A sign audit of a Hessian term absent from the standard MOND equation: action-consistent virial work and conditional Jeans tests in three ultra-faint dwarfs

This note recasts the UDCT v7.01–v7.06 calculations as a verification paper. Standard MOND-family field theories (AQUAL, QUMOND) employ a positive interpolating function μ or ν. Their weak-field equations do not contain the extra Hessian-sourced tensor Pij tested in this UDCT candidate. The object under audit is therefore not standard AQUAL or QUMOND. Where the density-weighted virial integral is negative, that sign is not produced by a negative interpolating function. It is produced because the action-derived Hessian contribution exceeds the positive leading term. A previously preregistered ultra-faint-dwarf velocity proxy (O8d / D8b) matched 0/22 objects within a factor of two; that historical gate is not reopened. This file is a wording revision of the 29 September 2026 verification draft; no new calculations were performed. Simulations, code and drafting in this series were carried out with substantial assistance from large language models (Anthropic Claude; OpenAI ChatGPT; Google Gemini; xAI Grok) under the author's direction. The author defined the research questions and released code for independent reproduction. The historical O8d/D8b result remains a prior registered gate (0/22). This v7.06 note is a post-outcome wording revision and does not reopen that gate.