Complete balanced four-gap chamber
Abstract
Unbounded polynomial endpoint bounds
The common minimum is s>=2 and q=2^s>=4. The sixteen Boolean offset patterns select explicit finite permutations of the four negative packets and a pre-negative ear slot. Doubled positive masses are (2^length-2) times the corresponding base. The three low-bit transfers add or subtract twice the actual source base. Each doubled seam and upper-cap slack is expanded at q=u+4 with u>=0. Ring normalization and nonnegative coefficients prove every endpoint bound for all q>=4; no finite sampling in s, native computation oracle or assumed feasibility is used.