What was already known
Earlier power-free-value results did not give this general squarefree-density theorem for irreducible quartics; the manuscript supplies the missing large-prime control.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Establishes the expected squarefree-value density across the stated quartic class.
Limitations
The pinned Lean scope note covers a stronger all-degree power-free statement that includes this quartic case. The machine check is reported by OpenAI and was not reproduced here.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean scope note states the positive-density power-free theorem in all degrees at least four, including squarefree quartics.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- Every irreducible integer quartic with no fixed prime-square divisor takes squarefree values with the predicted positive Euler-product density.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision