Paper 44 We apply the axiom calibration framework of constructive reverse mathematics (CRM) to the measurement problem of quantum mechanics. Rather than treating the measurement problem as a single conceptual puzzle, we examine three major interpretations — Copenhagen, Many-Worlds, and Bohmian mechanics — and determine the constructive principle each requires over Bishop's constructive mathematics (BISH). The Copenhagen postulate calibrates at WLPO in its minimal formalization, or at LPO in its strong formalization. The Many-Worlds postulate calibrates at DC (Dependent Choice). The Bohmian trajectory postulate calibrates at LPO (equivalently, Bounded Monotone Convergence). Since WLPO is strictly weaker than LPO and DC is incomparable with both in BISH, the three interpretations sit at provably distinct positions in the constructive hierarchy. The accompanying Lean 4 / Mathlib formalization (10 files, ~1,100 lines, zero errors) includes three sorry-free calibration directions. Paper 44 of the Foundation Relativity series.
Paul Chun-Kit Lee (Tue,) studied this question.