Paper 4 in the Friction Theory paper-series. The empirical-calibration companion to Paper 6 (matched-friction-under-hysteresis), tested on LLM substrate (Qwen2. 5-7B-Instruct + LoRA fine-tuning). Abstract. Friction Theory (FT; Lund 2026b, Paper 1) is the substrate-universal framework for bounded probabilistic computation systems satisfying the race axioms. The matched-friction-under-hysteresis formulation (Paper 6) predicts an inverted-U between substrate-level friction intensity and encoding outcome on any axis where friction scales monotonically. Behavioural Friction Theory (BFT; Lund 2026a, Paper 0) is the biological specialisation of FT for mobile, mortal, metabolism-constrained organisms (BFT ⊂ FT). Paper 4 is the empirical-calibration companion on LLM substrate. Methods. Eight friction-intensity axes tested via fine-tuning Qwen2. 5-7B-Instruct (4-bit NF4 LoRA, r=16, α=32) on fictive "Zorbetik" facts designed to eliminate pretraining priors, plus cross-substrate-paradigm tests on Mistral-7B-Instruct-v0. 3, Llama-3. 1-8B-Instruct, Llama-3. 1-8B-base, and Qwen2. 5-3B-Instruct via FT trajectory and ICL-inference paradigms. Headline results. Four of five intra-session axes produce genuine inverted-U parabels: task-friction (v10c, RLLM ratio ordering deepᵣeason 0. 66 passive ≈ surface in correctness or first-token CR distribution) is confirmed on 5 of 6 substrate × paradigm pairings spanning two model families (Qwen, Llama), three sizes (3B/7B/8B), and two paradigms (FT trajectory + ICL inference). The 6th pairing is ceiling-masked under the pre-flight test-informativeness criterion, consistent with that criterion. Two substrate-distinguishing friction-type axes (§11. 6). Race-level friction including reactance is substrate-universal (Paper 14, Paper 2B, Paper 5 empirical anchors). Two axes distinguish LLM substrate from biological substrate: self-continuity (confirmed substrate-absent via §4. 8 v10g), and surprise (biology-specific via §4. 3 v11c null + §11. 5 "Dunning-Kruger without Mount Stupid" theoretical extension). Scope and status. Paper 4 is a pilot-scale preprint timestamping preliminary empirical observations on LLM substrate. Per-condition n in the range 4–30; mixed-model, mixed-paradigm portfolio. Individual findings should be read as exploratory pilot results that constrain framework development, not as definitive cross-substrate calibrations. A planned v2 revision will scale per-condition n on the core axes; see §10. 1. A pilot scale-up attempt (Together SFT, n=100/condition at both LoRA r=16 and r=64) produced 0% accuracy — substrate-saturation finding documented in §10. 1 as scope-condition rather than framework-disconfirmation; v2 revision must combine n-expansion with paraphrase-augmentation per §4. 7. 3. Companion papers in the Friction Theory series: Paper 0 (BFT master): 10. 5281/zenodo. 19462500 Paper 1 (Friction Theory substrate): 10. 5281/zenodo. 20012655 Paper 2B (ICL/FT substrate-mechanism): 10. 5281/zenodo. 20145219 Paper 4B (Expertise reversal spinoff): 10. 5281/zenodo. 20059862 Paper 6 core (Matched friction under hysteresis): 10. 5281/zenodo. 20059863 Paper 6B (Effort-value attribution): 10. 5281/zenodo. 20309000 (cite-letter; in preparation) Paper 6C (Dynamic commitment timing): 10. 5281/zenodo. 20309001 (cite-letter; in preparation)
Tomas Pødenphant Lund (Wed,) studied this question.