Refitting DF-THC Weights on a Fixed Angle Table: the Problem, a Deterministic Method, and Open Questions

Many public chemistry gains in the Verifiable Quantum Circuit Compilation competition (Google Quantum AI, Kaggle) are weights-only refits: the QROM angle loaders stay fixed, so qubits and Toffolis are fixed, and new DF-THC weights lower λeff within the two accuracy limits and the Egap floor. This note states the problem exactly from the official verifier, describes a deterministic method (a constrained projected refit alternated with an exact Jacobi column gauge), explains three details that decide whether a refit moves on published weights (deliberate tiny weights, kinks from near-zero eigenvalues of h1′, and consistent targets), reports a reproduction test against public refits, and lists open questions. It is a local method on a non-convex problem; no optimality claim is made. The tool is the Apache-2.0 Kaggle utility script dfthc_refit. Thanks to the competitors whose public notebooks and Apache-2.0 circuits made this work possible. AI-assistance statement: code, analysis and the first draft of the text were produced with Claude, an AI model (Anthropic), under the author's direction; the author reviewed and approved the content.