What was already known
The Matiyasevich–Robinson–Davis–Putnam theorem gave Diophantine representations without uniqueness. The single-fold conjecture asked for exactly one complete witness; earlier work had reduced it to single-fold binary exponentiation.
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
Resolves the single-fold conjecture and therefore the finite-fold conjecture for recursively enumerable sets.
Limitations
The selected result counts every auxiliary variable in the witness. The separate undecidability consequence under an at-most-one-solution promise is outside the pinned Lean statement.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note covers the full unique-witness representation for every recursively enumerable subset of natural-number tuples.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- Every recursively enumerable subset of natural-number n-tuples, for n≥1, has an integer-polynomial Diophantine representation with exactly one complete natural-number auxiliary tuple for each member and none for nonmembers.
- 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