Bayesian Confidence Recalibration and Research-Equilibrium Criticality: Temporal Support in Robust Portfolios

Robust portfolio rules that reconstruct confidence sets after learning need not preserve the evaluator obtained by prior-by-prior Bayesian transport. In the Gaussian model, this discrepancy is summarized by natural-coordinate displacement: inherited transport preserves it whereas fresh reconstruction can replace it. We price evaluator replacement and trace the resulting optimized curvature through endogenous research. Optimized robust value represents protocol regret as a functional Bregman divergence, while a within-vintage rectangular Gaussian benchmark with constant absolute risk aversion (CARA) yields a stopped recalibration tax. In a versioned model-release economy, validated history propagates through a strictly causal network and a same-cycle share of current optimized marginal value feeds back into research supply. The capacity-constrained equilibrium reduces to a scalar equation with protocol-indexed gain \(\mathfrak g_I^P=\lambda\beta_{R,I}(W_R^P)''\). Purely causal validation cannot create a same-cycle unit mode; provenance changes criticality through optimized curvature. For a scalar primitive supplier-score shock \(z\) in direction \(h_I\) and financial outcome \(\mathcal O\), sensitivity factors as \(\omega_{\mathcal O,h,I}/(1-\mathfrak g_I^P)\). Conditional on a smooth equilibrium state and active cell, completion-time information sharply bounds this multiplier when all compatible timing laws are subcritical; no finite uniform bound exists when the timing set reaches the pole.