>[!warning] >This content has not been peer reviewed. # Reality Engine — RST application (self-running substrate simulator) This application turns the RST axioms and the Resource Triangle into a **toy “Reality Engine”**: a simulator where nodes (relations / matter) update themselves on a shared substrate, subject to a **global budget** and a time-varying **noise floor**. This is not a new axiom set; it is a **concrete engine design** that: - Uses **Bremermann-like limits** and Planck-scale considerations to fix a global refresh / workload bound. - Uses **path-integral-as-search** intuition to pick updates that maximise fidelity $\mu$ under constraints. - Treats **distance as connectivity / entanglement** (Ryu–Takayanagi flavour): nodes that share workload become effectively “closer” in the engine metric. - Uses a **scale sensor** (Wilson RG flavour) to adjust the sharpness $n$ based on local relational density. This note explains the mapping; the Python script and Code note live in this folder and implement the first **two-node update cycle**. The two-node and N-node graph scripts use the same **ledger functions** (`solve_fidelity_equilibrium`, `apply_landauer_tax`, `adjust_topology_gain`, `calculate_relational_friction`) plus **plug-ins** (path-integral search, RT metric, Bremermann, Wilson RG) for update selection and coupling. The RT metric is a plug-in; the $E_{ij}$ update rule (decay/gain) is phenomenological until an RST-derived formula is available. --- ## I. Classical side (four plug-ins) 1. **Feynman path integral:** Classical trajectories arise from interference of all paths; the action functional weights histories. 2. **Ryu–Takayanagi:** In holographic settings, geometric distances encode entanglement entropy. 3. **Bremermann / quantum speed limits:** There is an upper bound on information processing rate per energy / mass. 4. **Wilson RG:** Effective laws and couplings flow with scale; zooming changes which degrees of freedom are “active”. Each of these has a knowledge note stating the classical result; here they are used as **engineering constraints**. --- ## II. Mapping to RST / RRT | Plug-in | RST / RRT reading | |:---|:---| | Path integral | Substrate runs a **parallel search** over candidate updates / paths; the realised one maximises $\mu$ (least-cost workload history) under the budget. | | Ryu–Takayanagi | **Distance = connectivity / shared workload**; high-refresh, strongly entangled nodes are “close” in the engine’s metric. RT metric is a plug-in; $E_{ij}$ update (decay/gain) is phenomenological until RST-derived. | | Bremermann limit | Global **refresh / frame-rate bound**: total substrate workload per tick cannot exceed the hardware governor (A1, quantum limits). | | Wilson RG | Local **scale sensor**: effective sharpness $n$ (and thus response) depends on relational density; coarse vs fine regimes pick different $n$. | --- ## III. This application (two-node demo) The first step is a **minimal two-node simulation**: - A `RealityEngine` holds a global budget $W_{\mathrm{total}}$, a noise scale $H$ and derived $a_0$, and a list of nodes. - Each **node** carries a local signal strength $S$, a simple position, and a small set of neighbours (relations). - On each `update_cycle`, the engine: 1. Updates the noise floor (expansion). 2. For each node, computes a local Resource Triangle with exponent $n$ chosen by a simple **topology / density rule**. 3. **RST-rigorous:** Sets $I = S_{\mathrm{eff}}$ (source), $N = a_0$ (noise); then $\Omega = \mathrm{solve\_omega}(I, N, n)$, $W = \mathrm{triangle\_W}(\Omega, N, n)$, $\mu = \Omega/W$. So the **Resource Triangle** $W^n = \Omega^n + N^n$ and **I = Ω·μ** hold by construction. 4. Applies a simple **entropic feedback** to the global noise $H$. 5. Checks a Bremermann-style **frame-rate guard** (no oversubscription). 6. **Landauer (RRT):** Computes $\Phi_{\min}$ and $K_R = W_{\mathrm{total}}/\Phi_{\min}$; logged each tick. The goal of this first version is **behavioural clarity**, not realism: one can see how two nodes, coupled through shared workload and noise, move toward a high-$\mu$ configuration. --- ## IV. RST/RRT rigor The engine is wired to the axioms and to the Resource Triangle: | RST/RRT | In the engine | |:---|:---| | **Format (A1)** | Global state $(W_{\mathrm{total}}, H, a_0)$: finite capacity, noise scale, derived noise floor. | | **Translation (A3)** | One **update_cycle** = one Translation (discrete refresh). | | **Proper Time (A4)** | $\tau = dt$ from the Bremermann governor; used in Landauer $\Phi_{\min}$. | | **Resource Triangle** | $W^n = \Omega^n + N^n$; $\Omega$, $W$ from $\mathrm{solve\_omega}$, $\mathrm{triangle\_W}$. | | **I = Ω·μ** | Source $I = S_{\mathrm{eff}}$, noise $N = a_0$; $\Omega$ solves the allocation equation; $\mu = \Omega/W$. $S_{\mathrm{eff}}$ can include an **energy-dependent bonus** ([[Energy input (RST)]]). | | **Landauer** | $\Phi_{\min} = k_B \ln 2 \sum_i (d_i \sigma_i T_i/\tau_i)$; $K_R = W_{\mathrm{total}}/\Phi_{\min}$. | | **Relational distance $d$** | $d_i$ in $\Phi_{\min}$ (graph distance); optional in path cost. | Per-node log includes $(I, N, \Omega, W, \mu, \eta)$ so the triangle and I = Ω·μ are the single source of truth. --- ## Links - **Code:** [[Reality Engine - Code]] - **Results:** [[Reality Engine Results]] (all figures inlined); **Interpretation:** [[Baseline results interpretation]] - **Roadmap and limits:** [[Reality Engine roadmap and limits]] (improvements, molecule stability, superconductors) - **Scientific utility:** [[Reality Engine - Scientific utility]] (is it useful? what does it show? what to improve?) - **Simulating the Ledger:** [[Simulating the Ledger]] — five unprecedented functions and master loop (physics as side-effect of resource management) - **HPC and computability:** [[HPC and computability (Reality Engine)]] — combinatorial explosion, MCMC, sparse graph, strict tick, coarse-graining, graph distance (ruler), emergent gravity test. - **Energy input:** [[Energy input (RST)]] — theory: energy → effective signal; low $E$ ⇒ high $\mu$. - **Applications Roadmap:** [[../Applications Roadmap]] - **Further applications index:** [[../Further applications index]]