  Theories based upon strong real space (r-space) electron electron
interactions have long predicted that unidirectional charge density modulations
(CDM) with four unit cell (4$a_0$) periodicity should occur in the hole doped
cuprate Mott insulator (MI). Experimentally, however, increasing the hole
density p is reported to cause the conventionally defined wavevector $Q_A$ of
the CDM to evolve continuously as if driven primarily by momentum space
(k-space) effects. Here we introduce phase resolved electronic structure
visualization for determination of the cuprate CDM wavevector. Remarkably, this
new technique reveals a virtually doping independent locking of the local CDM
wavevector at $|Q_0|=2\pi/4a_0$ throughout the underdoped phase diagram of the
canonical cuprate $Bi_2Sr_2CaCu_2O_8$. These observations have significant
fundamental consequences because they are orthogonal to a k-space (Fermi
surface) based picture of the cuprate CDM but are consistent with strong
coupling r-space based theories. Our findings imply that it is the latter that
provide the intrinsic organizational principle for the cuprate CDM state.
