Escape Energy Closure Radius Ladder Three-Row Scan
Changing radius changes every term while the escape energy total remains zero.
Changing radius changes every term while the escape energy total remains zero. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Radius 4 closes at zero energy
Circular speed-square 4 doubles to escape speed-square 8. That gives kinetic 4 against potential negative 4, so total is zero.
2⋅4=8,4−4=0
Radius 2 closes at zero energy
Circular speed-square 8 doubles to escape speed-square 16. That gives kinetic 8 against potential negative 8, so total is zero.
2⋅8=16,8−8=0
Radius 1 closes at zero energy
Circular speed-square 16 doubles to escape speed-square 32. That gives kinetic 16 against potential negative 16, so total is zero.
2⋅16=32,16−16=0
Every radius closes the same zero-energy audit
The radius changes the circular square, escape square, kinetic term, and potential magnitude together. The final total stays exactly zero in all three rows.