Why unsigned 0 doesn't exist: Every integer N ≠ 0 has a positive standing tension rope around which the kata coil (w·L·Rᵏ, rose) and ana coil (w·R·Lᵏ, cyan) execute 2 matched Hitch Reversals (χ_AB = +1), out of phase by 1 step (k+2 vs k+1). Click Seam 0± to see both reversals vanish!
Theorem (Seamless-Loop Obstruction & Hitch Necessity): Slide friction μ_AB → 1⁺ to watch every open knot untie to the bare rail — proving a closed loop in nature can only exist by tying a friction hitch across its ends (paying Gallivan splice price L₁(c) = π·sgn(c)·c and spinor holonomy Δℓ = 2).
Un-gluing Rung V from Braid B₃ into Open Hitch Praxis: At n = 2 on Diophantus's (3, 4, 5), odd hitch posts 3 & 5 stay pinned (v₂(Δ_min) = 0, Level = 15, Genus = 1 — one hole holds the hitch!). For any odd prime p ≥ 5, every odd post wraps 2p·v_q ≡ 0 (mod p) and slips free, collapsing onto Γ₀(2) on {0/1, 1/1, 1/0} where Genus = 0 (open twine spills!).