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

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 (proposed in 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 (per-token measurement standard): 10.5281/zenodo.20012654 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 v6 (August 2026) — attribution and scope revision. The shape of Finding 1 — single-fact retrieval improving with scale faster than multi-step composition does — is the compositionality gap, measured and named by Press et al. (2023) in the GPT-3 family. This version says so where the finding is stated, and keeps the increment it earns: the gap is shown here on a domain no model can have been pretrained on, so it cannot be a residue of uneven pretraining exposure across single-hop and multi-hop items. Finding 2's plateau is placed inside Dziri et al. (2023) on error compounding with compositional depth; the open question is what sets its height, not that it exists. The invented-domain design is credited to the synthetic-world tradition (PrOntoQA; ProofWriter) rather than claimed as new, and the scorer-disagreement result is placed inside Kamalloo et al. (2023). The word “capacity” is now credited to the tradition it is borrowed from (Miller; Baddeley & Hitch; Cowan; Just & Carpenter), with an explicit statement that no claim is made that a language model’s in-context bound is that construct. In the other direction, the audit’s cross-family blind step is now reported at its own size: key agreement of 35/35 on the valid items is the strong result, while the re-adjudication at κ = 0.628 is a sensitivity analysis by one language model of another, with no human agreement collected. A companion study previously cited as forthcoming has been parked, and the text no longer promises it. Editorial pass. Earlier versions remain in the version history.