◆ THE GYRO-TRIAD · three gyros fix the orientation
STROBILOS · Top's domain — three orthogonal spinning gyros, one orientation. An IMU. A gyro is a spinning top; three of them find which way Top points.
verdict · self-test (fail-loud, computed live)
spinning up…
the triad → the orientation (dead-reckoned)
The x/y/z gyros read the body-frame angular velocity; integrating them (SO(3) exponential map) reconstructs the full orientation — the amber frame is TRUTH, the ghost frame is the integrated estimate. Turn on drift to quantize the readings and watch the estimate slowly diverge (the real IMU wall).
two-layer honest
LIT — real SO(3) integration. Each gyro reports one component of the body angular velocity ω; the orientation advances by R ← R·exp(ω·dt) (Rodrigues' formula). Proven live: for constant ω the accumulated rotation equals the exact axis-angle rotation to <1e-9; R stays a true rotation (RᵀR = I, det = 1) to machine precision; a rotation composed with its inverse returns to identity. |ω| = √(ω²ₓ+ω²ₔ+ω²ₕ) — the three components triangulate the single spin. Every number in-browser; fail-loud.
AMBER — the figure, and the honest wall. "Top is the axis the three fix" is the framing (a gyroscope really is a spinning top, so the image is close). The WALL is real, not decoration: with drift on, the readings are quantized and the dead-reckoned frame DRIFTS from truth — measured live — which is exactly why a real IMU needs an external fix. ◆ a STROBILOS sphere — three ways to find a point; this is the orientation way.