Dual anchor
v134_dual_anchor.py · registry
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THE DUAL ANCHOR LEMMA (the inverse flavor response of the anchor IS the Nariai root — the third purely algebraic leg of the flavor↔horizon bridge): d := aᵀR⁻¹ = aᵀL⁻¹ = (−1/2, −1/2, 1) with d·1 = 0, d·a = 1 and d = (3/2)(a − (4/3)1) — the normalised TRACELESS anchor — and (1,1,−2) = −2d: the inverse flavor response stores exactly the Nariai double-root structure (v101) up to sign and scale, so the horizon is not glued on afterwards — it sits inside the flavor compiler as a dual invariant [I]; WHY INVARIANT (Sherman–Morrison, exact): L = R + 6·1e₁ᵀ makes a covector winding-invariant iff it annihilates R⁻¹1 = (1,1,−1)/4, and the anchor does — the winding deformation lives in the democratic direction, which d kills [I]; CONTROL: 1, e₁ and n = (5,−9,6) do NOT lie on the invariance plane (1/4, 1/4, −5/2) — the membership is special, not generic [I]; THE DUAL NORMAL PAIR: d (sheet normal: kills 1, dual to a, ∝ Nariai root) and n (torsion normal: nᵀR = (8,0,0), nᵀL = (20,0,0), n·a = 8, n·1 = 2 = |Z₂|) form the dual basis of the flavor boundary [I]; consequence [P]: third algebraic bridge leg beside the shared clock spectrum (v126) and the entropy power law (v129); the R4′ selector programme acquires a geometric target — derive the PAIR (d, n), not n alone
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