Collatz on the Trefoil Torus

(2,3)-Torus Knot — k = 729 = 3⁶ Branch Locus

The golden diagonal band is the branch locus: 23,268 cells where Syracuse trajectories visit, out of 531,441 total (4.07%). The bright band has hard cutoffs on both edges — cyan pure-even cells on the foliation side, red pure-odd cells on the far side.

● Hensel attrition — 2-adic: danger density 2^−d
● Baker separation — |p − q log₂3| > C/q^κ
● Weyl equidistribution — uniform cell visits ≡ Collatz

P1 Linear ν₃ bound • P2 Finite deficit • P3 Equidist ⇒ deficit • P4 Cell equidist • P5 Valuation equidist • P6 Diophantine approx
Each ⇔ Collatz. Hover ♦ markers on the knot for details.

The trefoil is the (2,3)-torus knot: it winds 2× meridionally (powers of 2, even steps) and 3× longitudinally (powers of 3, odd steps). Rational slope 3/2 = 1.500 approximates critical foliation log₂3 ≈ 1.585. The gap encodes the deficit.

Torus heatmap Trefoil knot Ghost island glow P1-P6 markers Foliation line Divergence ribbon Auto-rotate Brightness Trefoil size Glow