Born-Convergence and Decision-Level Memory: A Δt-Sweep Operational Exclusion Criterion for Readout-Only Models

Quantum mechanics predicts outcome statistics via the Born rule, yet remains operationally under-specified with respect to how, and on what timescale, a single outcome becomes definite in an experimental record. In many platforms, identical Born-compliant outcome histograms can be produced either by a time-extended physical closure process, in which competing channels accumulate influence until a decision event, or by purely readout-level mappings and post-processing applied to measurement records. This under-determination motivates an operational question: which broad classes of readout-based explanations remain viable given finite-time, resolution-dependent data alone? Here we formulate an operational exclusion criterion relative to a broad null family of readout-only, memoryless models. In this null family, for each temporal resolution Delta t, the reported outcome is generated by a (possibly stochastic and nonlinear) mapping from a single-shot record R to an outcome Y, with no decision-level internal state persisting across Delta t settings and no dependence on sweep direction or parameter history. Under these structural assumptions, sweep-history dependence is excluded by construction. Using Delta t as a single experimentally controlled parameter, interpreted as an effective integration window, we define three operational quantities. The first is a Born distance D_B(Delta t), measuring the deviation between the observed outcome distribution at resolution Delta t and the corresponding Born-rule prediction. The second is a convergence-rate proxy gamma(Delta t), defined as the negative derivative of D_B with respect to the logarithm of Delta t, which quantifies the tendency toward convergence to Born statistics as temporal resolution is increased. The third is a hysteresis-based memory witness M(Delta t), defined as the absolute difference between Born distances obtained from increasing and decreasing Delta t sweeps. We then state a conditional trade-off for stateful closure explanations. Over Delta t ranges where these quantities are well defined, a positive convergence tendency gamma(Delta t) greater than zero is generically expected to be accompanied by nonzero path dependence M(Delta t) greater than zero. This expectation can be summarized by an upper bound of the form: gamma(Delta t) is less than or equal to C times M(Delta t), plus a correction term epsilon(Delta t). Here C depends on coarse structural features of the closure process, such as the number of competing channels and the sharpness of decision thresholds, while epsilon collects finite-sample and finite-resolution effects. An efficiency ratio eta(Delta t), defined as gamma(Delta t) divided by M(Delta t), is introduced as a diagnostic. Within the null family, where M(Delta t) is identically zero, any sustained claim of finite positive gamma necessarily drives eta to diverge, signaling incompatibility with the readout-only, memoryless assumptions. The framework does not propose new dynamics or modify quantum theory. Instead, it specifies an operational protocol and a coupled signature set whose robust observation would render the readout-only, memoryless null family insufficient as an explanation of finite-time Born convergence. Robustness controls, including sweep-rate variation, randomized Delta t ordering, and mapping-invariance checks, are outlined to separate decision-level path dependence from trivial instrumental artifacts.