diff --git a/CHANGELOG.md b/CHANGELOG.md
index 2c413ba8..990e8759 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ## [Unreleased]
 
 ### Added
+- **`ChaisemartinDHaultfoeuille.by_path` and `paths_of_interest` now compose with `heterogeneity="<col>"`** (Web Appendix Section 1.5, Lemma 7). Per-path heterogeneity coefficient is computed by re-running the Lemma 7 regression on each path-restricted switcher subsample. The path filter (`path_groups: Optional[Set[int]]`) restricts eligibility to switchers ON path `p` inside the inner regression; the variance machinery (standard WLS vcov for non-survey, cell-period IF allocator for Binder TSL, group-level allocator for Rao-Wu replicate) is unchanged from the global heterogeneity path. Cohort dummies in the design matrix absorb baseline by construction, so multi-baseline switcher panels do not produce R-divergence (no parallel `UserWarning` like `controls` / `trends_linear`). Surfaces on `results.path_heterogeneity_effects` keyed `{path: {l: {beta, se, t_stat, p_value, conf_int, n_obs}}}` and on `results.to_dataframe(level="by_path")` via new always-present `het_*` columns (`het_beta`, `het_se`, `het_t_stat`, `het_p_value`, `het_conf_int_lower`, `het_conf_int_upper`), populated for positive-horizon rows when `heterogeneity` is set and NaN otherwise (mirrors the `cband_*` and `cumulated_*` always-present convention). Composes with `survey_design` (analytical Binder TSL + replicate-weight bootstrap) via the existing PR #408 IF allocator path; under replicate weights, every per-(path, horizon) fit appends `n_valid` to the shared `_replicate_n_valid_list` accumulator and the final `_effective_df_survey` recomputation reflects all per-path appends. R parity verified against `did_multiplegt_dyn(..., by_path=3, predict_het=list("het_x", c(1,2,3)))` on the new `multi_path_reversible_by_path_predict_het` golden-value scenario; a sibling global anchor `multi_path_reversible_predict_het` introduces the FIRST `predict_het` R-parity baseline in the repo (no prior `TestDCDHDynRParityHeterogeneity` existed). Both R calls use `dont_drop_larger_lower=TRUE` to match the Python `drop_larger_lower=False` requirement and to provide cohort variation at every horizon under reversal paths. Per-path SE matches global SE bit-exactly on a single-path panel (telescope invariant, `atol=rtol=1e-14`). Multiplier bootstrap (`n_bootstrap > 0`) under `by_path + heterogeneity + survey_design` inherits the existing per-path multiplier-bootstrap-survey gate from PR #408. The `NotImplementedError` gate at `chaisemartin_dhaultfoeuille.py:1230-1234` is removed; `heterogeneity` precondition mutex with `controls` / `trends_linear` / `trends_nonparam` stays in place. Cross-surface invariants regression-tested at `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathHeterogeneity` (~13 tests across gate dispatch, behavior, single-path telescope, zero-signal anti-regression, multi-baseline UserWarning anti-regression, DataFrame integration, edge cases) + `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityHeterogeneity` (global anchor) + `::TestDCDHDynRParityByPathHeterogeneity` (per-path). See `docs/methodology/REGISTRY.md` §`ChaisemartinDHaultfoeuille` `Note (Phase 3 by_path ...)` → "Per-path heterogeneity testing" for the full contract.
 - **Tutorial 21: HAD Pre-test Workflow** (`docs/tutorials/21_had_pretest_workflow.ipynb`) — composite pre-test walkthrough for `HeterogeneousAdoptionDiD` building on Tutorial 20's brand-campaign framing. Uses a 60-DMA × 8-week panel close in shape to T20's but with the dose distribution drawn from `Uniform[$0.01K, $50K]` (vs T20's `[$5K, $50K]`); the true support is strictly positive but very near zero, chosen so the QUG step in `did_had_pretest_workflow` fails-to-reject `H0: d_lower = 0` in this finite sample and the verdict text fires the load-bearing "Assumption 7 deferred" pivot for the upgrade-arc narrative. (HAD's `design="auto"` selector — a separate min/median heuristic at `had.py::_detect_design`, NOT the QUG p-value — independently lands on the `continuous_at_zero` identification path with target `WAS` on this panel because `d.min() < 0.01 * median(|d|)`. The QUG test and the design selector are independent rules that point to the same identification path here.) Walks through three surfaces: (a) `did_had_pretest_workflow(aggregate="overall")` on a two-period collapse, where the verdict explicitly flags Step 2 (Assumption 7 pre-trends) as not run because a single pre-period structurally cannot support a pre-trends test, and the structural fields `pretrends_joint` / `homogeneity_joint` are both `None`; (b) `did_had_pretest_workflow(aggregate="event_study")` on the full multi-period panel, where the verdict reads "TWFE admissible under Section 4 assumptions" because all three testable diagnostics (QUG + joint pre-trends Stute over 3 horizons + joint homogeneity Stute over 4 horizons) fail-to-reject — non-rejection evidence under finite-sample power and test specification, not proof that the identifying assumptions hold; and (c) a side panel exercising both `yatchew_hr_test` null modes — `null="linearity"` (default, paper Theorem 7) vs `null="mean_independence"` (Phase 4 R-parity with R `YatchewTest::yatchew_test(order=0)`) — on the within-pre-period first-difference paired with post-period dose, illustrating the stricter null's larger residual variance (`sigma2_lin` 7.01 vs 6.53) and smaller p-value (0.29 vs 0.49). Companion drift-test file `tests/test_t21_had_pretest_workflow_drift.py` (16 tests pinning panel composition, both verdict pivots, structural anchors on both paths, deterministic QUG / Yatchew statistics, bootstrap p-value tolerance bands per `feedback_bootstrap_drift_tests_need_backend_tolerance`, and `HAD(design="auto")` resolution to `continuous_at_zero` on this panel). T20's "Composite pretest workflow" Extensions bullet updated with a forward-pointer to T21. T22 weighted/survey HAD tutorial remains queued as a separate notebook PR.
