Monomials Beyond n = 20 and Below 0.0005: n = 22 Arrives at φ_i = 8.9970, the Widened Bracket Ends at n = 24 — and Nothing at All Below 0.0005, Down to 0.0001

The monomial staircase is carried one member past paper #612 and the low end one decade further down. Gated digit-for-digit on the whole body of paper #612's notebook (Gates A-G: the exhibits of papers #595, #583, #549, #537 and the far-standard paper, every bisected bracket's ends re-run) and on paper #612's own beginnings and low-end maximum (Gate H), the paper scans the next even members on the widened bracket (-45, 15) under a rule stated before results: a member is bisected only if every sampled maximum stands in the bracket's interior, and the first member whose maxima touch the bracket's edge ends the scan. The n = 22 member begins at phi_i* = 8.9970 (bracket [8.99701, 8.99707]), within three thousandths of the expectation paper #612 printed at its own scan edge; its maxima are interior at every sampled point (argmax between log V0 = -44.5 and -42.0) and stable at the fourth decimal on the still wider bracket (-60, 15); its spacing from n = 20 is 0.7462, extending the spacing sequence to 0.87, 0.81, 0.80, 0.78, 0.77, 0.78, 0.75, 0.75, 0.74, 0.75 with the levelling confirmed across five consecutive spacings. The next member ends the scan: n = 24's sampled maximum sits at the bracket's low edge (argmax log V0 = -45.0) at all seven sampled phi_i from 8.50 to 10.00, so no arrival is read for it and the widened bracket's honest extent is computed to be exactly one member past paper #612's. The n = 22 crossing's own exit from the bracket between phi_i = 9.00 and 9.25 is measured in trial values (Omega_phi = 0.7056 already at log V0 = -45 for phi_i = 9.25, against 0.6748 for phi_i = 9.00), leaving its conditioned row (w0 = -0.465, H0 = 68.85) at phi_i = 9.00 alone on this bracket. Below, on the stated grid phi_i in {0.0001, 0.0002, 0.0003, 0.0004}, nothing conditions in [0.0001, 0.0005): the largest unrounded maximum is the quadratic's 1.26e-07 at phi_i = 0.0004, short of the conditioning by 0.6831, and joined with the parents' grids the class below the standard stands decided from 0.0001 upward. Grade: EXTENSION. Derivation-independence count: 0. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.