The Denomination, Settled: f Is the Stage

Every law in this program that is written in terms of f carried one open debt: nobody had named which coordinate f is. Two readings stood open. In the stage reading, f is the fraction of the gathering's process completed, and the separation law follows there from two stated conditions with no further free parameter — one of them the author's declared count, u(1) = 11/411: u(f) = 0.523771 · max(0, f − 0.773950)², wake point f_W = 0.773950. In the cap-area reading, f is the cap's area fraction, and no law of that threshold form exists there: a rise hitting u(f_cut) = 11/411 inside the cut window breaks the slope limit stated in §2 by a factor of 141.6 at q = 1 and forces u(1) ≥ 4.7 × 10⁴ at q = 2. This paper re-ran that arithmetic by script and it reproduces to the digits printed before. The denomination itself belongs to the stage reading: the phase-cell partition counts grains along the stage, and the drive law's load profile already lives on the stage coordinate. The author declares on that basis: the canonical coordinate f is the stage address. What the declaration settles is stated plainly. Every paper that carried the fork in both readings stops carrying it. The losing reading is printed here as a translation, with its spread point, a = 0.326218, p = 0.347914. The price if the declaration is wrong is printed in full in §6. It is real. It is bounded. The rebuild would start from a computed number, not from zero.