 - **`ChaisemartinDHaultfoeuille.by_path` and `paths_of_interest` now compose with `survey_design`** for analytical Binder TSL SE and replicate-weight bootstrap variance. The `NotImplementedError` gate at `chaisemartin_dhaultfoeuille.py:1233-1239` is replaced by a per-path multiplier-bootstrap-only gate (`survey_design + n_bootstrap > 0` under by_path / paths_of_interest still raises, since the survey-aware perturbation pivot for path-restricted IFs is methodologically underived). Per-path SE routes through the existing `_survey_se_from_group_if` cell-period allocator: the per-period IF (`U_pp_l_path`) is built with non-path switcher-side contributions skipped (control contributions are unchanged, matching the joiners/leavers IF convention; preserves the row-sum identity `U_pp.sum(axis=1) == U`), cohort-recentered via `_cohort_recenter_per_period`, then expanded to observations as `psi_i = U_pp[g_i, t_i] · (w_i / W_{g_i, t_i})`. Replicate-weight designs unconditionally use the cell allocator (Class A contract from PR #323). New `_refresh_path_inference` helper post-call refreshes `safe_inference` on every populated entry across `multi_horizon_inference`, `placebo_horizon_inference`, `path_effects`, and `path_placebos` so all four surfaces use the same final `df_survey` after per-path replicate fits append `n_valid` to the shared accumulator. Path-enumeration ranking under `survey_design` remains unweighted (group-cardinality, not population-weight mass). Lonely-PSU policy stays sample-wide, not per-path. Telescope invariant: on a single-path panel, per-path SE matches the global non-by_path survey SE bit-exactly. **No R parity** — R `did_multiplegt_dyn` does not support survey weighting; this is a Python-only methodology extension. The global non-by_path TSL multiplier-bootstrap path is unaffected (anti-regression test `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathSurveyDesignAnalytical::test_global_survey_plus_n_bootstrap_still_works` locks the per-path-only scope of the new gate). Cross-surface invariants regression-tested at `TestByPathSurveyDesignAnalytical` (~17 tests across gate / dispatch / analytical SE / replicate-weight SE / per-path placebos / `trends_linear` composition / unobserved-path warnings / final-df refresh regressions) and `TestByPathSurveyDesignTelescope`. See `docs/methodology/REGISTRY.md` §`ChaisemartinDHaultfoeuille` `Note (Phase 3 by_path ...)` → "Per-path survey-design SE" for the full contract.
 - **Inference-field aliases on staggered result classes** for adapter / external-consumer compatibility. Read-only `@property` aliases expose the flat `att` / `se` / `conf_int` / `p_value` / `t_stat` names (matching `DiDResults` / `TROPResults` / `SyntheticDiDResults` / `HeterogeneousAdoptionDiDResults`) on every result class that previously only carried prefixed canonical fields: `CallawaySantAnnaResults`, `StackedDiDResults`, `EfficientDiDResults`, `ChaisemartinDHaultfoeuilleResults`, `StaggeredTripleDiffResults`, `WooldridgeDiDResults`, `SunAbrahamResults`, `ImputationDiDResults`, `TwoStageDiDResults` (mapping to `overall_*`); `ContinuousDiDResults` (mapping to `overall_att_*`, ATT-side as the headline, ACRT-side accessible unchanged via `overall_acrt_*`); `MultiPeriodDiDResults` (mapping to `avg_*`). `ContinuousDiDResults` additionally exposes `overall_se` / `overall_conf_int` / `overall_p_value` / `overall_t_stat` aliases for naming consistency with the rest of the staggered family. Aliases are pure read-throughs over the canonical fields — no recomputation, no behavior change — so the `safe_inference()` joint-NaN contract (per CLAUDE.md "Inference computation") is inherited automatically (NaN canonical → NaN alias, locked at `tests/test_result_aliases.py::test_pattern_b_aliases_propagate_nan`). The native `overall_*` / `overall_att_*` / `avg_*` fields remain canonical for documentation and computation. Motivated by the `balance.interop.diff_diff.as_balance_diagnostic()` adapter (`facebookresearch/balance` PR #465) which calls `getattr(res, "se", None)` / `getattr(res, "conf_int", None)` without a fallback chain — pre-alias, every staggered result class returned `None` on those keys, silently dropping `se` and `conf_int` from the adapter's diagnostic dict. 23 alias-mechanic + balance-adapter regression tests at `tests/test_result_aliases.py`. Patch-level (additive on stable surfaces).
diff --git a/benchmarks/R/generate_dcdh_dynr_test_values.R b/benchmarks/R/generate_dcdh_dynr_test_values.R
index e6119720..a5caa5ee 100644
--- a/benchmarks/R/generate_dcdh_dynr_test_values.R
+++ b/benchmarks/R/generate_dcdh_dynr_test_values.R
@@ -618,6 +618,61 @@ extract_dcdh_by_path <- function(res, n_effects, n_placebos = 0) {
   list(by_path = out)
 }
 
+# Helper: extract global predict_het results. R's predict_het slot is at
+# res$results$predict_het, a data.frame with columns
+# {effect, covariate, Estimate, SE, t, LB, UB, N, pF}. Estimate is the
+# WLS coefficient on the heterogeneity covariate.
