--- >[!warning] >This content has not been peer reviewed. # Further applications index The **Reality Engine** is the ledger implementation (self-running substrate simulator); the list below includes both the engine and problem-focused applications (Millennium, homeostasis, Grand Map, etc.). Foundational building blocks live under **[[expanded theory applied/foundation/Foundation index|foundation/]]**. | Application | Note | |:---|:---| | **Graph Size Hierarchy** (forces → matter → chemistry → cosmology from $K_N$) | [[Graph Size Hierarchy (RST)]] | | **Navier–Stokes smoothness** | [[further applications/Navier-Stokes Smoothness/Navier-Stokes Smoothness (RST)]] | | **Birch–Swinnerton-Dyer** | [[further applications/BSD Conjecture/BSD Conjecture (RST)]] | | **Hodge conjecture** | [[further applications/Hodge Conjecture/Hodge Conjecture (RST)]] | | **P vs NP** | [[further applications/P vs NP/P vs NP (RST)]] | | **Riemann hypothesis** | [[further applications/Riemann Hypothesis/Riemann Hypothesis (RST)]] | | **Yang–Mills** | [[further applications/Yang-Mills/Yang-Mills (RST)]] | | **E₈ compatibility** | [[further applications/E8 Compatibility/E8 Compatibility (RST)]] | | **Homeostasis** | [[further applications/Homeostasis/Homeostasis (RST)]] | | **Grand Map** (complexity scale, Total ontology synthesis) | [[further applications/Grand Map/Grand Map (RST)]] | | **Solomonoff induction** (Total ontology: logic of selection) | [[further applications/Solomonoff Induction/Solomonoff Induction (RST)]] | | **Free Energy Principle** (Total ontology: optimisation of signal) | [[further applications/Free Energy Principle/Free Energy Principle (RST)]] | | **Protein folding / barrier crossing** (transition-path time, barrier shape ↔ \(n\), cost/fidelity landscape; zippering ↔ relational connectivity) | [[further applications/Protein Folding/Protein Folding Barrier Crossing (RST)]] | | **Nuclear pore complex** (selectivity, transit; disorder as substrate; same $\mu(\eta,n)$ as folding) | [[further applications/Nuclear pore complex (RST)/Nuclear pore complex (RST)]] | | **Periodic Table** (Relational Liquid Drop: Semi-Empirical Mass Formula from graph topology, **zero fitted parameters**; thermodynamic tension Strong/Pauli; Valley of Stability; discrete crystallography at small A) | [[further applications/Periodic Table (RST)/Periodic Table (RST)]] | | **Constructal law** (Total ontology: shape of the wires) | [[further applications/Constructal Law/Constructal Law (RST)]] | | **Tremaine Core–Cusp** (galactic dynamics: core–cusp from RST) | [[further applications/Tremaine Core-Cusp/Tremaine Core-Cusp (RST)]] | | **Milgrom MOND** (a₀ from first principles, μ as projection, redshift evolution, JWST signature) | [[further applications/Milgrom MOND/Milgrom MOND (RST)]] | | **Tensile Test** (stress–strain via inverted fidelity; 30 materials (22 pure metals + 8 alloys); n clusters by crystal structure FCC/BCC/HCP; temperature check; **experimental validation R²=0.987 on Al 6061-T651**) | [[further applications/Tensile Test/Tensile Test (RST)]] | | **Electronic Transport** (resistivity from fidelity: ρ = ρ₀ + A·[μ⁻¹−1]; 15 metals; n_el ≈ 5 reproduces Bloch-Gruneisen; R²=0.997) | [[further applications/Electronic Transport/Electronic Transport (RST)]] | | **Thermal Transport** (κ from WF bridge + free fit; 15 metals; Lorenz ratio separates electronic/phonon channels; **n_th ≈ 1.3–1.5 near backbone dimension**) | [[further applications/Thermal Transport/Thermal Transport (RST)]] | | **Fluid Dynamics** (viscosity from fidelity: 12 fluids (9 liquids + 3 gases); **Reynolds transition as μ-interpolation**; n_turb ≈ 20) | [[further applications/Fluid Dynamics/Fluid Dynamics (RST)]] | | **Enzyme Kinetics** (**Michaelis-Menten IS μ(η,1) EXACT** — Tier 1 identity; 8 enzymes verified to machine precision) | [[further applications/Enzyme Kinetics/]] | | **Hill Dose-Response** (**Hill equation IS μ(η,n)^n EXACT** — Tier 1 identity; 8 drug-receptor pairs verified to machine precision) | [[further applications/Hill Dose-Response/]] | | **Magnetic