>[!warning] >This content has not been peer reviewed. # Symbol Index — RRT / RST Quick Reference Short definitions for the main symbols used across [[Relational Resolution Theory (RRT)|RRT]] and [[Relational Substrate Theory (RST)]]. See the linked documents for full definitions and derivations. --- ## Triangle and allocation | Symbol | Meaning | Where | |:---|:---|:---| | $I$ | [[Signal]] — requested information; source field (e.g. $g_N$). Projection $I = \Omega^2/W$. | [[RST Core Reduction]], [[Signal]] | | $N$ | [[Noise Floor]] — environmental budget; in gravity $a_0 = cH/(2\pi)$. | [[Noise Floor]], [[Resource Triangle]] | | $\Omega$ | [[Workload]] — actual effort delivered by the substrate (e.g. observed $g$). | [[Workload]], [[Resource Triangle]] | | $W$ | Total budget — $W^n = \Omega^n + N^n$. | [[Resource Triangle]] | | $\mu$ | [[Fidelity]] — signal fraction $\mu = \Omega/W = \eta/(1+\eta^n)^{1/n}$. | [[Fidelity]], [[Fidelity Derivation]] | | $\nu$ | Noise fraction — $\nu = N/W$; $\mu^n + \nu^n = 1$. | [[Resource Triangle]], [[Noise Projection]] | | $\eta$ | Signal-to-noise ratio — $\eta = \Omega/N$. | [[Signal-to-Noise Ratio]] | | $n$ | Transition sharpness — exponent in $L^n$ norm; $n_0 \approx 1.24$ (derived); SPARC confirms. | [[Transition Sharpness]], [[Backbone Dimension]] | --- ## Time, resolution, and Landauer | Symbol | Meaning | Where | |:---|:---|:---| | $\tau$ | [[Proper Time]] — local refresh interval; duration between discrete translations. | [[Relational Resolution Theory (RRT)]] | | $\sigma$ | Resolution — effective bit-count for maintained distinctions. | [[Relational Resolution Theory (RRT)]] | | $d$ | [[Relational Distance]] — number of Translation steps to relate two systems (A5 in RST). | [[Relational Resolution Theory (RRT)]] | | $\Phi_{\min}$ | Minimum power to maintain resolution (Landauer floor). | [[Relational Resolution Theory (RRT)]] | | $K_R$ | Relational efficiency index — $\Phi_{\text{measured}}/\Phi_{\min}$; $K_R \geq 1$. | [[Relational Resolution Theory (RRT)]] | --- ## Cosmology and gravity | Symbol | Meaning | Where | |:---|:---|:---| | $\theta$ | Expansion scalar — $\theta = \nabla_\mu u^\mu = 3H$ in FLRW. | [[Relational Substrate Theory (RST)]], [[RST Core Reduction]] | | $a_0$ | Acceleration threshold — $a_0 = c\theta/(6\pi) = cH/(2\pi)$; MOND scale. | [[Noise Floor]], [[RST Core Reduction]] | | $H$ | Hubble parameter. | Standard cosmology | | $G$ | Gravitational constant — RST: throttling rate (Substrate Eigenvalue). | [[Substrate Eigenvalues]] | --- ## Four forces (projections) | Symbol / expression | Force | Where | |:---|:---|:---| | $\mu = \Omega/W$ | EM / gauge | [[RST Four-Force Bridge]] | | $\nu = N/W$ | Gravity | [[Noise Projection]] | | $1 - \mu$ | Strong (relational friction) | [[Relational Friction]] | | $\Gamma = I/\tau = \Omega^2/(W\tau)$ | Weak (refresh burden) | [[Refresh Burden]] | --- ## Graph hierarchy | Symbol | Meaning | Where | |:---|:---|:---| | $K_N$ | Complete graph on $N$ nodes — $K_2$ edge, $K_3$ triangle, $K_4$ tetrahedron. | [[Graph Size Hierarchy (RST)]] | | $N^2 - 1$ | Generator count for $SU(N)$ — traceless Hermitian information-flow matrices of $K_N$. | [[Graph Size Hierarchy (RST)]] | --- ## Other (constants, eigenvalues) | Symbol | Meaning | Where | |:---|:---|:---| | $\Lambda_{\text{QCD}}$ | QCD scale — resolution floor (Depth Identity). | [[Substrate Eigenvalues]], [[Relational Friction]] | | $v_{\text{EW}}$, $M_W$ | Electroweak scale — energy of one update (Refresh Identity). | [[Substrate Eigenvalues]], [[Refresh Burden]] | | $\kappa$ | Gate 3 drift — $\partial\ln(V_{L^n})/\partial\ln(H)$. | [[Substrate Eigenvalues]] | | $\Upsilon_{\text{disk}}$ | Stellar mass-to-light ratio (SPARC fit parameter). | [[SPARC Evaluation Verification]] | --- **Full theory:** [[Relational Substrate Theory (RST)]]. **Axioms:** [[Relational Resolution Theory (RRT)]].