Are the two live twin-prime bets two halves of one statement?
no run lists this probe in builds_on:
Status: open · laid 2026-09-14 · type: structural · relation: undetermined to CASE-07, P-005
Statement. Helfgott–Radziwiłł gives expansion at every scale; MRT uniformity at every scale would forbid the exceptional scales. So the two live bets may be one statement seen twice.
The argument (from the chat). c(y) is Lipschitz in log y with constant ≈ 2, so the only thing compatible with every window average is small and c(y) ↛ 0 is a sparse set of exceptional scales of log-width ≍ 1, where λ(n+1) ≈ λ(n) across a whole dyadic range. At such a scale λ has locally constant runs — a large short-interval Fourier coefficient, i.e. a failure of MRT uniformity at that scale.
The open question. Whether that implication can be made rigorous. Tao–Teräväinen's derivation of Chowla from uniformity still lands on the log-average.
Cross-reference, relation undetermined. Two obstructions turning out to be one statement is the same shape as CASE-07 and P-005. Whether it is the same mechanism is what the work would settle, not a call to make at filing. Source: notes/DIGEST-twin-prime-chat.md §2.
33 source lines, no addenda.