The J-lens reads the tangent at A and jumps to B — the middle goes dark. The K-lens brackets the jump: it samples the tangent just past A and just before B, and reads the angle between them — the rotation J hides. Here that rotation rides a Möbius strip, phase-locked to the traversal.
LIT — the tangent rotation (measured, ~5.7°)BRI — the Möbius is chosen geometry, not a topology claim
direction δ:
—
K-lens jump rotation
—
full-path tangent turn
a+.01 · b−.01
K sample brackets
—
phase (locked to traverse)
what's real: the tangent J·δ genuinely rotates ~4–6° traversing A→B (measured on a from-scratch transformer); the two K brackets recover it to 0.1°. that rotation is the curvature J hides in the jump. what's chosen: the Möbius strip is a visual for "a frame that rotates as it rides the path" — it is NOT a claim the transport is non-orientable or half-twisted. the phase-lock ties the animation's rotation to the traversal parameter so the visual turn = the measured turn. the K-lens nests J: J reads one tangent; K reads two and returns their difference. curvature is J watched by K.