Recursive PDA Micro-Drop Densification: A Hierarchical Cellular Solid Model for the Adaptive Matrix Ecosystem

The Adaptive Matrix Ecosystem achieves structural capacity through hierarchical water-filled elastic cellular units. This paper presents an analytical strength calculator for AME tubes densified with green (uncured) NRL micro-drops that reshape under vibration and confinement into a perfect n × n equilateral triangular prism tessellation. The post-cure structure is a recursive PDA lattice: a liquid-filled, elastically coupled, hierarchical cellular solid governed by the same Pressure Differential Architecture as the parent AME structure at larger scale. This is not a foam model, not a bonded-sphere aggregate, and not a granular packing; the compressive modulus is dominated by the bulk modulus of water under…