Capacity Scaling of Encoding-Through-Loading: Application vs. Cloze Asymmetry Across Three Orders of Magnitude

Paper 2 v4 in the friction-theory paper series. This version hardens the §2.5b race-architecture-floor finding introduced in v3, in response to an adversarial peer review. The capacity-scaling substance of Findings 1-3 (monotonic application scaling, bottleneck migration, MoE active-parameter scaling) is unchanged from v1-v3. What changed in v4: §2.5b re-measured at uniform n = 47. The race-architecture-floor finding was re-run on all high-capacity substrates at the full 47-question application bank (v3 reported two of the convergence models at n = 20). Every accuracy is now reported with a Wilson 95 % confidence interval. Reframed from "identical 85 % convergence" to a capacity-independent 79-85 % band. At uniform n = 47, four capable instruction-tuned substrates from three organisations — Cogito-V2.1-671B (85.1 %), Llama-3.3-70B-Instruct (80.9 %), DeepSeek-V3 (78.7 %), and Llama-3.1-405B-Instruct (78.7 %) — cluster in a narrow 79-85 % application band with fully overlapping 95 % CIs, spanning more than an order of magnitude of active parameters. Two further substrates sit 15-25 pp lower (Qwen3-235B-A22B 63.8 %, Hermes-4-405B 59.6 %). The band is capacity-independent and sits 5-11 pp below the cloze ceiling. The honest claim the data support is a floor band, not a single identical floor value; v3's "identical 85 %" rested on inconsistent sample sizes. Rival-explanations analysis added to §2.5b — shared pretraining/post-training culture, benchmark-specific artefact, arithmetic weakness, and lost-in-the-middle are each considered and bounded rather than dismissed. New §5.2b positioning the result against the scaling-laws literature (Kaplan et al. 2020; Hoffmann et al. 2022), evaluation-methodology literature (HELM; Liang et al. 2022), and the emergent-abilities debate (Wei et al. 2022). Hosted-API model-drift documented as a limitation. Accuracies are snapshots-in-time; the reproducibility appendix records platform and run date per model. New Appendix A — Reproducibility: generation parameters, prompt templates, scoring rubric, and a per-model platform/run-date table. §2.10 trimmed to a scope note; the full somatic-marker / per-session-encoding treatment is developed in Paper 4. §2.3 Schaeffer rebuttal strengthened with a metric-sensitivity argument; bibliography updated (Kaplan, Hoffmann, Liang, Wei added). Abstract. Large language models solve two differentiable task types on the same underlying knowledge base. Cloze retrieval saturates early (~90 % by 8 B parameters); application scales monotonically across three orders of magnitude. We document this asymmetry on a single invented knowledge domain ("Zorbetik") across nine models, using frontloaded in-context learning (Brown et al. 2020). Four findings: (1) application scales monotonically with capacity (Spearman ρ = +1.000 on Qwen2.5; cross-family panel ρ = +0.92, n=9; +40.8 pp per decade); (2) the bottleneck migrates with capacity; (3) Mixture-of-Experts models scale on active parameters, not total; (4) at uniform n = 47 with Wilson 95 % CIs, four capable instruction-tuned substrates cluster in a capacity-independent 79-85 % application band, the empirical signature of a race-architecture floor (Paper 1 §2.5; Paper 10 §1.5). A companion paper (Paper 2C, in preparation) re-tests the floor on an independent 327-substance domain and on the chain-depth axis. Companion papers in the series: Paper 0 (BFT): 10.5281/zenodo.19462500 Paper 1 (FT generalised): 10.5281/zenodo.20012655 Paper 2B (substrate-mechanism companion, in preparation) Paper 2C (chain-depth axis companion, in preparation) Paper 3 (Friction-guided inference): 10.5281/zenodo.20014122 Paper 10 (Race-architecture, physics scope): 10.5281/zenodo.20014568 Data, fine-tuning notebooks, analysis scripts: https://github.com/tplund/friction-theory-p2-capacity-scaling