- **Note (deviation in current covariance-source):** the shipped adapter uses different sources for the pre-period covariance depending on the result type. For `MultiPeriodDiDResults` it extracts the full pre-period sub-block from `results.vcov` when `interaction_indices` is populated, falling back to `diag(ses^2)` otherwise (`pretrends.py:592-601`). For `CallawaySantAnnaResults` and `SunAbrahamResults` it hard-codes `vcov = diag(ses^2)` even when an event-study VCV is available (`pretrends.py:609-652` for CS, `pretrends.py:660-687` for SA). The diagonal fallback drops the pre-period correlations the paper's Propositions rely on; the documented deviation is captured in `docs/methodology/REPORTING.md` as a conservative variance source for staggered adapters. The follow-up audit should decide whether to extend full-sub-VCV extraction to CS/SA (matching the MultiPeriodDiD path) or keep the staggered diag fallback as a deliberate variance-conservatism choice.

| **Proposition 2** | Under Assumption 1 (homoskedastic-equicorrelated Sigma) and monotone trend (delta_pre < 0, delta_post > 0): E[beta_hat_post | beta_hat_pre in B_NIS] > beta_post > tau_post | Justifies a WARN that conditional bias is worse than unconditional bias under monotone trends — applicable in many but not all empirical settings. Assumption 1 in the paper is a condition on the *model* covariance Σ (the population variance-covariance of β̂ in Equation 1), not on design metadata. Software can only inspect the *estimated* Σ̂, so any direct numerical check (e.g., approximately-constant diagonal entries + approximately-constant positive off-diagonal entries below the diagonal) is a heuristic implementation aid, not the paper's assumption itself. A library that surfaces a sharper warning based on Σ̂ should label it as a heuristic; without such a check, the library should issue only the generic caveat that the sign-of-bias result is ambiguous outside Assumption 1. |