v1.9 — the Li–Sekatskii lens note

Adds papers/li_lens_law.md, a short note on the Li–Sekatskii coefficients — the one-parameter family of Li coefficients obtained by shifting the Möbius map. The construction is Sekatskii's and the note names it in a prior-art table; what it adds is that the shift behaves as a lens with an exact optimal width. For a hypothetical zero at ρ = 1/2 + β + iT the detection rate is maximal at d = |ρ − 1/2|, where it equals artanh(β/|ρ − 1/2|), so matching the lens to the zero improves the detection index by a factor T; a previously measured empirical 30.9× improvement for a planted zero at height 30 turns out to be that T. The accompanying code/verify_li_lens.py runs eleven checks and verifies the proof of the optimum line by line.

The note also records a truncation artifact that manufactures a false detection, at the rate (1 + 1/|a|) which is Sekatskii's own exponential term, and asks the same optimisation question of the truncated Weil form, where the answer is the opposite: the support length has no interior optimum, being bounded by a Paley–Wiener price rather than a matching condition. It states how far its own prior-art search went and which sources it did not consult.