>[!warning] >This content has not been peer reviewed. # Navier–Stokes regulator — results Output from **[[Navier-Stokes Regulator - Code]]** (script: `rst_navier_stokes_regulator.py`). --- ## What is shown - **Radius:** Log-spaced from $10^{-2}$ to $10^1$ (500 points). - **Classical (continuum):** $v \sim 1/r$ — blows up as $r \to 0$. - **RST (regulated):** $v_{\text{rendered}} = v_{\text{ideal}} \cdot \mu(v_{\text{ideal}}/N)$ with $n = 4/3$, noise floor $N = 1$. The fidelity $\mu$ caps the output so that the curve stays bounded; no singularity. - **Horizontal line:** Substrate bandwidth limit (normalized to 1). The plot illustrates that the RST substrate acts as a **natural regulator**: where the continuum model would diverge, the finite-resolution response remains smooth. --- ## Output | File | Description | |:---|:---| | `navier_stokes_regulator.png` | Velocity vs radius: RST (regulated, blue) vs classical (blow-up, red dashed); bandwidth limit (black dotted). |  --- ## Run Script run successfully; figure written to the same folder as the script. --- ## Links - **Application:** [[Navier-Stokes Smoothness (RST)]] - **Code:** [[Navier-Stokes Regulator - Code]]