Singular Bernoulli convolutions at non-Pisot parameters

Lineage and corrections

Erdos, On a family of symmetric Bernoulli convolutions (1939) evidence for this event

This event attributed to Unreleased internal OpenAI model

Baker, Koivusalo, Troscheit, Zhang (2026), records the question open evidence for this event

VibeMathed record: Singular Bernoulli convolutions at non-Pisot parameters evidence for this event

Two non-Pisot singularity theorems. If $\beta\in(1,2)$ is a Salem number of degree four then $\nu_{1/\beta}$ is singular; explicit cases are the real roots of $x^4-x^3-x^2-x+1$ and $x^4-2x^3+x^2-2x+1$. An explicit degree-31 polynomial has a unique real root $\beta\in(1.8392,1.8393)$, not Pisot, with $\nu_{1/\beta}$ singular. The manuscript also proves a criterion: $\nu_\lambda$ is singular iff $\lambda$ lies in an explicit limsup set of one-sided approximations by finite sets of algebraic units; the paper says this is an infinite approximation condition, not a finite membership test, so it is not an effective classification. It does not decide Salem numbers of degree six or more, nor which non-Pisot parameters are singular in general. parent of this event

Singular Bernoulli convolutions at non-Pisot parameters parent of this event

Singular Bernoulli convolutions at non-Pisot parameters evidence for this event