Nodes: 3600 | Invaded: 1 | T_max: 0.00
Seed (t=0)
Wet Frontier (Isochrone Contours)
Optimal Geodesic
Direct Manipulation: Click or tap anywhere on the network grid to inject a fluid source or trace the minimal-passage geodesic path back to the origin seed. Watch wavefront isochrones self-organize into anisotropic limit shapes.
Wavefront Telemetry
Invaded Nodes
3600
Front Velocity (v)
1.48
Shape Anisotropy
1.12
Geodesic Wandering
3.42
completed
Proved vs. Conjectured Matrix
| Theorem / Milestone | Status | Physical / Mathematical Meaning |
|---|---|---|
| Cox-Durrett-Kesten Shape Theorem | Proved (1981) | Rescaled wet region B_t / t converges almost surely to a deterministic convex limit shape B. |
| Flooding Speed Bounds | Proved Dec 2025 | Resolved the long-standing open problem: established strict lower and upper bounds for asymptotic wetting speed across disordered media. |
| KPZ Geodesic Exponent (χ = 1/3) | Conjectured | Frontier variance should scale as t^(2/3) and geodesic wandering as r^(2/3); proven only in restricted integrable models. |
As reported by Quanta Magazine, five mathematicians resolved the flooding rate bounds on opened networks just before Christmas 2025, confirming how fast fluids penetrate percolating channels.