Beyond the Single Forgetting Curve: A Typologically-Extended Wickelgren Function, a Simulation Study, and a Pre-Registered Test of Error-Type-Specific Memory Decay

Background. A century of quantitative work has asked whetherone mathematical function describes all forgetting, or whetherdistinct kinds of memory require distinct functions (Rubin andWenzel, 1996). The Wickelgren (1974) power law is among themost accurate single functions (Wixted and Carpenter, 2007),yet it treats all to-be-remembered items as homogeneous,ignoring how the item was encoded. Modern trainable retentionmodels -- DASH, half-life regression, FSRS, attentive knowledgetracing -- condition on study history, but none conditionsmemory dynamics on the semantic type of the wrong answer. Theoretical contribution. I propose a typologically-extendedWickelgren function in which the cognitive error committed atencoding moderates the forgetting trajectory. Building on theConfusion Fingerprint Index taxonomy (Maurya, 2026) -- RecallFailure, Partial Knowledge, Confabulation, and Interference --I let initial retention strength, decay rate, and relearningsavings vary by error type, add a Confabulation reversion termgrounded in the documented one-week return of high-confidenceerrors (Butler, Fazio, and Marsh, 2011), and an exploratoryInterference damped oscillation. Simulation findings. A 7,200-fit operating-characteristicssimulation (120 replications x 60 grid cells) establishes thatthe registered four-time-point design recovers the RF-vs-PKdecay contrast at 0.90 power and the relearning savings contrastat essentially 1.00 across the realistic sample-size xCF-base-rate grid, and that the full typological model ispreferred over the homogeneous null in 100% of replications.Two predictions (PK-vs-CF decay ordering and Confabulationreversion magnitude) are critically under-powered due topartial parameter co-confounding at four time points; these arepre-registered as confirmatory-but-low-power with symmetricfalsification conditions. Pre-registered protocol. A Bayesian secondary analysis of theparent CFI three-arm RCT (n = 90; government junior highschools, Kanpur Dehat, India) is registered with PSIS-LOOmodel comparison, source-anchored informative priors, andsymmetric falsification rules. Pre-registration:doi.org/10.17605/OSF.IO/YU6P5. The paper contributes theory,simulation, and a registered analysis plan; it reports nohuman-participant results. All simulation code and model filesare deposited at the OSF project.