Environment Design for Stable Learning in Hierarchical Adaptive Systems

Large-scale adaptive multi-agent systems face a structural coordination pressure: under dense interaction, approximately local conflict generation, and bounded governance bandwidth, potential pairwise conflicts scale on the order of O(n2) while absorptive capacity grows sub-quadratically. Conventional stabilization strategies - direct agent control and rule proliferation - meet characteristic limits at scale and share a pathological failure mode, the silence signal: apparent stability produced by degraded detection rather than genuine alignment. Environment Design Theory (EDT) reframes stability as a property of interaction terrain: the deliberate design of boundaries, coupling structure, operating timescales, and exploration conditions so that local failures remain contained and the system's capacity to learn, recover, and observe is preserved, while dependence on continuous direct command is reduced. Version 2.0 replaces toy-model validation claims with conditional analysis. The formal core separates load conventions and resource allocation; local stability from tempo gating; stress direction from tracking capacity; and deterioration from model-domain exit. Its central results are the conditional desertification dynamics D1-D4 and constant-input seeding laws S1-S4, supplemented by a bounded-input first-activation bracket S5. Elementary branching, observation-reversal and cumulative-reference results make measurement conventions explicit. A proposed protection extension E1 separates learning suppression from damage attenuation through an instantaneous sign criterion; E2 extends it to trajectory comparison under prescribed ordered inputs, without a closed-loop claim. Generative seeding remains a definition-and-hypothesis proposal. Seven predictions use a two-layer protocol separating mathematical validity from prospective tests of model applicability; no empirical validation is claimed. The contribution is the specified hierarchical models and conditional results, not priority for environment design, capability erosion, safety supervision or observation integrity. Note on Version 2.0: this version revises the registered v1.0. The seven numerical toy experiments of the v1.0 supplementary material are withdrawn as validation evidence; their role is replaced by conditional analytic results stated and proved under explicit assumptions. Core definitions are corrected: the stability criterion, the gating interpretation, the risk-index system, the branching load conventions, the seeding release condition, and the validity domain of the state equations. Predictions are restated with tiered evidential status under a two-layer refutation protocol. Files: the main paper (v2.0) and a supporting archive containing the analytic supplement, the proposed study design, a manifest, and SHA-256 checksums. EDT is developed as the engineering implementation layer of the author's Deficit-Fractal Governance research programme.