Construction and exact scope

Abstract

Rounded reserve intervals

The internal ceilpos is the nonnegative integer ceiling of n/d. Its bounds include the strict previous-grid remainder and a capacity theorem. The rounded_reserve inference carries A<=S<=2e-A and E>=2e to E<=S+2e*ceilpos(E-S,2e)<=2E-A. The uniform strict mass margin is RTZ>3(RT+R+1) for independent R,T,Z>=4. These are reusable arithmetic steps, not a physical-order endpoint.