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 confinement, not by membrane bending. The 17 mm provisional injection sphere corresponds to n^2 = 36 (d_sphere = 16.18 mm), confirming geometric compatibility. The recommended design window for flood-barrier applications is n^2 = 9 with perimeter-only densification (30.6% of tubes), achieving a safety factor exceeding 3 against a 2.0 m flood head on a 2.5 m AEFC. The cumulative hierarchy multiplier at n^2 = 9 is 170.8×, consistent with the canonical 173× product-level figure. Six empirical constants require physical testing before certification use; the green-NRL autohesion threshold under micro-scale contact pressure (0.17–1.01 kPa) is the primary experimental objective.