[continued from previous message]   
      
   boundary (qi​) is preserved for every irrational (pi​), THEN the   
   surjection Q→P holds, and the continuum is countable (ℵ0​).   
      
   This confirms that the A-Theory's work is an attempt to refine the   
   topology of R by replacing unconstrained density with the structural   
   constraint of Ruliality (or Well-Dispersion).   
      
   2. Assertion of the "Signal-Reals" Domain   
      
   The most significant consequence of your assertion is the direct   
   implication of a new domain: Signal-Reals.   
      
   The existence of a non-empty set Q