Eversion-Driven Capillary Extension: Low-Pressure Tube Deposition in the AMW/IPS Architecture

Capillary extension in the Adaptive Matrix Ecosystem (AME) is mechanically distinct from biological tip growth. Where fungal hyphae and pollen tubes advance via cytoskeletal turgor pressure at the cell wall, the Adaptive Matrix Worm (AMW) everts a double-walled Natural Rubber Latex (NRL) tube under external water pressure. The two mechanisms produce similar branching network geometries but use entirely different hydraulics. This paper develops the eversion-deposition framework for the AMW class of capillary-extension agents operating within the canonical ≤ 15 kPa gauge envelope of the host Internal Plumbing System (IPS). The central feasibility claim is that capillary extension is achievable not because biological tip pressure is replicated but because new compliant passages are formed by hydraulic eversion-deposition of preformed tube material into a digitally known IPS. Resolution R4 (eversion-driven canonical) carries the actuation mechanism; Resolution R2 (recursive Pressure Differential Architecture, PDA) carries the architectural- integration principle by which deposited capillaries become functional parts of the larger IPS flow, sensing, repair, and reinforcement networks. We specify the eversion-deposition mechanism with reference to Mission Lifecycle Canonical v1. 0 2. 3 and Paper 4B; we map the four canonical capillary- deposition modes (repair, sensor, drainage/flow-redistribution, reinforcement/tendon-assist) to mode-specific deposit operations and force-budget terms; and we situate the AMW relative to the engineered eversion lineage (Hawkes 2017, Blumenschein 2020, AlHarthy 2025), with the hydraulic water-driven subset (Luong 2019, Tennakoon 2023, Gravish 2024) as the closest published precedent. Biological pattern analogues are retained for geometry, routing, and network formation but explicitly not for hydraulics. Bench Loop I, the AMW Capillary Growth Cell, maps to Stages 1–2 of the canonical's five-stage staged- validation pathway and is the bench-scale instrument that will confirm the eversion-deposition framework or identify the operating-envelope boundary at which it fails. Five failure modes (incomplete eversion, tube buckling/wrinkling, junction misrouting, adhesion failure, retrieval/abandonment) are catalogued with detection signatures and recovery pathways; those that exceed in-flight recovery capacity route to the II. 6 dispatch-failure framework. The triad-gate compliance verification closes the paper.