A Catalog-Level Test of Localized and Directionally Modulated Balance in BOSS DR12 Void–Galaxy Structure

We present a catalog-level test of localized signed-extrema balance in BOSS DR12 void–galaxy structure using LOWZ South, LOWZ North, CMASS South, and CMASS North subsamples. Random-corrected count and ratio residual fields are constructed on a common Cartesian grid, and signed local extrema are analyzed globally and within void-centric geometry zones. While global ratio-residual extrema remain approximately balanced, void-wall and outer-wall/filament-proxy regions exhibit a localized positive-extrema excess. The LOWZ samples provide the strongest same-family pilot support, whereas the CMASS samples show a configuration-sensitive and directionally modulated extension. An anisotropic-sector diagnostic indicates that the localized excess is not uniformly distributed across coordinate sectors. The result is interpreted as localized and directionally modulated catalog-level pilot evidence. The analysis does not establish a universal 70:30 law, a microscopic physical mechanism, or a challenge to the standard cosmological framework. Future work includes mock-catalog validation, independent survey replication, and physically aligned anisotropy diagnostics.