>[!warning] >This content has not been peer reviewed. # Overview — RRT, RST, and applications This vault is a **relational web** of theory, mappings, and applications — not a single linear paper. Here is how it is structured, what it is, why it matters, and how the **Python code** (which Obsidian Publish does not host) stays **accessible and reproducible**. **New here?** Read **[[How to read this vault]]** to understand how to move through the graph. **Submission narrative:** The canonical paper is the **theory paper** ([Zenodo v2](https://zenodo.org/records/18928300)): full axioms, 14 sectors, Sovereign Chain, Gate 1 prediction. See **[[Entry paper — RRT, RST, and applications]]** for version history and metadata. For the full linear story and derivations, follow the links from this Overview. --- ## 1. The 5-part reading pipeline (Axioms → Derivation → Verification) A peer reviewer should encounter **theory first**, **derivation second**, and **empirical confirmation last**. Follow this strict order: | Part | Content | Where to go | | :--- | :--- | :--- | | **1. Foundational Axioms** | Axioms A1–A5, Pure Axiom Substrate specification | [[Relational Resolution Theory (RRT)]], [[Axiom A1 - Bandwidth]], [[Axiom A2 - Workload]], [[Axiom A3 - Environment]], [[Axiom A4 - Events]], [[Axiom A5 - Distance]], [[further applications/Micro-Graph Generator/Micro-Graph Generator (RST)]] | | **2. Cosmogenesis & Thermodynamics** | Hot Genesis (p=1.0 Complete Graph), Relational Cooling (N₀ = density), FSS deriving $n \approx 1.24$, emergence of 3D space $D_f \approx 1.86$ | [[expanded theory applied/Derivation Chain Overview]], [[further applications/Cosmic Visualizer (RST)/Cosmic Visualizer (RST)]] | | **3. The Sovereign Chain (Geometric Derivations)** | Deriving 10 SM constants from $n \approx 1.24$, $\alpha_s$ from Gravity–QCD mirror, proton mass ($m_p/m_e$) from $d_B \approx 1.22$ | [[expanded theory/The Sovereign Chain]] | | **4. Empirical Verifications** | SPARC galaxy rotation curves confirming $n = 1.25 \pm 0.05$; JWST $z=2$ prediction (Gate 1) | SPARC Evaluation, Gate 1 ([[expanded theory/RST Baseline 1.0]]) | | **5. Mesoscopic Physics** | Topological Liquid Drop Model, Relational Nucleosynthesis | [[further applications/Periodic Table (RST)/Periodic Table (RST)]], [[expanded theory/knowledge/Relational Liquid Drop Model]] | **Rationale:** Start with five basic rules. Watch them build a universe and output $n \approx 1.24$. Watch that number generate the mass of the Z boson. *Only then* introduce SPARC telescope data as the empirical confirmation of the exact number the topology derived. SPARC shifts from "foundation" to "proof." --- ## 2. Structure at a glance (full map) | Layer | What it is | Where to go | | :----------------------------- | :--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | :--------------------------------------------------------------------------------------- | | **RRT** | Meta-ontology: axioms (Format, Information, Translation, Proper Time, Relational Distance), Relational Landauer Principle. The rules that make "relational" physics possible. | **[[Relational Resolution Theory (RRT)]]** | | **Graph** | Pure Axiom Substrate: parameter-free evolution from axioms; derives $n$, $d_B$; provides `run_cycle`, `omega_tot`, `protected_edges` for graph-based applications (Nuclear Fusion, etc.). See **[[expanded theory applied/Derivation Chain Overview]]**. | **[[further applications/Micro-Graph Generator/Micro-Graph Generator (RST)]]** | | **RST** | Physical theory built on RRT and graph-derived $n$: Resource Triangle $W^n = \Omega^n + N^n$, fidelity $\mu(\eta,n)$, main equation $I = \Omega \cdot \mu$, Noise Floor $a_0 = cH/(2\pi)$. Newton, MOND, and dark energy as one framework. **Dimensional Ladder** (14 sectors by $n$); **Sovereign Chain** (10 SM constants from $n \approx 1.24$, zero SM