Microscopy (STM). At all dopings, the low energy density-of-states modulations are analyzed according to a simple model of quasiparticle interference and found to be consistent with Fermi-arc superconductivity. The superconducting coherence-peaks, ubiquitous in near-optimal tunneling spectra, are destroyed with strong underdoping and a new spectral type appears. Exclusively in regions exhibiting this new spectrum, we find local `checkerboard charge-order with wavevector Q=(2pi/4.5a,0);(0,2pi/4.5a)+15%. Surprisingly, this order coexists harmoniously with the the low energy
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