+extract_dcdh_predict_het <- function(res, n_effects) {
+  ph <- res$results$predict_het
+  horizons <- list()
+  if (is.null(ph) || nrow(ph) == 0) return(list(predict_het = horizons))
+  for (h in seq_len(min(n_effects, nrow(ph)))) {
+    horizons[[as.character(ph$effect[h])]] <- list(
+      beta = as.numeric(ph$Estimate[h]),
+      se = as.numeric(ph$SE[h]),
+      t = as.numeric(ph$t[h]),
+      ci_lo = as.numeric(ph$LB[h]),
+      ci_hi = as.numeric(ph$UB[h]),
+      n_obs = as.numeric(ph$N[h]),
+      p_value = as.numeric(ph$pF[h])
+    )
+  }
+  list(predict_het = horizons)
+}
+
+# Helper: extract per-path predict_het results. Under by_path=k +
+# predict_het, R's per-by_level dispatcher writes a predict_het table to
+# each res$by_level_i$results$predict_het. Output mirrors
+# extract_dcdh_by_path's shape with a horizons dict keyed by horizon.
+extract_dcdh_by_path_predict_het <- function(res, n_effects) {
+  by_levels <- res$by_levels
+  out <- list()
+  for (i in seq_along(by_levels)) {
+    slot <- res[[paste0("by_level_", i)]]
+    ph <- slot$results$predict_het
+    horizons <- list()
+    if (!is.null(ph) && nrow(ph) > 0) {
+      for (h in seq_len(min(n_effects, nrow(ph)))) {
+        horizons[[as.character(ph$effect[h])]] <- list(
+          beta = as.numeric(ph$Estimate[h]),
+          se = as.numeric(ph$SE[h]),
+          t = as.numeric(ph$t[h]),
+          ci_lo = as.numeric(ph$LB[h]),
+          ci_hi = as.numeric(ph$UB[h]),
+          n_obs = as.numeric(ph$N[h]),
+          p_value = as.numeric(ph$pF[h])
+        )
+      }
+    }
+    out[[i]] <- list(
+      path = by_levels[i],
+      frequency_rank = i,
+      horizons = horizons
+    )
+  }
+  list(by_path_predict_het = out)
+}
+
 # Scenario 13: mixed_single_switch + by_path=2 (basic 2-path case).
 # The mixed_single_switch DGP produces joiners (path 0,1,1,1) and
 # leavers (path 1,0,0,0) as its only two observed paths at L_max=3, so
@@ -1018,6 +1073,136 @@ cat("  Scenario 19: multi_path_reversible_by_path_non_binary\n")
   )
 }
 
+# Scenarios 20 + 21: predict_het R-parity (Wave 5 #11). Scenario 20 is
+# the global anchor (predict_het without by_path); scenario 21 is the
+# per-path version (by_path + predict_het). Both use the same DGP so the
+# Python-side parity tests can calibrate atol on the global scenario and
+# inherit the same atol for the per-path test. R's predict_het syntax
+# requires a 2-element list: list(covariate_name, horizons_vec).
+#
+# DGP shape: 90 switchers + 30 never-treated controls, 10 periods, 3
+# paths (0,1,1,1) / (0,1,0,0) / (0,1,1,0), F_g varies in {3,4,5}
+# INDEPENDENTLY of path so each path has multiple cohorts. het_x is
+# binary {0,1}, balanced across both switchers and controls. Effect =
+# 5.0 + 3.0 * het_x to produce a detectable heterogeneity signal.
+# Never-treated controls are required for R's predict_het to compute
+# horizons l>=2 under reversal paths (otherwise R returns
+# "max effects = 2" or empty cohort dummies). `dont_drop_larger_lower
+# = TRUE` matches the Python by_path requirement that
+# `drop_larger_lower=False`.
+cat("  Scenarios 20/21: multi_path_reversible_predict_het + by_path version\n")
+{
+  set.seed(120L)
+  n_switchers20 <- 90L
+  n_controls20 <- 30L
+  n_groups20 <- n_switchers20 + n_controls20
+  n_periods20 <- 10L
+  paths20 <- list(c(0L, 1L, 1L, 1L), c(0L, 1L, 0L, 0L), c(0L, 1L, 1L, 0L))
+  D20 <- matrix(0L, nrow = n_groups20, ncol = n_periods20)
+  het_x20 <- integer(n_groups20)
+  group_fe20 <- rnorm(n_groups20, 0, 2.0)
+  # Switchers (groups 1..n_switchers20)
+  for (g in seq_len(n_switchers20)) {
+    F_g_choice <- ((g - 1L) %/% 3L) %% 3L
+    F_g <- 3L + F_g_choice
+    path_idx <- ((g - 1L) %% 3L) + 1L
+    pp <- paths20[[path_idx]]
+    het_x20[g] <- if (g <= n_switchers20 %/% 2L) 1L else 0L
+    for (j in seq_along(pp)) {
+      t <- F_g - 1L + j
+      if (t >= 1L && t <= n_periods20) D20[g, t] <- pp[j]
+    }
+    if (F_g - 1L + length(pp) <= n_periods20) {
+      tail_t <- (F_g - 1L + length(pp)):n_periods20
+      D20[g, tail_t] <- pp[length(pp)]
+    }
+  }
+  # Never-treated controls (groups n_switchers20+1..n_groups20).
+  # Balanced het_x assignment so the heterogeneity covariate has
+  # variation in the control pool too.
