The Branch Beyond λ = 70.0: The Far-V₀ Branch Runs to λ = 80.0 on a Ceiling Stated from the Trend Alone, the Ninth Fit Gains 0.01 — and the Limit Is Computed Again: the New Gain Ratio, 0.50, Qualifies Under Paper #622's Rule, and the Limiting Slope Stands at 22.96, Inside the Bracket That Held It

The far-V0 branch of the exponential rolling field is followed past the Wave 29 paper's scan end, and the limiting slope's standing is ruled on under paper #622's rule as the record now stands (paper #632's caveat, fired in Wave 29, is spent). Gated digit-for-digit on the whole body of the Wave 29 branch notebook (Gates A-M and its eighth scan) and on the Wave 29 paper's printed exhibits (Gate N: twenty members, census, eighth fit 22.94 lambda - 51.07 with unrounded slope 22.9396, gains 1.18, 0.24, 0.09, 0.05, 0.04, 0.02, 0.02, gain ratios 0.20, 0.38, 0.56, 0.80, 0.50, 1.00, unrounded gains 0.0152 and 0.0259 with ratio 0.587, half-range fits 22.94 and 22.94), the paper states a ninth scan before its results by the parents' rule -- lambda from 70.5 to 80.0 in steps of 0.5, the widened search carried to log V0 = 1885, the ceiling set as the eighth fit's end prediction at lambda = 80 (1784.13) plus a margin of about one hundred, on the trend's arithmetic alone. The branch is present at all twenty sampled lambda values (log V0 1566.184 rising to 1784.201, w0 +0.995 to +0.998, H0 76.49 to 76.74) and does not terminate inside the scan; the census of upward crossings at step 2 in log V0 finds exactly one crossing at every lambda (157 sampled lambda across nine scans). The ninth release-line fit is 22.95 lambda - 51.74, completing the gains sequence 1.18, 0.24, 0.09, 0.05, 0.04, 0.02, 0.02, 0.01 with half-range fits 22.95 and 22.95. The ninth gain ratio is 0.50 at the printed convention the line has used for every gain and ratio -- below 0.56, so the range qualifies under paper #622's printed rule and the limiting slope is computed by its three stated extrapolations at 22.9600, 22.9600 and 22.9621: the limit stands at 22.96, every estimate inside the bracket 22.9307 to 23.0600, which survives whole a second time. The unrounded reading (gain 0.0096, ratio 0.633, above the threshold) is printed beside the verdict at full size; the paper follows the printed convention, the convention that carried the adverse verdict one range ago. The bound at the largest observed ratio below one reads limit <= 22.9900; at the largest observed ratio itself (1.00) the bound form has no finite value, printed rather than hidden. The fallen limit of 22.94 does not revive: the new computation gives a different number. Grade: EXTENSION. Derivation-independence count: 0. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.