Approximate Equilibrium in Real Time: POMCP, Bounded Rationality, and the Counter-Harvest Trap

Priority record and pre-registration for Paper 4 of the MOMentum Project, lodged before Race 2 (China, Shanghai, approximately 20 March 2026). Predictions P4-1 through P4-5 are locked as of 12 March 2026. This document establishes priority for the computational completion of the four-paper series: rolling-horizon POMCP as the tractable approximate solver for the non-stationary POSG proved in Paper 3, with the Paper 1 40-state belief state as root input and the Paper 3 sequential equilibrium characterisation as opponent model. The central theoretical object is a suboptimality bound V* minus V^k of the form f(k, rationality level, H), decreasing in lookahead depth k. Five open problems from Papers 1 through 3 are addressed: computational intractability, ERS-tyre separability, common-knowledge relaxation, in-race rho_c variation, and full-season empirical validation. Builds on: arXiv:2603.01290 (Paper 1, 27 February 2026), ResearchGate DOI 10.13140/RG.2.2.27003.17448 (Paper 2, 8 March 2026), Zenodo DOI 10.5281/zenodo.18986619 (Paper 3, 12 March 2026).