Economic Autonomy of Computational Agents under Resource Constraints: A Proof-Forward Framework with Trust Geometry, Phase Thresholds, and Computability Limits

We develop a rigorous mathematical theory for the economic behavior of computational agents, achieving unification across three levels: the geometric layer (trust-delay metric), the dynamical layer (mean-field games), and the topological layer (resource manifold). Main contributions: (1) Dual-Scale Graph Limit Theory (Graphon-BS): A unified framework for both dense and sparse networks using Graphon limits and Benjamini-Schramm local weak convergence. (2) Phase Transition Theorem: Rigorous proof of critical phase transitions between geometric parameters and Nash equilibrium organizational forms, with physically calibrated estimates (r* ≈ 100 AU). (3) Chaitin Incomputable Risk Theory: Mapping contract default probabilities to the Chaitin Ω number, proving certain risk metrics are ontologically incomputable. (4) Complexity-Ambiguity Correspondence: A conjectured correspondence between logical undecidability and Knightian uncertainty. All main results are given with complete proofs or explicitly labeled as conjectures.