============================================================ OMEGA local geometric object ============================================================ a = 1.000000000000000 φ = 1.618033988749895 Ω₀ = φ + π = 4.759626642339688 ε = 4.848136811095360e-06 rad δ = ε/2 = 2.424068405547680e-06 rad s = sin(δ) = 2.424068405545306e-06 c = cos(δ) = 0.999999999997062 Positive baseline levels: x0 = s = 0.000002424068406 x1 = 1 + s = 1.000002424068406 x2 = φ^2 + s = 2.618036412818300 Six marked points (left to right): p2,- = (-2.618036412818300, -0.999999999997062, 0.000000000000000) p1,- = (-1.000002424068406, -0.999999999997062, 0.000000000000000) p0,- = (-0.000002424068406, -0.999999999997062, 0.000000000000000) p0,+ = ( 0.000002424068406, -0.999999999997062, 0.000000000000000) p1,+ = ( 1.000002424068406, -0.999999999997062, 0.000000000000000) p2,+ = ( 2.618036412818300, -0.999999999997062, 0.000000000000000) Consecutive separations along the baseline: |p2,- - p1,-| = 1.618033988749895 (expected aφ) |p1,- - p0,-| = 1.000000000000000 (expected a) |p0,+ - p0,-| = 4.848136811090612e-06 (expected 2as) |p1,+ - p0,+| = 1.000000000000000 (expected a) |p2,+ - p1,+| = 1.618033988749895 (expected aφ) Center-relative radii: ρ0 = 1.000000000000000 ρ1 = 1.414215276447264 ρ2 = 2.802519341384933 Seed angle check: θ_seed = 4.848101439241487e-06 rad difference = 3.537185387325029e-11 Normalized scalar shares: λ = φ/(φ+π) = 0.339949771344779 μ = π/(φ+π) = 0.660050228655221 λ + μ = 1.000000000000000 Geometric definition: Major arc: γ(t) = (a sin t, -a cos t, 0), ε/2 ≤ t ≤ 2π - ε/2 Extensions: E±(r) = (±a r, -a c, 0), s ≤ r ≤ s + φ^2 Object = major arc ∪ left extension ∪ right extension ============================================================ LOCAL OBJECT PASS: seed pair at radius a; major arc ∪ E₋ ∪ E₊; consecutive separations aφ, a, 2as, a, aφ; not a diameter figure.