. `solve_fidelity_equilibrium(signal, noise, n)` — RST core
**Difference:** No `apply_force()`. This solves the **self-consistent equation** $I = \Omega^2/W$ (Resource Triangle). Equivalently, $I = \Omega \cdot \mu = \Omega^2/W$ (projection of signal onto hypotenuse).
**Function:** Takes the "requested state" (signal $I$) and "environmental noise" ($N$), and finds the equilibrium the substrate can afford to render. Returns $(\Omega, W, \mu)$.
**Unprecedented result:** **MOND / dark matter** (galaxies) and **vacuum polarization** (particles) emerge without coding a single law of physics — they fall out of the ledger.
**Code:** `rst_engine.ledger.solve_fidelity_equilibrium(signal, noise, n)` → (Omega, W, mu).
---
## 3. `apply_landauer_tax(sigma, T, tau, d)` — A2
**Difference:** In standard engines, things stay the same for free. Here **identity is a dissipative process** (A2). Every entity pays a bit-tax every refresh to stay "resolved."
**Function:** Returns the tax (energy/budget) to subtract this cycle, from $\Phi_{\min}$-style cost: $k_B \ln 2 \cdot d \cdot \sigma \cdot T / \tau$. If the entity cannot pay (energy ≤ 0), the engine triggers `blur()` or `decay()`.
**Unprecedented result:** **Second Law** and **radioactive decay** derive from a CPU-usage limit — the substrate cannot afford to maintain the bit.
**Code:** `rst_engine.ledger.apply_landauer_tax(sigma, T, tau, d)` → tax (float). Engine does `entity.energy -= tax`; if `entity.energy <= 0` then `entity.decompose()`.
---
## 4. `adjust_topology_gain(local_snr)` — Wilson RG
**Difference:** Standard engines assume space is 3D ($n=3$ or $n=2$). Here **dimension is a variable**: the exponent $n$ in the Resource Triangle depends on local signal-to-noise.
**Function:** Given local SNR ($\eta = S/N$), returns effective $n$. High SNR (e.g. atomic scale) → $n \to 2$ (Euclidean/EM). Low SNR (e.g. galactic) → $n \to 1.25$ (fractal/MOND).
**Unprecedented result:** The simulation **seamlessly transitions** between Standard Model and General Relativity with zoom — the "geometry" of the network changes with how "crowded" it is.
**Code:** `rst_engine.ledger.adjust_topology_gain(local_snr)` → n (float).
---
## 5. `minimize_prediction_error(agent, N_global)` — Friston
**Difference:** "Life" in this engine is a cluster of relations that **predicts the noise** ($N$) to lower its own **tax** (A2).
**Function:** Agents maintain an internal model of $N$. Each step, the agent updates its model toward observed $N$ and receives a **tax discount** when prediction error is low. So effective tax = Landauer tax × discount.
**Unprecedented result:** **Emergence of intelligence** as a mathematical necessity of a finite substrate. Life is not "added"; it is what happens when the ledger tries to optimize itself.
**Code:** `rst_engine.ledger.minimize_prediction_error(agent, N_global)` → tax_discount (float). Protocol: `FristonAgent` with `get_sigma`, `get_N_predicted`, `update_model`, `prediction_error`. Concrete: `SimpleFristonAgent`.
---
## The Master Loop
```python
while simulation_running:
# 1. Update the Noise Floor (expansion / entropic feedback)
N_global = substrate.get_total_overhead()
# 2. Each entity requests to continue existing
for entity in registry:
n = adjust_topology_gain(entity.SNR)
Omega, W, mu = solve_fidelity_equilibrium(entity.S, N_global, n)
entity.energy -= apply_landauer_tax(entity.sigma, N_global, tau, d)
if mu < 1.0:
entity.apply_mond_boost()
if entity.energy <= 0:
entity.decompose()
# 3. Life: agents try to lower their bill (active inference)
for agent in life_registry:
perform_active_inference(agent, N_global)
```
**Script:** `rst_reality_engine_ledger_loop.py` implements this loop with the five functions. The two-node engine (`rst_reality_engine_two_node_demo.py`) uses the same ledger API: `solve_fidelity_equilibrium`, `adjust_topology_gain`, `calculate_relational_friction` in the path-integral cost.
---
## Why this is "Physics 2.0"
The engine does not "cheat" with fixed laws. It **discovers** them from the ledger:
- **Gravity / attraction:** Two heavy nodes "attract" because **merging their workload is cheaper** than keeping them separate (workload discount).
- **Quantum flicker:** Zoom into a node and it **flickers** (probability) because the engine's resolution limit cannot draw a perfect point.
The engine is a simulator where "Physics" is a side-effect of "Resource Management."
---
## Links
- **Code:** [[Reality Engine - Code]]; ledger API: `rst_engine.ledger`; loop: `rst_reality_engine_ledger_loop.py`
- **Theory:** [[../../expanded theory/Resource Triangle]], [[../../expanded theory/Relational Friction]], [[../../expanded theory/Relational Resolution Theory (RRT)]], Axioms A1–A5