Claims · 2 dated claims on The second moment of the rays, each with its tag and its witness; newest 2026-08-31.
Refuted The non-shift residual of the second moment converges as R(n)/phi^(2n) -> C ~ 3 at rate phi^2 - the normalised ratio reads 2.498, 3.045, 3.238, 3.182, 3.113, 2.983, 2.895 at n = 8, 10, 12, 13, 14, 15, 16, peaking at n = 12 and falling by 0.9724 per level, and R(n)/R(n-1) sits at 2.573, 2.561, 2.509, 2.541, a rate near 2.54, strictly below phi^2 = 2.618; what survives is R(n) = O(phi^(2n)) on n <= 16, lim R/phi^(2n) undecided, R = o(3^n) with room 3/2.54 rather than 3/2.618, and Conjecture Z untouched. Witness: lemma-b-pincer.
Refuted The majorant Sum_z M_n(z)(M_n(z)-1) is a route to Conjecture W - it grows 2.907 a level at n = 13 against 2.573 for R itself, because it drops the coprimality of (s,t) and so counts each collinear pair once per common divisor; the exact identity R(n) = Sum_z P_n(z) survives and the golden ceiling M_n(z) <= F(n+1) - 1 survives, but the step from P_n(z) to M_n(z)^2 - M_n(z) does not. Witness: lab/py/gasket-witness-weights.