The Combined Fit, Run: One Parametrization, Both Transition Laws, and a Valley Where the Answer Should Be

The combined sigmoid-by-kink fit priced by packet #542 (item NTA22-A1-R1, closing NT-A1 in its literal form). A single parametrization containing both parents' laws is built in the deceleration parameter -- the kink's q(z) (#251) plus the sigmoid's deviation from the LambdaCDM spine at the same Omega_m (#250) -- and gated on both parents' best fits as exact limiting cases (kink limit at w0 = -1 verified to 1.1 x 10^-8; sigmoid limit with the kink sector off verified to 5.8 x 10^-8 mag; both parents' instruments re-run digit-for-digit first). Fitted once on a noiseless combined mock in the parents' own designs, with all nine parameters free including (Omega_m, r, q_i): the fit returns the fiducial and a second distant solution at chi2 about 3 x 10^-4 (Omega_m at its 0.50 bound); Fisher errors exceed the parameters' ranges (sigma(Omega_m) = 44.6, sigma(r) = 12.0, sigma(q_i) = 7.7; condition number 2.1 x 10^7); the two parents' freezes are one degeneracy direction (corr(Omega_m, q_i) = +0.962); and every frozen excursion, including all three freezes displaced at once, refits at chi2 < 0.01. Verdict: freeing the three frozen inputs jointly does not locate the transition -- it dissolves it. The parents' real-data killers stand untouched. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.