Construction and exact scope
Abstract
Complete chamber masks
The internal baseWord implements the complete supplied physical-mask algorithm at d0=max(a,b,c)+2. labels selects the original index off+i by its binary digit and lists indices in increasing order. Four positive blocks are separated by U-,V-,W-,X-, with X- last. The template permits nested U reserves, nested V reserves, disjoint advanced and reserved V masks, and a W reserve. Monotone ascending chambers release U labels; strict valleys release either U or V labels; strict peaks may advance V labels. The descending boundary Z=4,R=2T advances the actual lowest X-positive label and uses its sharper remaining charge. Equal dyadic ratios are included by the literal branch conditions. physicalWord prepends the new low U labels and shifts each inherited index for larger d. The unbounded correctness obligations still include chamber mask capacity and nesting, exact endpoint inequalities and the resulting common physical permutation with both centered prefix strips. The constructor definition alone does not close the max-plus-two cone or unrestricted four-gap J.