Empirical Evaluation of Quaternary Iteration Control on a Deterministic Looped Transformer

Abstract

We report a preregistered empirical test of the quaternary iteration control contract on Loom, a deterministic looped transformer with analytical weights that executes programs compiled from C. The contract specifies a four-valued evaluator interface (NO with a named failure mode, YES, MAYBE with a typed missing-evidence or further-pass payload, and IFF with a named dependency) and a controller that accounts for the finite resource each continuing transition consumes. The published note proves a termination bound and a fixed-count specialization but makes no empirical claim. We preregistered six hypotheses with explicit thresholds and ran 7,172 trials across four conditions: unmodified Loom, instrumentation-only, a binary controller with matched state and iteration budgets (checkpoint and rollback), and the QICT controller. The initial run encountered a preregistered stop condition: a 25% false-negative rate on the pc_out_of_range detector, associated with coupled evaluator-locality and retry-sequencing violations. The corrective replication supports this diagnosis, but does not isolate the causal contribution of each correction. A diagnostic audit localized the cause, the integration was corrected, and a data-informed corrective replication was run under the same preregistration. The original results are preserved and reported alongside the replication. The implementation exhibited no termination-bound violation across 1,793 QICT runs (H1), and all 114 straight_line cases conformed exactly to k=q=L (H2). Across the admitted detectors and recorded evaluator calls, H5 observed 0/840 false positives and 0/3,349 false negatives after correction. Dependency use was observed on 10 of 26 branch cases (38.5%), below the preregistered 50% threshold (H3). This QICT-on-Loom integration did not meet the preregistered 95% correct-final-output floor for any admitted fault class, and the B2 checkpoint-and-rollback condition produced more correct final outputs than the QICT exclusion-and-retry condition in every class (H4). The measured instruction ratio (QICT/B0) was 1.033; the observed wall-clock ratio was 0.993, with no inference drawn (H6). The experiment separates detection from correct final output. After correction, the task-independent evaluator produced typed fault diagnoses with no observed FP or FN errors on the admitted detectors and recorded calls, but diagnosis did not produce correct final outputs at the preregistered rate on this deterministic substrate. The preregistered stop-and-correct procedure exposed the integration defect, bounded its observed impact, and preserved a traceable correction while retaining the initial results.