- **`ChaisemartinDHaultfoeuille.by_path` is now compatible with `trends_linear` (DID^{fd} group-specific linear trends) and `trends_nonparam` (state-set trends).** For `trends_linear`, the first-differencing transform runs once globally before path enumeration, so per-path raw second-differences `DID^{fd}_{path, l}` surface on `path_effects[path]["horizons"][l]` automatically. Per-path **cumulated level effects** `delta_{path, l} = sum_{l'=1..l} DID^{fd}_{path, l'}` (the quantity R returns under `did_multiplegt_dyn(..., by_path, trends_lin)`) surface on the new `results.path_cumulated_event_study[path][l]` field, mirroring the global `linear_trends_effects` cumulation. `to_dataframe(level="by_path")` exposes `cumulated_effect` / `cumulated_se` columns (always present, NaN-when-None — mirrors the `cband_*` convention from PR #374); `summary()` renders a "Cumulated Level Effects (DID^{fd}, trends_linear)" sub-section under each per-path block. SE on the cumulated layer is the conservative upper bound (sum of per-horizon component SEs, NaN-consistent), matching the global `linear_trends_effects` convention. Path enumeration runs on the post-first-differenced `N_mat_fd`: switchers with `F_g==2` fail the window-eligibility check and are dropped from path enumeration entirely (the existing global `F_g >= 3` warning still surfaces the issue), so a path whose switchers all have `F_g < 3` is silently absent from `path_effects` rather than present-with-NaN. Placebo under `trends_linear` returns RAW per-horizon values — there is no per-path placebo cumulation surface in either Python or R. For `trends_nonparam`, the set membership column is validated and stored once globally as `set_ids_arr`; the `set_ids` parameter is now threaded through the four per-path IF helpers (`_compute_path_effects`, `_compute_path_placebos`, `_collect_path_bootstrap_inputs`, `_collect_path_placebo_bootstrap_inputs`) so per-path analytical SE, bootstrap, placebos, and sup-t bands all consume the set-restricted control pool automatically. Per-period effects remain unadjusted under both extensions, consistent with the existing per-period DID contract. Validated against R via two new golden-value scenarios: `single_baseline_multi_path_by_path_trends_lin` (n_periods=13, F_g >= 4, cohort-single-path; per-path cumulated point estimates match R bit-exactly with `POINT_RTOL=1e-9`, cumulated SE within `CUM_SE_RTOL=0.20`) and `multi_path_reversible_by_path_trends_nonparam` (per-path point estimates AND placebos match R bit-exactly with `POINT_RTOL=1e-9`, per-path SE within `SE_RTOL=0.15`). **F_g=3 boundary-case divergence (`by_path + trends_linear`):** `F_g=3` switchers have only 1 valid pre-window Z value after first-differencing, triggering 30%+ relative divergence between Python and R per-path point estimates on paths whose switchers include `F_g=3`. A targeted `UserWarning` fires at fit-time on this regime; R parity is asserted only on the `F_g >= 4` parity fixture. Placebo parity for `trends_linear` is intentionally skipped (R's per-path placebo computation re-runs on the path-restricted subsample with different control eligibility than Python's global-then-disaggregate architecture surfaces; placebo + `trends_linear` is exercised via internal regression only). Cross-path cohort-sharing SE deviation from R documented for `path_effects` is inherited unchanged. Gates at `chaisemartin_dhaultfoeuille.py:1014-1023` removed; `by_path` docstring updated to add the two new compatibility paragraphs and remove `trends_linear` / `trends_nonparam` from the incompatible list. R-parity tests at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPathTrendsLinear` and `::TestDCDHDynRParityByPathTrendsNonparam`; cross-surface regressions at `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathTrendsLinear` and `::TestByPathTrendsNonparam`. See `docs/methodology/REGISTRY.md` §ChaisemartinDHaultfoeuille `Note (Phase 3 by_path ...)` → "Per-path linear-trends DID^{fd}" and "Per-path state-set trends" for the full contract.
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