What was already known
The law was known for ordinary integers. Ford, Konyagin and Luca conjectured it for p−1; unconditional shifted-prime correlations covered only restricted mass, while the full law required stronger distribution assumptions.
AI involvement
OpenAI credits its internal model with the manuscript. No named human is documented as checking or explaining this proof.
OpenAI is the credited author and explicitly calls the repository's manuscripts internal-model products.
Importance
The unconditional full joint law resolves the Ford–Konyagin–Luca conjecture.
Limitations
No completed check of the marked Type II estimates or the full passage to the joint law is documented. Companion smooth-predecessor bounds do not establish this law.
Technical verification
The source states and proves a broad asymptotic claim, but the release provides no documented completed human or machine check of the marked Type II input and full extraction. The Lean formalization catalogue does not list this result.
Human understanding
No identified human explanation of the marked-correlation and size-biased extraction mechanism was located; Few reflects missing documentation.
Correction and publication history
If correct, the unconditional full joint law resolves the Ford–Konyagin–Luca conjecture.
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