+  for (g in (n_switchers20 + 1L):n_groups20) {
+    k <- g - n_switchers20
+    het_x20[g] <- if (k <= n_controls20 %/% 2L) 1L else 0L
+  }
+  noise20 <- matrix(rnorm(n_groups20 * n_periods20, 0, 0.5),
+                    nrow = n_groups20, ncol = n_periods20)
+  period_arr20 <- 0:(n_periods20 - 1L)
+  effect20 <- 5.0 + 3.0 * het_x20  # heterogeneity signal
+  Y20 <- matrix(group_fe20, nrow = n_groups20, ncol = n_periods20) +
+    matrix(0.5 * period_arr20, nrow = n_groups20, ncol = n_periods20, byrow = TRUE) +
+    matrix(effect20, nrow = n_groups20, ncol = n_periods20) * D20 +
+    noise20
+  d20 <- data.frame(
+    group = rep(seq_len(n_groups20) - 1L, each = n_periods20),
+    period = rep(period_arr20, n_groups20),
+    treatment = as.vector(t(D20)),
+    outcome = as.vector(t(Y20)),
+    het_x = rep(het_x20, each = n_periods20)
+  )
+
+  # Scenario 20: global predict_het anchor (no by_path).
+  # `dont_drop_larger_lower = TRUE` preserves multi-switch cohorts so the
+  # heterogeneity regression has cohort variation at every horizon.
+  # Without this, R drops off-switch paths at l>=2, leaving a single
+  # cohort and triggering the `prod_het_l_XX ~ het_x + ` empty-cohort
+  # error. dCDH `by_path` requires `drop_larger_lower=False` on the Python
+  # side anyway, so this flag is consistent with the per-path scope.
+  res20 <- did_multiplegt_dyn(
+    df = d20, outcome = "outcome", group = "group", time = "period",
+    treatment = "treatment", effects = 3,
+    dont_drop_larger_lower = TRUE,
+    predict_het = list("het_x", c(1, 2, 3)),
+    ci_level = 95, graph_off = TRUE
+  )
+  scenarios$multi_path_reversible_predict_het <- list(
+    data = list(
+      group = as.numeric(d20$group),
+      period = as.numeric(d20$period),
+      treatment = as.numeric(d20$treatment),
+      outcome = as.numeric(d20$outcome),
+      het_x = as.numeric(d20$het_x)
+    ),
+    params = list(pattern = "multi_path_reversible_predict_het",
+                  n_switchers = n_switchers20, n_controls = n_controls20,
+                  n_groups = n_groups20, n_periods = n_periods20,
+                  seed = 120L, effects = 3,
+                  predict_het_var = "het_x",
+                  predict_het_horizons = c(1, 2, 3),
+                  ci_level = 95,
+                  dont_drop_larger_lower = TRUE),
+    results = extract_dcdh_predict_het(res20, n_effects = 3)
+  )
+
+  # Scenario 21: by_path + predict_het (per-path version on same DGP).
+  # `dont_drop_larger_lower = TRUE` matches scenario 20 + Python
+  # by_path's `drop_larger_lower=False` requirement.
+  res21 <- did_multiplegt_dyn(
+    df = d20, outcome = "outcome", group = "group", time = "period",
+    treatment = "treatment", effects = 3, by_path = 3,
+    dont_drop_larger_lower = TRUE,
+    predict_het = list("het_x", c(1, 2, 3)),
+    ci_level = 95, graph_off = TRUE
+  )
+  scenarios$multi_path_reversible_by_path_predict_het <- list(
+    data = list(
+      group = as.numeric(d20$group),
+      period = as.numeric(d20$period),
+      treatment = as.numeric(d20$treatment),
+      outcome = as.numeric(d20$outcome),
+      het_x = as.numeric(d20$het_x)
+    ),
+    params = list(pattern = "multi_path_reversible_by_path_predict_het",
+                  n_switchers = n_switchers20, n_controls = n_controls20,
+                  n_groups = n_groups20, n_periods = n_periods20,
+                  seed = 120L, effects = 3, by_path = 3,
+                  predict_het_var = "het_x",
+                  predict_het_horizons = c(1, 2, 3),
+                  ci_level = 95,
+                  dont_drop_larger_lower = TRUE),
+    results = extract_dcdh_by_path_predict_het(res21, n_effects = 3)
+  )
+}
+
 # ---------------------------------------------------------------------------
 # Write output
 # ---------------------------------------------------------------------------
diff --git a/benchmarks/data/dcdh_dynr_golden_values.json b/benchmarks/data/dcdh_dynr_golden_values.json
index 38b6a847..fe4e6f44 100644
--- a/benchmarks/data/dcdh_dynr_golden_values.json
+++ b/benchmarks/data/dcdh_dynr_golden_values.json
@@ -1437,6 +1437,185 @@
           }
         ]
       }
+    },
+    "multi_path_reversible_predict_het": {
+      "data": {
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+                "ci_hi": 3.3854261657,
+                "n_obs": 30,
+                "p_value": 8.1857621596e-11
+              }
+            }
+          }
+        ]
+      }
     }
   },
   "generator": "generate_reversible_did_data v1",
diff --git a/diff_diff/chaisemartin_dhaultfoeuille.py b/diff_diff/chaisemartin_dhaultfoeuille.py
index 55bfb883..463f5b86 100644
--- a/diff_diff/chaisemartin_dhaultfoeuille.py
+++ b/diff_diff/chaisemartin_dhaultfoeuille.py
@@ -26,7 +26,7 @@
 """
 
 import warnings
-from typing import Any, Dict, List, Optional, Sequence, Tuple
+from typing import Any, Dict, List, Optional, Sequence, Set, Tuple
 
 import numpy as np
 import pandas as pd
@@ -468,10 +468,22 @@ class ChaisemartinDHaultfoeuille(ChaisemartinDHaultfoeuilleBootstrapMixin):
         ``NotImplementedError``. Top-k path ranking under
         ``survey_design`` remains group-cardinality-based (unweighted),
         not population-weight-based — survey weights do not affect
-        which paths are selected as "top-k". Incompatible with
-        ``heterogeneity``, ``design2``, and ``honest_did`` (each
-        combination raises ``NotImplementedError`` in the current
-        release).
