YIN · π ZEROS YANG · ζ ZEROS explicit formula · sovereign spine · anti-hallucination gate γ₁ = 14.134725141734693 WORMHOLE FCS FLOOR RASENGAN
Theorems · New Work
YIN · π ZEROS
sin(πn) = 0 · n ∈ ℤ
Spacing = 1 everywhere. Variance = 0. Perfect regularity. The stable ground. The floor of counting.
YANG · ζ ZEROS
ζ(½ + iγₙ) = 0
Irregular spacing. GUE variance ≈ 0.12. Prime-encoded. Unpredictable without computing all prior zeros. γ₁ = 14.134725141734693
HELIX SPINE · EXPLICIT FORMULA
ψ(x) = x − Σ xᵖ/ρ − log(2π)
YIN arm: x (smooth, π-regular). YANG arm: Σ xᵖ/ρ (oscillatory, ζ-encoded). They wind together to give the exact prime count.
PHASE IDENTITY
γ₁/π ≈ 9/2 = 4.4992...
The first ζ zero sits at almost exactly 4.5π. Half rotation shy of 5π. Phase offset = γ₁ mod 1 = 0.13472...
FCS FLOOR IDENTITY
FCS floor = 1 − 1/γ₁ = 0.92924
The sovereign confidence floor IS the complement of the yang phase offset. YIN = 0.92924 (stable). YANG = 0.07076 (residual uncertainty).
OPEN SORRY · S-YZ-001
γ₁/π =? 9/2 exactly
Gap = 0.0008. γ₁ believed transcendental over π. No closed form. The near-miss is the sorry. Next wave seed.
ζ ZEROS · Real Data
πYIN ARM
ζYANG ARM
0.92924FCS FLOOR
9/2γ₁/π NEAR
γ₁14.134725141734693