NFW Fermat potential and physics-led viewport upgrade

[Biswajit1999]

Scope

This draft turns the former NFW/Fermat limitation into a validated circular thin-lens component, then improves interaction feedback without adding decorative pseudo-physics to the viewport.

Physics contract

For x = r / theta_s, the implementation evaluates the standard piecewise circular-NFW functions with stable small-radius branches:

• alpha = 4 kappa_s theta_s g(x) / x
• psi = 2 kappa_s theta_s^2 h(x)

The TypeScript and Python checks use central finite differences to verify grad(psi) = alpha below, around, and above the scale radius. Extra guards cover the halo-centre series and the scale-radius transition.

Rendering and interaction

• NFW and composite scenes now render a complete Fermat surface.
• The old procedural warp grid was removed.
• The optional ray-shooting overlay now plots the actual mapping theta -> beta(theta) from the shared physics core.
• Preset cards and panels keep restrained CSS interaction feedback; no new runtime dependency is required.

Boundaries

This is a circular thin-lens NFW component, not elliptical NFW, multi-plane coupling, or inference-grade time-delay cosmography.