Once the Lissajous structure crystallized, the model's algorithm is the curve.
To steer the prediction from class c to a new class c',
the honest move is along the manifold: shift dlog by Δ, walk Δ beads along the curve.
The naive linear steering vector draws a straight chord — and for any non-trivial Δ,
that chord cuts straight through the empty interior of the cube, where the model has nothing to predict.
Walk = dlog shift
Δ ∈ ℤ96, c' = c · gΔ mod p l' = (l + Δ) mod 96
new phase on K-circle: 2π·K·Δ/96
Legend
source class c
steered target c · gΔ
manifold walk (each step = real class)
linear steering chord (through the void)
W_U — final Lissajous knot · steering Δ
Source
class c—
dlog l—
Steered
Δ0
target c'—
dlog l'—
Walk vs chord
walk steps0
chord / max0%
Chord length grows toward the cube diameter as Δ approaches 48 (Nyquist).
Source class · dlog index5l=0
Steering Δ (dlog shift)0
Try Δ:
Drag in the 3D scene to rotate · scroll to zoom · the source ring is anchored, the coral
target ring jumps along the curve. The chord shows what the linear-steering vector would point to.