inputs, including $\alpha_s$); **Gate 1** prediction at $z=2$. | **[[expanded theory/Relational Substrate Theory (RST)]]** | | **RST mappings (foundations)** | The bridge: how classical maths and physics (information theory, Landauer, measure, scaling, spectral, PDEs, gauge, cosmology, complexity, algebraic geometry) map onto RRT/RST. 14 topics; first 10 are the core building blocks. | **[[expanded theory applied/foundation/Foundation index]]** | | **Engines** | **(a) Graph engine:** Pure Axiom Substrate (`rst_axiom_pure.py`) — derivation + nuclear. **(b) Fidelity engine:** `rst_engine` — $\mu$, triangle, ledger. **(c) Reality Engine:** application using fidelity engine. | **[[expanded theory applied/Derivation Chain Overview]]**, **[[rst_engine/README]]**, **[[further applications/Reality Engine/Reality Engine (RST)]]** | | **Further applications** | Concrete problems reframed in RST: Millennium (Navier–Stokes, BSD, Hodge, P vs NP, Riemann, Yang–Mills), homeostasis, and more. Each has an application note and, where relevant, a script and results. | **[[expanded theory applied/further applications/Further applications index]]** | | **Knowledge notes** | Established results (Landauer, Shannon, Solomonoff, Friston, Bejan, QEC, etc.) and the **Great Map** (thermodynamics, information, fractal geometry, dynamics, intelligence). Speaking titles; complexity-scale plot: $\mu$ from Planck to biological. | **[[expanded theory/knowledge/Knowledge index]]** | The table above is the full map of the graph. Applications roadmap (all problems, foundational + further): **[[expanded theory applied/Applications Roadmap]]**. **Entry points (5-part pipeline):** **[[Axiom A1 - Bandwidth]]** → [[Axiom A2 - Workload]], [[Axiom A3 - Environment]], [[Axiom A4 - Events]], [[Axiom A5 - Distance]] → **[[Fidelity Derivation]]** → **[[expanded theory applied/Derivation Chain Overview]]** (Pure Axiom, Cosmogenesis) → **[[expanded theory/The Sovereign Chain]]** (10 SM constants) → SPARC / Gate 1 (empirical verification) → **[[further applications/Periodic Table (RST)/Periodic Table (RST)]]** (mesoscopic physics). --- ## 2. What this is - **RRT** states that reality is a resource-constrained substrate: resolution, persistence, and translation have a minimum cost (Landauer 1961). There is no "free" bit; relations across distance cost energy. - **RST** turns that into equations: one **Resource Triangle** and one **fidelity function** $\mu(\eta,n)$ that govern how "signal" and "noise" share a finite budget. The gravity sector has the form of MOND (Milgrom 1983; Famaey & McGaugh 2012) but is derived from axioms. Gravity, dark matter, and dark energy emerge as three regimes of the same relation; the same structure appears in fluid smoothness, elliptic curves, and computation. The transition sharpness $n$ is **derived** from the Pure Axiom Substrate (parameter-free graph evolution); SPARC measures $n = 1.25 \pm 0.05$, confirming the prediction. The **Dimensional Ladder** organizes 14 sectors (gravity, materials, fluids, enzyme kinetics, etc.) by $n$; the **Sovereign Chain** derives 10 Standard Model constants (including $\alpha_s$) ($\alpha$, $\theta_W$, mass ratios, $m_Z$, $m_t$) from $n \approx 1.24$ alone, within lt;0.07\%$. **Gate 1** is a falsifiable prediction: at redshift $z=2$, flat rotation velocities $\sim 31\%$ higher than at $z=0$ for fixed baryonic mass — testable with JWST/ALMA. See **[[expanded theory applied/Derivation Chain Overview]]**. - **Foundations** are the building blocks: which bits of maths and physics are needed to map any given problem into RRT/RST (e.g. measure theory for the triangle, spectral theory for BSD/Riemann). - **Applications** are the concrete reframes: Navier–Stokes smoothness, BSD conjecture, homeostasis, etc., each with a short note (and often a script) showing how the problem sits on the same curve. So: **one axiom set (RRT) → one physical formalism (RST) → one curve $\mu(\eta,n)$** applied across disciplines. The vault is the graph of that derivation and those applications. --- ## 3. Why this matters and why it is not coincidental - **Single curve:** Black holes, galaxy rotation, quantum measurement, and metabolism are usually treated as separate domains. Here they are different regimes of the **same** fidelity curve $\mu(\eta,n)$ and the same Resource Triangle. That is a **structural** claim: the maths is shared, not fitted per domain. - **Derived, not fitted:** $n$ and $a_0$ are **derived** from axioms and cosmology, not fitted per domain. The Pure Axiom Substrate computationally derives $n \approx 1.24$; SPARC confirms ($1.25 \pm 0.05$). - **Reproducible numerics:** Two engines: **(a)** the **graph engine** (Pure Axiom Substrate in Micro-Graph Generator) derives $n$, $d_B$ and drives graph-based applications (Nuclear Fusion). **(b)** The **fidelity engine** (`rst_engine`) implements $\mu$, the Resource Triangle, and solvers — used by SPARC, foundations, and most further applications. Clone the repo, run the scripts, get the same numbers and figures. The importance is that **one relational ontology (RRT) and one physical theory (RST) unify gravity, dark matter, dark energy, and a range of open problems** without domain-by-domain fitting. The vault is the place where that claim is fully written down and linked. --- ## 4. Foundational results (one picture) The **foundation** topics (14 in total: information theory, Landauer, measure, scaling, spectral, continuum/PDEs, gauge, cosmology, complexity, algebraic structure, and others; see **[[expanded theory applied/foundation/Foundation index]]**) each have a short RST mapping and a small Python script that plots the same fidelity/triangle maths in that context. The runner script combines their outputs into one figure: ![[expanded theory applied/foundation/all_foundation_results.png]] *Combined output of all ten foundation scripts (2 per row). This image is generated by running the foundation runner; see "Python code" below. If you do not see it, run the script once in the repo.* That one image shows the **same** $\mu(\eta,n)$ and budget split appearing across information, thermodynamics, measure, scaling, spectral, continuum, gauge, cosmology, complexity, and algebraic structure. It is evidence that the framework is one curve applied many times, not ten different models. --- ## 5. Python code — accessible and reproducible (not in Publish) Obsidian Publish does **not** serve `.py` files. The code lives in the **same repository** as this vault (or in a linked repo). **Repository (clone or download):** [Codeberg — RRT_RRS](https://codeberg.org/ChristophTripstoph/RRT_RRS) — clone with `git clone https://codeberg.org/ChristophTripstoph/RRT_RRS.git` or use "Download ZIP" / "Download TAR.GZ" on the Codeberg page. To keep everything **accessible and reproducible**: - **Where the code is:** In the **workspace root** (the folder that contains this vault): - **`rst_engine/`** — fidelity engine: $\mu(\eta,n)$, Resource Triangle, and solvers. - **`expanded theory applied/further applications/Micro-Graph Generator/`** — graph engine: **`rst_axiom_pure.py`** (Pure Axiom Substrate) derives $n$, $d_B$; used by Nuclear Fusion. - **`expanded theory applied/foundation/`** — one script per foundation topic; **`run_all_foundation_scripts.py`** runs them and builds the combined image above. - **`expanded theory applied/further applications/`** — one script per application (e.g. Navier–Stokes, Grand Map, Homeostasis, Solomonoff, QEC); **`run_all_further_scripts.py`** runs them. - **`expanded theory/sparc evaluation/`** — SPARC pipeline (rawt + notebooks); uses **`rst_engine`** for $\mu$ and the solver. - **How to run it:** From the **workspace root** (e.g. the repo root): - Foundation: `python "expanded theory applied/foundation/run_all_foundation_scripts.py"` - Further applications: `python "expanded theory applied/further applications/run_all_further_scripts.py"` - **Core calculated proofs** (super-relational, equilibrium, lensing): run the four proof scripts in `expanded theory/python calculations/`, then `python "expanded theory/python calculations/build_all_calculated_proofs.py"` → **`expanded theory/python calculations results/all_calculated_proofs.png`**. - Single scripts are documented in each application's Code note (e.g. **[[expanded theory applied/How we do applications]]**). - **Reproducibility:** One engine, one formula set. Clone the repo, install dependencies (`pip install -r requirements.txt` in sparc evaluation if you run SPARC), run the scripts from the root. Outputs (figures, CSVs) are written next to the scripts or in `notebooks/output/`. The vault notes reference those outputs (e.g. the combined foundation image); the reader can regenerate them by running the same commands. So: **the published vault explains and links the theory and applications; the repo holds the code and the exact commands to reproduce every figure and number.** --- ## 6. Links (entry points) | Link | Purpose | |:---|:---| | **[[Relational Resolution Theory (RRT)]]** | Axioms and Landauer (RRT). | | **[[RST Theory Map]]** | Theory structure at a glance: RRT → Derivation → Graph Hierarchy → Sovereign Chain → Applications. | | **[[Interaction ontology index]]** | Interaction meta-ontology: inter-System stances, 3×3×μ matrix. | | **[[expanded theory/Relational Substrate Theory (RST)]]** | Physical theory: triangle, fidelity, main equation. | | **[[expanded theory/The Spectrum of Relational Topologies]]** | Dimensional Ladder (14 sectors), ladder regimes, Sovereign Chain overview. | | **[[expanded theory/The Sovereign Chain]]** | Derivation of 10 SM constants from $n \approx 1.24$ alone (lt;0.07\%$). | | **[[Graph Size Hierarchy (RST)]]** | Graph size $N$ as unifying scale: forces → matter → chemistry → cosmology. | | **[[expanded theory applied/Derivation Chain Overview]]** | Full derivation path: Axioms → Pure Axiom Substrate → emergent n, d_B → Sovereign Chain. | | **[[expanded theory applied/foundation/Foundation index]]** | Foundation mappings (14 topics; maths/physics → RRT/RST). | | **[[expanded theory applied/further applications/Further applications index]]** | Millennium + other applications. | | **[[expanded theory applied/Applications Roadmap]]** | Full list and priority of all applications. | | **[[How to read this vault]]** | How to navigate the graph. | | **[[Entry paper — RRT, RST, and applications]]** | Version history (v1 entry, v2 theory), metadata, suggested citation. | | **Theory paper (Zenodo v2)** | Canonical paper: [doi.org/10.5281/zenodo.18928300](https://doi.org/10.5281/zenodo.18928300) — full axioms, 14 sectors, Sovereign Chain, Gate 1. | | **[[expanded theory applied/How we do applications]]** | How applications and code are documented and linked. | | **[[expanded theory/knowledge/Knowledge index]]** | Hard knowledge: Landauer, Bekenstein, Shannon, percolation, K41, Jacobson, BTFR, etc. | | **Repository** | Code and scripts: [Codeberg — RRT_RRS](https://codeberg.org/ChristophTripstoph/RRT_RRS) (clone or download ZIP). | --- ## 7. Key references | Topic | Reference | |:---|:---| | Landauer principle | Landauer (1961), IBM J. Res. Dev. 5, 183 | | MOND | Milgrom (1983), ApJ 270, 365; Famaey & McGaugh (2012), Living Rev. Relativ. 15, 10 | | Emergent/entropic gravity | Verlinde (2017), SciPost Phys. 2, 016 | | Relativistic MOND, lensing | Bekenstein (2004), Phys. Rev. D 70, 083509 (TeVeS) | | SPARC data | Lelli et al. (2016), Astron. J. 152, 157 | | This work (Zenodo v2) | Janke (2026), theory paper, doi:[10.5281/zenodo.18928300](https://doi.org/10.5281/zenodo.18928300) |