What was already known
The human main theorem already gave a positive-probability nonaligned trajectory under a measurable Clarke selection. It did not establish the appendix's selection independence or robustness across the stated dynamics.
AI involvement
Memana credits GPT-5.6 Sol conversations and a model draft for the strengthened appendix; Memana developed the main text and reviewed and edited the appendix.
The strengthened appendix theorems and draft are expressly credited to GPT-5.6 Sol conversations; the original main counterexample was human work.
- Supporting source (arxiv.org) — AI disclosure; §1 Theorem 1.5; Appendix A, Theorems A.1–A.4 and scope remark
Importance
Shows the nonalignment example persists under several precisely stated training dynamics.
Limitations
The human main theorem already supplied a positive-probability nonaligned trajectory. The smooth case needs an exact dead half-line, and the discrete case is fixed-step full-batch descent. A completed check of the appendix proofs is not documented.
Technical verification
The appendix provides proofs and the author reviewed and edited them, but a completed rigorous check of these strengthened results is not explicitly documented.
Human understanding
The author explains the gate-sliding, dead-neuron and Fourier-energy mechanisms in the adjoining human main argument and edited appendix.
Correction and publication history
Shows the nonalignment example persists under several precisely stated training dynamics.
Read this published revision