  Extensive research into high temperature superconducting cuprates is now
focused upon identifying the relationship between the classic 'pseudogap'
phenomenon$^{1,2}$ and the more recently investigated density wave
state$^{3-13}$. This state always exhibits wave vector $Q$ parallel to the
planar Cu-O-Cu bonds$^{4-13}$ along with a predominantly $d$-symmetry form
factor$^{14-17}$ (dFF-DW). Finding its microscopic mechanism has now become a
key objective$^{18-30}$ of this field. To accomplish this, one must identify
the momentum-space ($k$-space) states contributing to the dFF-DW spectral
weight, determine their particle-hole phase relationship about the Fermi
energy, establish whether they exhibit a characteristic energy gap, and
understand the evolution of all these phenomena throughout the phase diagram.
Here we use energy-resolved sublattice visualization$^{14}$ of electronic
structure and show that the characteristic energy of the dFF-DW modulations is
actually the 'pseudogap' energy $\Delta_{1}$. Moreover, we demonstrate that the
dFF-DW modulations at $E=-\Delta_{1}$ (filled states) occur with relative phase
$\pi$ compared to those at $E=\Delta_{1}$ (empty states). Finally, we show that
the dFF-DW $Q$ corresponds directly to scattering between the 'hot frontier'
regions of $k$-space beyond which Bogoliubov quasiparticles cease to
exist$^{31,32,33}$. These data demonstrate that the dFF-DW state is consistent
with particle-hole interactions focused at the pseudogap energy scale and
between the four pairs of 'hot frontier' regions in $k$-space where the
pseudogap opens.
