TWPR Re-read: Index Atoms, Occupancy-Preserving Nulls, and Residual Prime-Block Grammar in the 6-Wheel

The TWPR papers introduce an aligned prime-rank coordinate and a defect for existing twin-prime events. Factor-incidence geometry ordinally recodes the same trace in an ordered 6k±1 matrix and supplies the scale-free coordinate ρgeom n . The index-atom repair exactly separates one prime-rank slot already fixed by the tested boundary state from the residual quantity subsequently studied. Only this count decomposition is exact; proportional transfer of the density proxy to the remaining slots remains a declared heuristic model step.