KCGT-MEM Annealed Lagging: Pre-registered Study of GNC-Synchronized λ₁ Scheduling in the Lagged-Diffusivity Estimator (pre-registration, paper, code, and data)

This deposit accompanies a pre-registered companion study to the KCGT-MEM main paper (Zenodo record 10.5281/zenodo.20652756, v3). The study asks whether a GNC-synchronized dynamic λ₁ schedule ("annealed lagging") can bridge the diameter–continuity trade-off established by the bang-bang result in §7.5 of the main paper. The pre-registration document was filed on 2026-06-13, before any experiment was run, and is included in this deposit. Key findings: • H1(b) CONFIRMED: geometric annealing recovers 70% of the fill gap on the fragmented three-lines phantom (Holm-corrected p < 10⁻⁵). • H1(a) NOT CONFIRMED: diameter bias is unchanged (ann ≈ lag). Mechanistic account: diameter is determined at the final GNC stage, which all tested schedules leave fully lagged. • H2 FALSIFIED: schedule shape matters significantly (15/27 pairwise comparisons significant after Bonferroni correction); the schedule is a new tunable parameter. • H3 CONFIRMED: no annealing schedule achieves Pareto dominance over both lag and anc on any tested condition (6 medical + 4 cosmological conditions).