What was already known
Earlier work covered a disjoint-indicator model or sufficiency under finite fourth moments and identical distributions. The human authors first proved the full qualitative characterization by a different compactness argument.
AI involvement
LLMs generated the quantitative combinatorial strategy after guidance and access to the authors’ original proof. Abdalla, de Dios Pont, Ramos and Taylor rewrote it and reviewed the formal statements.
The source identifies a model-generated quantitative combinatorial strategy but says it depended on the authors' prior proof and substantial guidance.
Importance
The alternative proof gives explicit stability bounds without those earlier distribution and moment restrictions.
Limitations
The Lean verification is reported for the quantitative Theorem 6.1 under its indexed hypotheses. It does not transfer AI credit to the authors’ earlier qualitative proof.
Technical verification
The authors report Lean 4 verification of the quantitative statement in Theorem 6.1 and identify showcase.lean as its direct translation. The machine check is source-reported; independent checking of statements is not counted as human proof checking.
Formal checking
Lean kernel checking of showcase.lean and the QuantitativePR proof
- Checker
- Lean 4 using the authors' RandomVarSPR formalization
- Scope
- Theorem 6.1 quantitative real L2 stable-phase-retrieval bound under independent, centred, normalized variables and indexed L1 bounds
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the head–tail decomposition, concentrated and diffuse branches, and anticoncentration mechanism, with a separate human compactness proof of the same theorem.
Correction and publication history
The alternative proof gives explicit stability bounds without those earlier distribution and moment restrictions.
Read this published revision