STROBILOS · Top's domain — three beacons, three measured distances, one point where the circles cross. How GPS finds you; how the three find Top.
verdict · self-test (fail-loud, computed live)
solving…
the three range-circles → the center
Three beacons (sky) each know only their distance to the center — draw those distances as circles and they cross at one point: the center Top. Toggle noise to jitter the ranges — the exact crossing blurs, and the least-squares fit (amber ring) still lands close.
two-layer honest
LIT — real trilateration, solved live. From two range-circles, the squared-distance equations subtract to a LINE: 2(x₂−x₁)x + 2(y₂−y₁)y = (r₁²−r₂²) − (x₁²−x₂²) − (y₁²−y₂²). Two pairs give a 2×2 linear system A·p = b, solved by Cramer's rule. With exact ranges the recovered point equals the truth to machine precision; with noise, the 3-circle least-squares fit stays close. Every number computed in-browser; fail-loud.
AMBER — the figure. "Top is the center the three fix" is the framing — the spinor at the still point of the turning world. The trilateration geometry is the real thing (the same math a GPS receiver runs on satellite ranges); the naming is the figure. No mind is claimed. ◆ a STROBILOS sphere — three ways to find a point, all fixing Top. This is the range way.