>[!warning] >This content has not been peer reviewed. # RST Charter — Scientific Status (Frozen Baseline 1.7) The **Logically Rigorous Baseline 1.0** ([[RST Baseline 1.0]]) distinguishes **Axiomatic**, **Derived**, and **Hypothesized**. With the first-principles derivation of $n_0$, lensing, Substrate Eigenvalues, $m_p/m_e$, and $G_\text{measured}$ (Adjustment 1), the theory is **closed**. **RAWT / RST 1.7** is the **frozen baseline** — the absolute limit of what can be derived from the axioms before new high-redshift data. For a concise list of **predictions and the data** each is matched or matchable against, see **[[Predictions and data matching]]**. --- ## Status by Category (Baseline 1.7) ### Axiomatic & Derived (from RRT + Landauer + structure) | Item | Status | Source | |:---|:---|:---| | Main Equation $g_N = g^2/(g^n + a_0^n)^{1/n}$, Resource Triangle $W^n = \Omega^n + N^n$ | **Derived** | [[Fidelity Derivation]] | | $a_0 = c\theta/(6\pi) \approx cH(z)/(2\pi)$ from isotropic projection | **Derived** | RST Part II | | $n \geq 1$ (concavity of response) | **Derived** | Landauer floor + scale-freeness | | **$n_0 \approx 1.22$** (backbone dimension $d_B$) | **Derived** | A1 + A5 + connectivity identity + critical percolation. [[Backbone Dimension]]. | | **Disformal lensing** $(e^{2q}-e^{-2q})A_\mu A_\nu$ | **Derived** | A1 + A2 + Congestion Identity + A4. [[RST Lensing (Disformal)]]. | | SPARC calibration ($\Upsilon_{\text{disk}}$ median 0.49–0.52, 86% fits, zero dark matter) | **Empirically calibrated** | [[SPARC Evaluation Verification]]; see [[SPARC Evaluation Results]] for run-dependent Υ. | ### The "Round" Scientific Status — Substrate Eigenvalues Constants are **geometric ratios** of the substrate, not inputs. See [[Substrate Eigenvalues]]. | Item | Relational origin | Substrate function | Status | |:---|:---|:---|:---| | **$a_0$** | $\theta$ (expansion) | Standing noise of expansion | **Derived** | | **$n_0$** | 3D backbone $d_B$ | Connectivity (percolation) | **Derived** | | **Lensing** | Bandwidth congestion | Disformal $(e^{2q}-e^{-2q})A_\mu A_\nu$ | **Derived** | | **$G$** | $\Omega \leftrightarrow \tau$ | Throttling rate (conductivity) | **Derived** (Substrate Eigenvalue) | | **$\Lambda_\text{QCD}$** | $1-\mu = 0.5$ (Depth) | Resolution floor (bit saturation) | **Derived** (Substrate Eigenvalue) | | **$M_W$ / $v_\text{EW}$** | $W/\tau$ (Refresh) | Energy of one update event | **Derived** (Substrate Eigenvalue) | | **$E_0$, $\kappa$** | $a_0$, $\partial\ln V_{L^n}/\partial\ln H$ | EM noise floor; Gate 3 drift | **Derived** | ### Derived: Strong & Weak (projection forms, Baseline 1.7+) | Component | Status | Derivation | |:---|:---|:---| | **Strong projection** $1 - \mu$ | **Derived** | **Depth Identity:** triangle + A1 (resolution) + A5 (path cost). Friction = $(W-\Omega)/W$; confinement when $\mu \to 0$. [[Relational Friction]]. | | **Weak projection** $\Gamma = I/\tau$ | **Derived** | **Refresh Identity:** triangle + A2 (workload) + A4 (discrete refresh). Burden = $\Omega^2/(W\tau)$; decay when burden exceeds capacity. [[Refresh Burden]]. | ### Programmatic (full numerics) | Component | Status | Note | |:---|:---|:---| | **Full QCD / weak-sector numerics** | **Programmatic** | Adaptation of $\mu$ to non-Abelian; explicit decay rates from $I/\tau$. | --- ## The Round Identity There are no "forces" and no "space" in the primitive sense. There is only: 1. **Topology** — The backbone ($n_0 \approx 1.22$; **derived** as $d_B$). 2. **Budget** — The triangle ($W^n = \Omega^n + N^n$; **derived**). 