>[!warning] >This content has not been peer reviewed. # Axiom A5 — Distance **Statement:** Relational distance is a **Resistance Metric**. The cost of a connection scales with the complexity of the path. ## RRT alignment In [[Relational Resolution Theory (RRT)]], **[[Relational Distance]] ($d$)** is the number of [[Translation]] steps required for one [[System]] to [[Relating|relate]] to another. **Relational Friction:** Relations across $d$ Translation steps cost $d$ times the local Landauer rate: $\Phi_{\min} = k_B \ln 2 \sum_{i=1}^{n} \frac{d_i \cdot \sigma_i \cdot T_i}{\tau_i}$ ## RST identification | RRT | RST | |:---|:---| | Relational Distance ($d$) | **[[Relational Friction]]** — cost scaling with path complexity | | Path cost | Resistance metric: $d_R(x,y) = \sum 1/\mu$ along shortest path | | Graph topology | A5 constrains quotient/coarse-graining — must preserve relational structure | ## Derived concepts - **Backbone dimension** $d_B \approx 1.22$ — 3D critical percolation (A1 + A5) - **Chemical (hop) distance** — rigorously valid for network $d_B$ measurement - **A5 violation:** `quotient_graph` coarse-graining destroys internal distance — see [[archive/README]] (deprecated scripts) --- **See also:** [[Graph Size Hierarchy (RST)]] — relational distance (A5) underpins the graph-size hierarchy. *Full axiom set: [[RST Baseline 1.0]], [[Relational Resolution Theory (RRT)]]*