What was already known
Uniqueness was known for smoother scalar conductivities in dimensions at least three and for bounded measurable scalar conductivities in the plane. Rough anisotropic examples did not give this three-dimensional scalar result.
AI involvement
OpenAI is credited as author of the model-produced construction. The release identifies no named human checker or explanation of its nested-block mechanism.
The manuscript is institutionally credited to OpenAI and included among model-produced research artifacts.
Importance
The counterexample marks a sharp change in the three-dimensional Calderón uniqueness picture at bounded measurable regularity.
Limitations
The Lean target covers the three-dimensional full weak boundary operator. No named human review of its trace-space interpretation was identified; higher dimensions are not claimed.
Technical verification
The release reports a Lean proof OAI.ScalarConductivity.main_nonuniqueness; the target statement includes uniform positivity, boundary collar, positive-measure difference, unique weak solutions and the same full boundary operator on the trace quotient.
Formal checking
OAI.ScalarConductivity.main_nonuniqueness in OAI/Analysis/Conductivity/Main.lean against ComparatorChallenges/Conductivity.lean
- Checker
- Lean 4 development in the OpenAI release
- Scope
- Two distinct positive bounded measurable scalar conductivities on the three-dimensional ball have the same full weak Dirichlet-to-Neumann operator
- 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 model's source-annihilation and nested-block mechanism was documented; Few is the evidence default.
Correction and publication history
If correct, the counterexample marks a sharp change in the three-dimensional Calderón uniqueness picture at bounded measurable regularity.
Read this published revision