M. A. R. s Algorithm n - 1 Hundred Million Tested

Protocol Structure & Well-Defined Operational Sections Section Scope & Step-by-Step Operational Definition Section 1 Governing Polynomial-Power & Quotient Formula — Direct number substitution into ζ(s) = P∞ n−1 1 n^s across γ = 1 to 100, 000, 000 without extra variables, square roots, or negative terms. Section 2 Canonical Parameters, Quotient Division & Decimal Shift (R, q, and r) — Step-by-step anchor definitions, 32-decimal master scaling quotient R, Mode A (932 Carry Shift ×10), and Mode B (032 Direct Register Shift ÷10). Section 3 Worked Number Substitutions (γ = 1 to 100, 000, 000) — Six complete step-by-step worked transitions L with full 32-digit post-decimal expansions followed by ............. to denote infinite continuation. Section 4 End-Result Scaling Audit & Blank Offline Execution Worksheet — Performance audit across eight decadal bands (100.00% pass rate) and double-spaced pencil-and-paper execution worksheet. Section 5 Multi-Decade Milestone & Horizon Reference Table — Verified 10-decimal zero heights γN , scaled quotients qN = γN /R, registers r, and step residuals ∆ from N = 1 to N= 248, 008, 026. Section 6 High-Altitude Continuous Horizon Window Slices — Six 60-zero continuous blocks at N = 104, 105, 106, 107, 108 and the γ = 108 horizon crossing. Section 7 Expanded Continuous Offline Reference Table (γ1 to γ1,080) — Complete 1,080-zero continuous reference tables with pre-calculated quotients qn = γn/R.