>[!warning] >This content has not been peer reviewed. # Foundations — maths and physics for RRT mapping This folder is the **bridge layer** between classical mathematics/physics and **[[Relational Resolution Theory (RRT)|RRT]]** / **[[Relational Substrate Theory (RST)|RST]]**. Each note explains how one essential discipline maps onto the axioms and the Resource Triangle. Together they support the **[[Applications Roadmap|applications]]** (Millennium problems, biology, cosmology, etc.). **Vault level:** RRT (top) → **Foundations** (bridge) → RST (second) → Applications (third). See **[[Overview — RRT, RST, and applications]]** for the full structure. **Run all scripts:** From the foundation folder, run `python run_all_foundation_scripts.py`. Results stay **next to each mapping** (each topic folder keeps its own `.png`). The runner also builds **one combined image**, **[[all_foundation_results]]**, and writes **[[Foundation scripts — run results]]**. See **[[Run all foundation scripts - Code]]** for details. --- ## Priority list (building blocks for mapping any problem to RRT) | Priority | Note | RRT/RST link in one line | |:---|:---|:---| | 1 | **[[foundation/Information and Entropy/Information and Entropy (RST)]]** | Resolution $\sigma$; $I$, $N$, $\Omega$; A2. | | 2 | **[[foundation/Thermodynamics and Landauer/Thermodynamics and Landauer (RRT)]]** | $\Phi_{\min}$, $k_B T \ln 2$; A2, A3. | | 3 | **[[foundation/Measure and budget allocation/Measure and budget allocation (RST)]]** | $W^n = \Omega^n + N^n$, $\mu^n + \nu^n = 1$; Resource Triangle. | | 4 | **[[foundation/Scaling and dimensional analysis/Scaling and dimensional analysis (RST)]]** | $\mu(\eta,n)$, $n$; MOND/Newton; transition sharpness. | | 5 | **[[foundation/Spectral and analytic structure/Spectral and analytic structure (RST)]]** | $L$-functions, zeta, zeros; BSD, Riemann; primes as scales. | | 6 | **[[foundation/Continuum limits and PDEs/Continuum limits and PDEs (RST)]]** | Smoothness, blow-up; Navier–Stokes; A1. | | 7 | **[[foundation/Gauge theory and field theory/Gauge theory and field theory (RST)]]** | Relational maintenance, mass gap; Yang–Mills, $\Lambda_{\mathrm{QCD}}$. | | 8 | **[[foundation/Cosmology and GR/Cosmology and GR (RST)]]** | $\theta = 3H$, $a_0$; Noise Floor; Newton / MOND / $\Lambda$. | | 9 | **[[foundation/Complexity and computation/Complexity and computation (RRT)]]** | Polynomial scaling, P vs NP; Landauer, step-count; A2, A3. | | 10 | **[[foundation/Algebraic and geometric structure/Algebraic and geometric structure (RST)]]** | Cohomology, algebraic cycles; Hodge; A1, A5. | | 11 | **[[foundation/Statistical mechanics and free energy/Statistical mechanics and free energy (RST)]]** | Partition functions, free energy; typical states as high-fidelity macrostates. | | 12 | **[[foundation/Control and feedback/Control and feedback (RST)]]** | Identity loop, setpoint tracking, robustness; loop gain as signal-to-noise. | | 13 | **[[foundation/Networks and connectivity/Networks and connectivity (RST)]]** | Substrate as graph; percolation, backbones, giant component. | | 14 | **[[foundation/Variational principles/Variational principles (RST)]]** | Least action, minimum cost histories; laws as variational statements. | --- ## Why a separate foundations folder? - **Not applications:** Applications (in `expanded theory applied/`) are *concrete problems* (Navier–Stokes, BSD, etc.). Foundations are *disciplines* (information theory, Landauer, measure theory) that underpin the theory itself. - **Bridge, not RST-only:** These topics map **into** RRT (axioms) and **into** RST (equations). They sit between classical knowledge and the relational framework. - **Relational net:** Each foundation note links up to **RRT** (which axioms), down to **RST** (which symbols/equations), and across to **applications** that depend on it. --- ## Links - **RRT (top level):** [[Relational Resolution Theory (RRT)]] - **RST (second level):** [[Relational Substrate Theory (RST)]] - **Applications (third level):** [[Applications Roadmap]] - **Overview (structure):** [[Overview — RRT, RST, and applications]]