Hysteresis** (anhysteretic M(H) = M_s·μ(H/H_c, n); 8 materials incl. ferrites; n ≈ 1.5–4.2; R² = 0.9999; **RST outperforms Langevin and tanh**) | [[further applications/Magnetic Hysteresis/]] | | **Relational Dynamics** (**Lorentz factor γ = 1/μ(η,2) EXACT**; dynamical friction h(X) ≈ μ^α; n = 2 from quadratic metric) | [[further applications/Relational Dynamics/Relational Dynamics (RST)]] | | **Standard Model** (Quantum Gate: gauge generators → n; U(1)=1, SU(2)=3, SU(3)=8; running coupling calibration; **RST-logarithmic boundary** revealed: algebraic μ vs logarithmic loop running) | [[further applications/Standard Model/Standard Model (RST)]] | | **Quantization** (L^n energy levels: **particle-in-box n=2 R²=1 EXACT**; **hydrogen n=-2 R²=1 EXACT**; harmonic oscillator n≈1.24; Heisenberg limit from L^2 constraint; Lacunarity Spectrum) | [[further applications/Quantization/Quantization (RST)]] | | **Quantum Geometry** (Berry curvature, quantum metric; conceptual bridge to holonomy; Bloch-sector $\mu(\eta,n)$; in progress conceptual; calibration Phase 2) | [[further applications/Quantum Geometry/Quantum Geometry (RST)]] | | **Substrate Hardware** (Constants from L^n geometry: **Sovereign Chain derives α⁻¹=137.07 (0.022%), θ_W (0.058%), m_μ/m_e (0.021%), m_τ/m_e (0.013%), m_p/m_e (0.038%) from n=1.25 alone**; α_G ~ α^18; Gravity-QCD mirror symmetry. See [[expanded theory/The Sovereign Chain\|The Sovereign Chain]]) | [[further applications/Substrate Hardware/Substrate Hardware (RST)]] | | **Fidelity Inversion** (gravity ↔ materials duality: same μ, inverted argument; falsifiability conditions; six sectors) | [[expanded theory/Fidelity Inversion — Gravity and Materials]] | | **Quantum error correction** (Total ontology: hardware for A3) | [[further applications/Quantum Error Correction/Quantum Error Correction (RST)]] | | **Bell nonlocality and measurement dependence** (Bacciagaluppi et al. extended; equiprobability vs signalling on fidelity curve) | [[further applications/Bell Nonlocality and Measurement Dependence/Bell Nonlocality and Measurement Dependence (RST)]] | | **Micro-Graph Generator** (**Pure Axiom Substrate** = canonical derivation engine; rst_axiom_pure derives $n$, $d_B$; used by Nuclear Fusion, Sovereign Chain. Ledger/genesis alternatives; rst_genesis_automaton = alternative genesis. See [[expanded theory applied/Derivation Chain Overview]]) | [[further applications/Micro-Graph Generator/Micro-Graph Generator (RST)]] | | **Cosmic Visualizer** (Cinematic 3D animation of Relational Big Bang; maps topology → geometry; MP4/GIF output. See [[further applications/Cosmic Visualizer (RST)/Cosmic Visualizer (RST)]]) | [[further applications/Cosmic Visualizer (RST)/Cosmic Visualizer (RST)]] | | **Reality Engine** (self-running substrate simulator) | [[further applications/Reality Engine/Reality Engine (RST)]] | | **Material layer** (parts, scale registry, layer-to-layer translation) | [[further applications/Material layer/Material layer (RST)]] | | **Path Integral Optimization** (plug-in: parallel search over histories) | [[further applications/Path Integral Optimization/Path Integral Optimization (RST)]] | | **Ryu-Takayanagi Metric** (plug-in: metric from entanglement) | [[further applications/Ryu-Takayanagi Metric/Ryu-Takayanagi Metric (RST)]] | | **Bremermann Governor** (plug-in: hardware governor / time throttling) | [[further applications/Bremermann Governor/Bremermann Governor (RST)]] | | **Wilson RG Sensor** (plug-in: zoom slider / regime switching) | [[further applications/Wilson RG Sensor/Wilson RG Sensor (RST)]] | **Run all scripts:** From workspace root, run **`python "expanded theory applied/further applications/run_all_further_scripts.py"`** to execute every `rst_*.py` in each app folder, keep outputs in place, and build **`all_further_results.png`** plus **`run_results_summary.md`**. **Parent:** [[../Applications Roadmap|Applications Roadmap]] Scripts under this folder use **three** levels up to reach the workspace root (same as `foundation/`); see [[../How we do applications|How we do applications]].