The Pulse Sets the Echo: At Full Strength the Pre-Echo Tracks the Pulse's Own Width, Not the Grain
Year: 2026
Type: preprint
Abstract: All-Fields programme paper (All-Fields Run, Batch 8 (AF)), November 2026. Written November 2026; publicly deposited 9 November 2026. Every pulse row this line has printed coupled two variables: the grain g, which sets the operator ratio τ₀/g, and the pulse width W = 5g, which sets the pulse's width in grain units. AF-26's alternate — the same dressing at both grains, the pulse width set by the other grain's scale — decouples them. This paper runs that 2×2 on AF-21/AF-26/AF-31's bench verbatim (dress S, two-point symbol, full strength w = 1, Hann pulse, 160g margin, dt = g/16, trapezoid energies), the matched rows reproducing AF-31 digit for digit as calibration (7.868703×10⁻² at τ_cell, 6.981292×10⁻¹ at τ_b) before the cross rows are read. The cross rows: at grain τ_cell, a pulse spanning τ_b inside one cell (W/g = 0.6458) returns **E_early = 5.280529×10⁻¹** — ×6.71 against its own grain's matched row, ×0.756 of the other grain's; at grain τ_b, a pulse spanning τ_cell across 38.71 cells returns **E_early = 7.956461×10⁻²** — ×0.114 against its own grain's matched row, ×1.011 of the other grain's. The reading rule was declared before the numbers were read, and the table meets the pulse-driver clause at both rows. On
Author: Aldred, William Alexander
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225466108