+        which paths are selected as "top-k".
+
+        Compatible with ``heterogeneity="<col>"`` — per-path
+        heterogeneity coefficient is computed by re-running the
+        Lemma 7 regression on each path-restricted switcher
+        subsample. Cohort dummies absorb baseline (no R-divergence
+        warning needed). Surfaces on
+        ``results.path_heterogeneity_effects`` keyed
+        ``{path: {l: {beta, se, t_stat, p_value, conf_int, n_obs}}}``
+        and on ``to_dataframe(level="by_path")`` via ``het_*``
+        columns. Mirrors R ``did_multiplegt_dyn(..., by_path,
+        predict_het)`` per-by_level. Composes with ``survey_design``
+        (analytical Binder TSL + replicate-weight) via the existing
+        cell-period IF allocator path. Incompatible with
+        ``design2`` and ``honest_did`` (each combination raises
+        ``NotImplementedError`` in the current release).
 
         Mutually exclusive with ``paths_of_interest`` — use
         ``by_path=k`` for top-k automatic ranking by frequency, or
@@ -633,10 +645,12 @@ class ChaisemartinDHaultfoeuille(ChaisemartinDHaultfoeuilleBootstrapMixin):
         Compatible with all downstream surfaces inherited by
         ``by_path``: bootstrap, per-path placebos, per-path joint
         sup-t bands, ``controls``, ``trends_linear``,
-        ``trends_nonparam``, and ``survey_design`` (analytical Binder
+        ``trends_nonparam``, ``survey_design`` (analytical Binder
         TSL + replicate-weight; multiplier bootstrap under survey
-        remains gated, same as ``by_path=k``). Mechanical extension
-        to path enumeration; no methodology change.
+        remains gated, same as ``by_path=k``), and ``heterogeneity``
+        (per-path heterogeneity coefficient surfaces on
+        ``results.path_heterogeneity_effects``). Mechanical
+        extension to path enumeration; no methodology change.
 
         **Order semantics**: paths appear in
         ``results.path_effects`` in the user-specified order, modulo
@@ -952,7 +966,11 @@ def fit(
             Partial implementation: post-treatment regressions only
             (no placebo regressions or joint null test). Cannot be
             combined with ``controls``, ``trends_linear``, or
-            ``trends_nonparam``. Requires ``L_max >= 1``.
+            ``trends_nonparam``. Requires ``L_max >= 1``. Under
+            ``by_path`` / ``paths_of_interest``, per-path
+            heterogeneity coefficients also surface on
+            ``results.path_heterogeneity_effects`` and on
+            ``to_dataframe(level="by_path")`` via ``het_*`` columns.
         design2 : bool, default=False
             If ``True``, identify and report switch-in/switch-out
             (Design-2) groups. Convenience wrapper (descriptive summary,
@@ -1227,11 +1245,6 @@ def fit(
                             f"[F_g-1, ..., F_g-1+L_max]); got path "
                             f"{p!r} of length {len(p)}."
                         )
-            if heterogeneity is not None:
-                raise NotImplementedError(
-                    "by_path / paths_of_interest combined with "
-                    "heterogeneity testing is deferred to a future release."
-                )
             if design2:
                 raise NotImplementedError(
                     "by_path / paths_of_interest combined with design2 "
@@ -3861,6 +3874,36 @@ def fit(
                 replicate_n_valid_list=_replicate_n_valid_list,
             )
 
+        # Per-path heterogeneity (mirrors R `did_multiplegt_dyn(...,
+        # by_path, predict_het)` per-by_level dispatch). Empty-state
+        # contract: None when not requested (no `heterogeneity` kwarg
+        # or no `by_path`/`paths_of_interest` selector); `{}` when
+        # requested but no path is observed (mirrors `path_effects`).
+        path_heterogeneity_effects: Optional[Dict[Tuple[int, ...], Dict[int, Dict[str, Any]]]] = (
+            None
+        )
+        if heterogeneity is not None and (
+            self.by_path is not None or self.paths_of_interest is not None
+        ):
+            path_heterogeneity_effects = _compute_path_heterogeneity_test(
+                Y_mat=Y_het,
+                N_mat=N_het,
+                baselines=baselines,
+                first_switch_idx=first_switch_idx_arr,
+                switch_direction=switch_direction_arr,
+                T_g=T_g_arr,
+                X_het=X_het,
+                L_max=L_max,
+                by_path=self.by_path,
+                paths_of_interest=self.paths_of_interest,
+                D_mat=D_mat,
+                alpha=self.alpha,
+                rank_deficient_action=self.rank_deficient_action,
+                group_ids_order=np.array(all_groups),
+                obs_survey_info=_obs_survey_info,
+                replicate_n_valid_list=_replicate_n_valid_list,
+            )
+
         twfe_weights_df = None
         twfe_fraction_negative = None
         twfe_sigma_fe = None
@@ -4006,6 +4049,25 @@ def fit(
                         _info_r2["t_stat"] = _t_r2
                         _info_r2["p_value"] = _p_r2
                         _info_r2["conf_int"] = _ci_r2
+            # Per-path heterogeneity (Wave 5 #11): per-(path, l) entries
+            # snapshot df_inference at compute-time. Refresh with final df
+            # so t/p/CI match `survey_metadata.df_survey`. Schema differs
+            # from per-path event-study (`{path: {l: ...}}` vs
+            # `{path: {"horizons": {l: ...}}}`), so inline loop here
+            # rather than reusing `_refresh_path_inference`.