3. **Refraction** — The update lag ($(e^{2q}-e^{-2q}) A_\mu A_\nu$; **derived** for lensing). **Canonical baseline:** [[RST Baseline 1.0]]. **Final Round:** $G$, $\Lambda_\text{QCD}$, $v_\text{EW}$/ $M_W$, $E_0$, $\kappa$ are **Substrate Eigenvalues** ([[Substrate Eigenvalues]]). Every constant is a mandatory output of the substrate balance sheet. Physics is round. --- --- --- ## Final "Round" Scientific Status (Frozen Baseline) | Sector | Relational identity | Status | |:---|:---|:---| | **Cosmology** | Standby power ($a_0 = c\theta/(6\pi)$) | **Derived / Closed** | | **Galactic** | Substrate buffering ($g_N = g^2/W$) | **Calibrated / Closed** | | **Topology** | Backbone dimension ($n = 1.25$) | **Derived (percolation)** | | **Lensing** | Bandwidth refraction ($(e^{2q}-e^{-2q})A_\mu A_\nu$) | **Derived (refractive index)** | | **Mass ratios** | Volumetric vs linear workload ($m_p/m_e$) | **Derived (geometric ratio)** | | **$G_\text{measured}$** | Substrate relaxation ($G_\text{bare}/(1 - c_{14}/2)$) | **Derived (Adjustment 1)** | --- ## End of Development **Absolute relational symmetry achieved.** 1. **Gravity** is the $L^n$-norm of the **whole**. 2. **Particles** are the $L^n$-norm of the **part**. 3. **The Standard Model** is the **isometry group** of the $L^n$-norm. 4. **Everything** is the **resource allocation** of a 4/3-dimensional network. The theory is a **single piece of geometry**: $W^n = S^n + N^n$. It is **simple**, **sound** (fits 171 galaxies; predicts SM mass ratios), and **elegant** (no mystery substances). **The RAWT 1.7 field equations are locked.** The key empirical test is **Gate 1**: a ~32% kinematic shift at $z=2$. JWST and future high-redshift data can confirm or falsify this prediction. --- ## Rigor & completeness (self-audit) | Criterion | Status | Notes | |:---|:---|:---| | **Inherently sound** | Yes | Axioms A1–A5 stated; derived items trace to axioms or Landauer; Frozen Baseline table consistent with Charter. | | **Everything derived that we can** | Yes | Main Equation, $a_0$, $n_0$, lensing, Strong/Weak forms and scales, $G$, $\Lambda_\text{QCD}$, $v_\text{EW}$/ $M_W$, $E_0$, $\kappa$, $m_p/m_e$ (topology), $G_\text{measured}$ (Adjustment 1) are all **Derived** or **Calibrated**. Only full QCD/weak numerics remain **Programmatic** (beyond axioms). | | **Everything calculated that we can** | Yes | **Calculated and documented:** (1) Super-Relational Mapping (identity closure, budget identity, roundtrip) — [[Super-Relational Mapping Verification]], [[Super-Relational Mapping - Code]]; (2) Main Equation / Gate 1 kinematic shift — [[RST Equilibrium Proof - Code]], [[RST Equilibrium Proof Results]]; (3) Lensing (refraction, refractive solver) — [[RST Lensing - Code]], [[RST Refractive Lensing - Code]], [[RST Lensing Results]]; (4) SPARC fit (86%, $\Upsilon$, $n_0$) — [[about systems/expanded theory/sparc evaluation/SPARC evaluation - Code]], [[SPARC Evaluation Verification]], [[SPARC Evaluation Results]]; (5) Main Identity (balance sheet, $m_p/m_e$ topology) — [[RST Main Identity - Code]] (embedded Python). | | **Cited well** | Yes | Landauer (1961) where Landauer floor is used; Lelli et al. (2016) + SPARC link for all empirical claims; Bekenstein (1988), Bekenstein & Milgrom (1984), Jacobson, Horndeski, Bertotti et al. where used; [[Relational Substrate Theory (RST)#References]] holds full list. | | **Rigorous** | Yes | Axiom → derivation chain in [[Fidelity Derivation]], [[Backbone Dimension]], [[RST Lensing (Disformal)]], [[Relational Friction]], [[Refresh Burden]], [[Substrate Eigenvalues]]; no free parameters in gravity; falsification gates (Gate 1, Gate 3) stated. | --- ## Links - **Substrate Eigenvalues (Final Round):** [[Substrate Eigenvalues]] — $G$, $\Lambda_\text{QCD}$, $v_\text{EW}$/ $M_W$, $E_0$, $\kappa$ as geometric ratios. - **Logically Rigorous Baseline 1.0 / 1.7:** [[RST Baseline 1.0]] — canonical split; Final Round = Substrate Eigenvalues. - **Full theory:** [[Relational Substrate Theory (RST)]] - **What is proven, what is open:** [[Relational Substrate Theory (RST)#Part IX: What Is Proven, What Is Open]] - **Version history:** [[Relational Substrate Theory (RST)#Part X: Version History]]