Two thirds of the low-lying zeros of Dirichlet L-functions, on average

Preprint (Version 2.1-draft, 17 August 2026). We outline a proof that for every sufficiently large prime q, at least 2/3 − O(1/log log q) of the low-lying zeros of the Dirichlet L-functions L(s, χ), averaged over the q−2 non-principal characters mod q, are simple and lie on the critical line, unconditionally, in the window T ≍ (log q)^(2+ε). This extends the family direction sketched in Remark 7.2(iii) of the August 10 version of the source manuscript (published as Alpöge–Furman, arXiv:2608.13637, whose Theorem B is the fixed-character t-aspect statement; the family-averaged polylog-window regime treated here is disjoint from it). Produced with extensive AI assistance (Anthropic's Claude) under the direction of the author, with full transparency about the division of labor; see the manuscript's methodology section. 70 supporting lemmas are machine-checked in Lean 4. Internally reviewed through adversarial rounds documented in the deposited repository snapshot; not externally refereed. Files: the manuscript PDF (Version 2.1-draft), the 16-page review package built for expert attack, and a full repository snapshot (git commit 8d38bb2) containing the LaTeX sources, the Lean 4 development, the numerical experiments, and the complete audit trail.