# Weakly mixing polygonal billiards — reading guide

Jon Chaika and Giovanni Forni. Native review source: arXiv 2003.00890v2,
14 August 2025 (43 pages). A separate user-supplied journal PDF is preserved:
Annals of Mathematics 203 (2026), 695–735 (41 pages).

Read the introduction's three different conclusions and quantifiers first.
Section 2 defines horocycle sections, Hodge norms and distances to integral
cohomology. Sections 3–4 develop vector growth, recurrence and curve estimates;
Section 5 supplies a controlled-growth input. Section 6 applies Veech's criterion
to a fixed nonzero frequency, and Section 7 deduces the billiard conclusion.

[Journal PDF](journal.pdf) · [arXiv v2 PDF](arxiv-v2.pdf) ·
[Expanded native source](manuscript-expanded.tex) ·
[Interactive argument map](argument.roadmap.html) ·
[Edition record](source-editions.json).

The structural inventory has 51 claim-like elements and 35 bibliography entries.
The displayed source labels are authoritative; the map is a reading aid and its
dependency audit is partial. External results must be dated against the journal
received date, 12 March 2020. Later developments remain separate context.

Independent notes:

- Exact hypotheses and quantifiers:
- Required imported results:
- Norm, integral-lattice and invariant-bundle comparisons:
- Recurrence and parameter-dependent times:
- Remaining obligations: