Conjecture S: the even-half transient

• 2026-08-28 [Verified] The two-step census contraction 9 b(2j+2) <= fill^2 b(2j) with 3 b(2j+1) < fill b(2j) has zero violations through index 400 at every even dim <= 50, margin peaking near (dim-2)/(dim+2), and in exact integers at even dim = 2..30 to index 40 the margin sits strictly below (dim-2)/(dim+2) and rises toward it, 0.8704914 against 0.875 at dim = 30; with irreducibility and nonvanishing it would close the even half. Witness: slice-recurrence-order.
• 2026-08-28 [Conjecture] Every weighted-L2 certificate for the even half fails, the transfer norm being at least sqrt(3) fill for every positive weight, and two Abel pairings fail with it.
• 2026-08-28 [Refuted] The even half's early W_k sign alternation at base 3 persists, and a conjecture can be built on it - the alternation is a transient: over all even dim the first break is dim = 6, k = 4, then (8,6), (10,8), the rule k = dim - 2 dying at dim = 16 where the first break is k = 16, then 20, 24, 28, 34, 40 at dim = 18..26 and none through k = 40 for dim = 28..40 (inside the window even 12 <= dim <= 22 the first break is (dim,k) = (12,10)); structurally W_level ~ C 3^(level-1) rho^(level-1)(3 rho - fill) makes the eventual W-sign the even half itself; the pointwise route is dead too, V_2 < 0 for even dim >= 6. Witness: slice-recurrence-order, slice-sign-even-half.