Monomials Beyond n = 28: n = 30 Arrives at φ_i = 11.9735 on the Widened Bracket (−95, 15) — the Stated Rule's Widening Fires — n = 28's Conditioned Rows Are Printed, the Surfaces of n = 26, n = 24 and n = 22 Are Carried to Their Declared Tops — and t

The monomial staircase is carried one member past the Wave 29 paper, the newest member's conditioned rows are printed, three carried surfaces are carried to declared tops in the residue's printed order, and the low end is carried at its stated scope. Gated digit-for-digit on the whole body of the Wave 29 monomial notebook (the exhibits of the distance machinery and the earlier staircase papers, every bisected bracket's ends re-run) and on the Wave 29 paper's printed exhibits (a final gate: n = 28 at 11.2236 in [11.22357, 11.22363]; the spacing 0.7087; n = 28's maxima and argmax list on (-70, 15); n = 26's rows' endpoints; n = 22's carried rows' endpoints; the below-0.0001 largest maximum at the parent's own notebook precision, 1.966e-09), the paper states its scan before results: the standing bracket is tested before it is widened -- n = 30's maxima are read on (-70, 15) first, and only a computed edge verdict widens the low edge by the parents' 25-unit step to (-95, 15). The verdict fires: n = 30's maxima stand at the edge -70.0 at the grid's top two points (phi_i = 12.00, 12.25), the widening is taken, the same maxima stand interior on (-95, 15) unchanged at the fourth decimal, and the member begins at phi_i* = 11.9735 (bracket [11.97351, 11.97357]) -- a fifteenth located beginning, its sampled maximum at phi_i = 12.25 agreeing at the fourth decimal on (-110, 15) (0.7060 on both). Its spacing from n = 28's beginning is 0.7499, back at the centre of the band the last paper restated (last six spacings 0.74, 0.75, 0.74, 0.77, 0.71, 0.75), which survives unamended. n = 28's conditioned rows are printed at phi_i = 11.25, 11.50, 11.75, 12.00 (w0 = -0.474 to -0.564, H0 = 68.93 to 69.37); the grid's first point, phi_i = 11.00, stands below the member's own beginning and is printed as unreachable, not skipped. n = 26's surface is carried above phi_i = 11.50 through the declared top 12.50 (w0 -0.609 to -0.656, H0 69.71 to 70.12), n = 24's surface above phi_i = 10.00 through the declared top 11.00 (w0 -0.551 to -0.617, H0 69.27 to 69.78), and n = 22's surface above phi_i = 12.00 through the declared top 13.00 (w0 -0.741 to -0.770, H0 70.89 to 71.16), every row landing inside. The low end is carried, not computed: below phi_i = 0.00001 and between the stated points {0.00001, 0.00002, 0.00005} the class stands decided only at the stated points, exactly as the parents decided them (largest maximum 1.966e-09, short of the conditioning by 0.6831); no denser grid is computed and no interval claim beyond the points is made. Grade: EXTENSION. Derivation-independence count: 0. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.