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Volumetric additive manufacturing promises near-instantaneous fabrication of 3D objects, yet achieving high fidelity at the micro-scale remains challenging due to the complex interplay between optical diffraction and chemical effects. We present Single-View Holographic Volumetric Additive Manufacturing (SHVAM), a mechanically static system that shapes volumetric dose distributions using time-multiplexed, phase-only holograms projected from a single optical axis. To achieve high resolution with SHVAM, we formulate hologram synthesis as a coupled inverse problem, integrating a differentiable wave-optical forward model with a simplified photochemical model that explicitly captures inhibitor diffusion and non-linear dose response. Optimizing hologram sequences under these coupled constraints allows us to pre-compensate for chemical blur, yielding higher print fidelity than optical-only optimization. We demonstrate the efficacy of SHVAM by fabricating simple 2D and 3D structures with lateral feature sizes of approximately 10 μm within a 0.8 mm × 0.8 mm × 3 mm volume in seconds.