+            if path_heterogeneity_effects:
+                for _path_r2, _horizons_r2 in list(path_heterogeneity_effects.items()):
+                    for _l_r2, _info_r2 in list(_horizons_r2.items()):
+                        if np.isfinite(_info_r2["se"]):
+                            _t_r2, _p_r2, _ci_r2 = safe_inference(
+                                _info_r2["beta"],
+                                _info_r2["se"],
+                                alpha=self.alpha,
+                                df=_final_inf_df,
+                            )
+                            _info_r2["t_stat"] = _t_r2
+                            _info_r2["p_value"] = _p_r2
+                            _info_r2["conf_int"] = _ci_r2
             # Normalized effects: another public surface built with the
             # pre-heterogeneity `_df_survey`. Recompute inference with
             # the final df so t/p/CI match the other surfaces (and the
@@ -4116,6 +4178,7 @@ def fit(
             linear_trends_effects=linear_trends_effects,
             trends_linear=_is_trends_linear,
             heterogeneity_effects=heterogeneity_effects,
+            path_heterogeneity_effects=path_heterogeneity_effects,
             design2_effects=(
                 _compute_design2_effects(
                     D_mat=D_mat,
@@ -4828,6 +4891,7 @@ def _compute_heterogeneity_test(
     group_ids_order: Optional[np.ndarray] = None,
     obs_survey_info: Optional[Dict[str, Any]] = None,
     replicate_n_valid_list: Optional[List[int]] = None,
+    path_groups: Optional[Set[int]] = None,
 ) -> Dict[int, Dict[str, Any]]:
     """Test for heterogeneous treatment effects (Web Appendix Section 1.5).
 
@@ -4959,6 +5023,8 @@ def _compute_heterogeneity_test(
         cohort_keys = []
 
         for g in range(n_groups):
+            if path_groups is not None and g not in path_groups:
+                continue
             f_g = first_switch_idx[g]
             if f_g < 0:
                 continue  # never-switcher
@@ -6390,6 +6456,85 @@ def _compute_path_placebos(
     return path_placebos
 
 
+def _compute_path_heterogeneity_test(
+    Y_mat: np.ndarray,
+    N_mat: np.ndarray,
+    baselines: np.ndarray,
+    first_switch_idx: np.ndarray,
+    switch_direction: np.ndarray,
+    T_g: np.ndarray,
+    X_het: np.ndarray,
+    L_max: int,
+    by_path: Optional[int],
+    paths_of_interest: Optional[List[Tuple[int, ...]]],
+    D_mat: np.ndarray,
+    alpha: float = 0.05,
+    rank_deficient_action: str = "warn",
+    group_ids_order: Optional[np.ndarray] = None,
+    obs_survey_info: Optional[Dict[str, Any]] = None,
+    replicate_n_valid_list: Optional[List[int]] = None,
+) -> Optional[Dict[Tuple[int, ...], Dict[int, Dict[str, Any]]]]:
+    """Per-path heterogeneity test (Web Appendix Section 1.5, Lemma 7).
+
+    For each selected path ``p``, runs ``_compute_heterogeneity_test`` on
+    the path-restricted switcher subsample. Cohort dummies absorb baseline
+    by construction, so the path-restricted regression is methodologically
+    well-posed even when path switchers span multiple baselines.
+
+    Mirrors R ``did_multiplegt_dyn(..., by_path, predict_het)`` semantics:
+    the R per-path dispatcher re-runs ``did_multiplegt_main(...,
+    predict_het=...)`` on each path-restricted subsample, which is exactly
+    what this helper does in Python.
+
+    The ``_enumerate_treatment_paths`` call here re-derives the path
+    enumeration (already computed elsewhere in fit() for ``path_effects``).
+    The call is wrapped in ``warnings.catch_warnings()`` to suppress
+    duplicate unobserved-path / by_path-exceeds-observed warnings; the
+    upstream ``_compute_path_effects`` call already surfaced them.
+
+    Returns
+    -------
+    Dict[Tuple[int, ...], Dict[int, Dict[str, Any]]]
+        ``{path: {l: {beta, se, t_stat, p_value, conf_int, n_obs}}}``.
+        Returns ``{}`` if ``selected_paths`` is empty. Return type is
+        ``Optional[...]`` for caller-contract symmetry; the helper itself
+        never produces ``None`` (the empty-state distinction
+        ``None`` not requested vs ``{}`` requested but empty lives at
+        the caller site in ``fit()``).
+    """
+    with warnings.catch_warnings():
+        warnings.simplefilter("ignore", UserWarning)
+        selected_paths, path_to_group_mask, _ = _enumerate_treatment_paths(
+            D_mat=D_mat,
+            first_switch_idx=first_switch_idx,
+            N_mat=N_mat,
+            L_max=L_max,
+            by_path=by_path,
+            paths_of_interest=paths_of_interest,
+        )
+    out: Dict[Tuple[int, ...], Dict[int, Dict[str, Any]]] = {}
+    for path in selected_paths:
+        mask = path_to_group_mask[path]
+        path_groups: Set[int] = {int(g) for g in np.flatnonzero(mask)}
+        out[path] = _compute_heterogeneity_test(
+            Y_mat=Y_mat,
+            N_mat=N_mat,
+            baselines=baselines,
+            first_switch_idx=first_switch_idx,
+            switch_direction=switch_direction,
+            T_g=T_g,
+            X_het=X_het,
+            L_max=L_max,
+            alpha=alpha,
+            rank_deficient_action=rank_deficient_action,
+            group_ids_order=group_ids_order,
+            obs_survey_info=obs_survey_info,
+            replicate_n_valid_list=replicate_n_valid_list,
+            path_groups=path_groups,
+        )
+    return out
+
+
 def _collect_path_bootstrap_inputs(
     D_mat: np.ndarray,
     Y_mat: np.ndarray,
diff --git a/diff_diff/chaisemartin_dhaultfoeuille_results.py b/diff_diff/chaisemartin_dhaultfoeuille_results.py
index 9d907c83..b32ffd21 100644
--- a/diff_diff/chaisemartin_dhaultfoeuille_results.py
+++ b/diff_diff/chaisemartin_dhaultfoeuille_results.py
@@ -424,6 +424,20 @@ class ChaisemartinDHaultfoeuilleResults:
         cohort-sharing SE deviation from R documented for
         ``path_effects``. See REGISTRY.md
         ``Note (Phase 3 by_path ...)`` → "Per-path placebos".
+    path_heterogeneity_effects : dict, optional
+        Per-path heterogeneity test results (Web Appendix Section 1.5,
+        Lemma 7) when ``heterogeneity`` is set AND (``by_path=k`` or
+        ``paths_of_interest=[(...), ...]``) is set. Inner dict keyed by
+        horizon directly (no ``"horizons"`` wrapper); each entry holds
+        ``{"beta", "se", "t_stat", "p_value", "conf_int", "n_obs"}``,
+        where ``beta`` is the WLS coefficient on the heterogeneity
+        covariate on the path-restricted switcher subsample. Cohort
+        dummies in the design matrix absorb baseline by construction.
+        Empty-state contract mirrors ``path_effects``: ``None`` when not
+        requested; ``{}`` when requested but no path has eligible
+        switchers. Mirrors R ``did_multiplegt_dyn(..., by_path,
+        predict_het)`` per-by_level dispatch. See REGISTRY.md
+        ``Note (Phase 3 by_path ...)`` → "Per-path heterogeneity testing".
     path_cumulated_event_study : dict, optional
         Per-path cumulated level effects ``delta_{path, l} =
         sum_{l'=1..l} DID^{fd}_{path, l'}`` for ``l = 1..L_max``,
@@ -580,6 +594,18 @@ class ChaisemartinDHaultfoeuilleResults:
     path_placebo_event_study: Optional[Dict[Tuple[int, ...], Dict[int, Dict[str, Any]]]] = field(
         default=None, repr=False
     )
+    # Per-path heterogeneity test (Web Appendix Section 1.5, Lemma 7)
+    # under `by_path` / `paths_of_interest`. Inner dict keyed by horizon
+    # directly: `{path: {l: {beta, se, t_stat, p_value, conf_int, n_obs}}}`.
+    # Mirrors the simpler `path_placebo_event_study` shape — no metadata
+    # wrapper because frequency_rank / n_groups already live on
+    # `path_effects[path]` for the same path. Empty-state contract
+    # mirrors `path_effects`: None when not requested (no `heterogeneity`
+    # kwarg or no `by_path` / `paths_of_interest` selector); `{}` when
+    # requested but no path is observed.
+    path_heterogeneity_effects: Optional[Dict[Tuple[int, ...], Dict[int, Dict[str, Any]]]] = field(
+        default=None, repr=False
+    )
     # Per-path cumulated event study (level effects under `trends_linear`
     # = True). `path_effects[path]["horizons"][l]` surfaces raw
     # `DID^{fd}_l` per path; this field surfaces the cumulated level
@@ -1392,6 +1418,29 @@ def _render_path_effects_section(
                                 ce["p_value"],
                             )
                         )
+            # Per-path heterogeneity rows (under heterogeneity=col).
+            # Mirrors the global `_render_heterogeneity_section` block
+            # but scoped to this path. Skip silently when
+            # path_heterogeneity_effects is None or this path lacks an
+            # entry (e.g., when `heterogeneity` was not requested).
+            if (
+                self.path_heterogeneity_effects is not None
+                and path in self.path_heterogeneity_effects
+            ):
+                het_horizons = self.path_heterogeneity_effects[path]
+                if het_horizons:
+                    lines.append("  Heterogeneity Test (Section 1.5, partial):")
+                    for l_h in sorted(het_horizons.keys()):
+                        het = het_horizons[l_h]
+                        lines.append(
+                            _format_inference_row(
+                                f"  l={l_h}",
+                                het["beta"],
+                                het["se"],
+                                het["t_stat"],
+                                het["p_value"],
+                            )
+                        )
             # Per-path joint sup-t critical value (when populated).
             # Mirrors the OVERALL sup-t crit print at line ~1019.
             if self.path_sup_t_bands is not None and path in self.path_sup_t_bands:
@@ -1482,8 +1531,10 @@ def to_dataframe(self, level: str = "overall") -> pd.DataFrame:
               ``effect``, ``se``, ``t_stat``, ``p_value``,
               ``conf_int_lower``, ``conf_int_upper``, ``n_obs``,
               ``cband_lower``, ``cband_upper``, ``cumulated_effect``,
-              ``cumulated_se``. The ``horizon`` column takes negative
-              ints for placebo rows when ``placebo=True``. The
+              ``cumulated_se``, ``het_beta``, ``het_se``,
+              ``het_t_stat``, ``het_p_value``, ``het_conf_int_lower``,
+              ``het_conf_int_upper``. The ``horizon`` column takes
+              negative ints for placebo rows when ``placebo=True``. The
               ``cband_*`` columns mirror the OVERALL
               ``level="event_study"`` schema (joint sup-t simultaneous
               bands); they are populated for positive-horizon rows of
@@ -1495,7 +1546,13 @@ def to_dataframe(self, level: str = "overall") -> pd.DataFrame:
               positive-horizon rows when ``trends_linear=True`` is
               also set, NaN for placebo rows or non-trends_linear fits
               (always-present, NaN-when-None — same convention as
-              ``cband_*``).
