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§3.2 rested on 5 unpaired replicates while §3.2a used a paired design. Re-running the delta_max 4/8/16/32 grid with common random numbers and 20 replicates (configs/countable-vs-old-paired.yaml) changes the answer at the design end. The cost is resolved at EVERY delay and grows monotonically with load: delta_max=4 (rho 0.36) -0.0013 t= 4.0 (unpaired: not resolved) delta_max=8 (rho 0.56) -0.0034 t= 9.8 (unpaired: not resolved) delta_max=16 (rho 0.96) -0.0102 t=17.5 delta_max=32 (rho 1.76) -0.0228 t=22.4 So §3.2's claim that "at the operating loads (rho < 1) no difference between the models is detectable at all" was an artefact of the weak design, not a property of the system. There is a difference; it is just small — 0.13% and 0.34% at the two sub-unit loads. The new delta_max=4 figure (-0.0013 at 20 reps) independently reproduces §3.2a's (-0.0011 at 40 reps) from a separate sweep. 11 of 12 U>=1 cells resolve individually; max t = 29.0 against a Bonferroni threshold of 2.87 for twelve tests. The U=0 control is exact: 80/80 replicate pairs differ by 0.0. New finding at U=1 under overload: the sign FLIPS and the countable rule wins, +0.0127 (t = 7.6), positive in 19 of 20 pairs. Both models have collapsed at rho ~ 1.76 with a single uncle slot, but when capacity is the binding constraint the countable rule's occupied-slot exclusion means its one reference always recovers a NEW slot, while the unrestricted rule dedups by block id and can spend that reference on an orphan whose slot is already counted. Measured recovery agrees: q_u = 0.591 countable vs 0.579 unrestricted. The slot-vs-block distinction of §2.1 is worth most exactly where references are scarcest. Code: paired_gaps and pooled_by_delay move from scripts/plot_fine_delay into figures_pernode so both plot scripts share one implementation; plot_countable_vs_old now detects paired runs and uses the per-replicate difference, falling back to the unpaired two-sample test otherwise. Two hardcoded reporting values fixed — the Bonferroni threshold was pinned to 2.935 and printed nan for any grid that was not 15 cells, and a per-cell comparison line had a hardcoded /15 denominator; both now derive from the grid actually run. Figures 30-32 regenerated from the paired grid. Tests: 214 passed. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
