Pre-registered tests of solid-state-physics-inspired LLM compression: a cluster-level negative result at small-language-model scale

Jun-qiang Lu

We report a three-month autonomous research-agent program testing five solid-state-physics-inspired compression mappings on pretrained language models, with predictions committed to git before any pilot data and a 3-sigma gate deciding PASS or SHELVE. The common anchor -- area-law / Kohn-nearsighted decay of the one-particle density matrix -- has a distance face (P001 Wannier, P002 tight-binding) and a rank face (P003 DMRG-truncated MLPs, P005 Wilson-RG, P011 tensor-train embeddings). P005 was pre-empted at Phase 1; three of four Phase-3 pilots were falsified. On the attention face, GPT-2-medium attention-versus-distance is best fit by a stretched exponential in 12 of 16 median-layer heads once probe padding is excluded, and a tight-binding cutoff costs +96% perplexity (P002); on Pythia-160M the Wannier sparsity 0.054 +/- 0.004 is indistinguishable from PCA, random-Haar and identity baselines (P001). On the rank face, per-token tensor-train bond dimension does not track surprisal (r = 0.016 vs a pre-registered 0.65) and the format inflates rather than compresses (P011). P003 is mixed: its scaling claim shelved (r = -0.434), its MPO premise died at stage-0, and its cross-paper…