What was already known
Talagrand posed this original-density covering statement. Park and Pham proved a related positive-selector conclusion, not this arbitrary-family formulation.
AI involvement
OpenAI authors the manuscript and credits an internal model with its mathematical results; the degree of human guidance for this theorem is not specified.
OpenAI authorship and the cited repository’s model-production account support model-led mathematics, but not a documented independent session.
Importance
The stated theorem resolves Talagrand’s original-density discrete-convexity question.
Limitations
The cited Lean theorem matches the stated constant and exceptional family; no completed human proof review is documented.
Technical verification
The cited Lean theorem states the finite-family original-density result with k=2^75 and the same p-small exceptional family as the manuscript. This is a source-reported machine proof.
Formal checking
Lean proof of talagrand_discrete_convexity
- Checker
- Lean 4 kernel, as represented by the OpenAI proof artifact
- Scope
- Talagrand original-density discrete-convexity theorem with k=2^75 for arbitrary finite families
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation of the central coupling and density-reduction mechanism is documented. Few is the evidence default, not a claim that people cannot understand it.
Correction and publication history
The stated theorem resolves Talagrand’s original-density discrete-convexity question.
Read this published revision