This model is a deterministic TPMS-based porous filter generated with the PAPP protocol from a Schwarz P field and a balanced radial grading strategy. Compared with denser TPMS families, Schwarz P produces fewer, larger, and more direct flow channels, giving the structure a clearer cellular logic while preserving full topological closure. The final validated mesh is watertight and manifold, with 0 boundary edges, 0 non-manifold edges, and 0 degenerate faces. Topology audit: genus 268. Balanced version metrics: body porosity 0.5984, porous-region porosity 0.6701, surface area 33.2451, 1,565,940 vertices, 3,132,948 faces. This piece is both a mathematical surface realization and an engineering-ready porous architecture, intended for studies of flow, filtration, topology, and fabrication-aware design.