The last few solves you'll ever pay for: certified accelerator + identification layer over any black-box parametric solver, built on resona's effective-rank dial.

Reproducible LoRA useful-rank diagnostics from activation-whitened early-gradient spectra, with theory, controlled simulations, GPT-2/WikiText-2 validation, and Zenodo data artifacts.

Null result on entropy collapse; reproducible figures; Course Correct Labs

Effective rank, RankMe, E1, CKA and anisotropy on transformer hidden states are determined by one direction. The exact identity, and the attention sink behind it.

Do we really need quantum computing? A runnable essay: one matrix-free dial — the effective rank Φ₁ — flags which quantum speedups survive a classical attack, and which were never quantum at all.

What does one answer actually cost? 35 nonlinear PDEs, a 7-solve Chebyshev kernel at machine precision, Cramér–Rao-optimal inversion, and a field map from one noisy snapshot — with the blind zones measured.

Code + derived-data companion for three RMT preprints: effective-rank collapse (Firma B note), a random-matrix account of structure formation in neural networks (main paper), and the plate-network unification note.