+              ``cband_*``). The ``het_*`` columns surface the per-path
+              heterogeneity coefficient (Web Appendix Section 1.5,
+              Lemma 7) when ``heterogeneity="<col>"`` is also set;
+              populated for positive-horizon rows and NaN for placebo
+              rows / non-heterogeneity fits / the requested-but-empty
+              fallback DataFrame (always-present, NaN-when-None — same
+              convention as ``cband_*`` and ``cumulated_*``).
 
         Returns
         -------
@@ -1759,6 +1816,12 @@ def to_dataframe(self, level: str = "overall") -> pd.DataFrame:
                         "cband_upper",
                         "cumulated_effect",
                         "cumulated_se",
+                        "het_beta",
+                        "het_se",
+                        "het_t_stat",
+                        "het_p_value",
+                        "het_conf_int_lower",
+                        "het_conf_int_upper",
                     ]
                 )
             rows = []
@@ -1788,6 +1851,14 @@ def to_dataframe(self, level: str = "overall") -> pd.DataFrame:
                     if self.path_cumulated_event_study is not None
                     else {}
                 )
+                # Per-path heterogeneity entries (under heterogeneity=col).
+                # Always-present het_* columns, NaN when not requested or
+                # when the path's per-horizon entry is missing.
+                path_het = (
+                    self.path_heterogeneity_effects.get(path, {})
+                    if self.path_heterogeneity_effects is not None
+                    else {}
+                )
                 for lag_key in sorted(placebo_horizons.keys()):
                     ph_entry = placebo_horizons[lag_key]
                     # Placebos do not get joint sup-t bands in this
@@ -1816,6 +1887,15 @@ def to_dataframe(self, level: str = "overall") -> pd.DataFrame:
                             "cband_upper": ph_cband[1] if ph_cband else np.nan,
                             "cumulated_effect": np.nan,
                             "cumulated_se": np.nan,
+                            # Heterogeneity is forward-only (R doesn't ship
+                            # per-path predict_het on placebos); placebo
+                            # rows always emit NaN here.
+                            "het_beta": np.nan,
+                            "het_se": np.nan,
+                            "het_t_stat": np.nan,
+                            "het_p_value": np.nan,
+                            "het_conf_int_lower": np.nan,
+                            "het_conf_int_upper": np.nan,
                         }
                     )
                 for l_h in sorted(horizons.keys()):
@@ -1826,6 +1906,8 @@ def to_dataframe(self, level: str = "overall") -> pd.DataFrame:
                     # `TestByPathSupTBands::test_path_sup_t_to_dataframe_emits_cband_columns`.
                     h_cband = h_entry.get("cband_conf_int", (np.nan, np.nan))
                     cum_entry = path_cumulated.get(l_h, {})
+                    het_entry = path_het.get(l_h, {}) if path_het else {}
+                    het_ci = het_entry.get("conf_int", (np.nan, np.nan))
                     rows.append(
                         {
                             "path": path,
@@ -1843,6 +1925,16 @@ def to_dataframe(self, level: str = "overall") -> pd.DataFrame:
                             "cband_upper": h_cband[1] if h_cband else np.nan,
                             "cumulated_effect": cum_entry.get("effect", np.nan),
                             "cumulated_se": cum_entry.get("se", np.nan),
+                            # Per-path heterogeneity (Wave 5 #11). Always-
+                            # present, NaN when not requested or when the
+                            # entry is missing (mirrors cband_*/cumulated_*
+                            # convention).
+                            "het_beta": het_entry.get("beta", np.nan),
+                            "het_se": het_entry.get("se", np.nan),
+                            "het_t_stat": het_entry.get("t_stat", np.nan),
+                            "het_p_value": het_entry.get("p_value", np.nan),
+                            "het_conf_int_lower": het_ci[0] if het_ci else np.nan,
+                            "het_conf_int_upper": het_ci[1] if het_ci else np.nan,
                         }
                     )
             return pd.DataFrame(rows)
diff --git a/diff_diff/guides/llms-full.txt b/diff_diff/guides/llms-full.txt
index 6245f62b..e3eaa251 100644
--- a/diff_diff/guides/llms-full.txt
+++ b/diff_diff/guides/llms-full.txt
@@ -242,8 +242,8 @@ ChaisemartinDHaultfoeuille(
     placebo: bool = True,                        # Auto-compute single-lag placebo
     twfe_diagnostic: bool = True,                # Auto-compute Theorem 1 TWFE decomposition
     drop_larger_lower: bool = True,              # Drop multi-switch groups (matches R DIDmultiplegtDYN)
-    by_path: int | None = None,                  # Top-k per-path event study; requires drop_larger_lower=False, L_max>=1; supports binary or integer-coded discrete D (D in Z); composes with survey_design (analytical TSL + replicate-weight; multiplier bootstrap n_bootstrap>0 still gated under survey); mutex with paths_of_interest
-    paths_of_interest: list[tuple[int, ...]] | None = None,  # User-specified path subset, alternative to by_path=k (Python-only API; mutex with by_path; composes with survey_design same as by_path=k)
+    by_path: int | None = None,                  # Top-k per-path event study; requires drop_larger_lower=False, L_max>=1; supports binary or integer-coded discrete D (D in Z); composes with survey_design (analytical TSL + replicate-weight; multiplier bootstrap n_bootstrap>0 still gated under survey) and heterogeneity (per-path predict_het, mirrors R did_multiplegt_dyn(..., by_path, predict_het)); mutex with paths_of_interest
+    paths_of_interest: list[tuple[int, ...]] | None = None,  # User-specified path subset, alternative to by_path=k (Python-only API; mutex with by_path; composes with survey_design and heterogeneity same as by_path=k)
     rank_deficient_action: str = "warn",         # Used by TWFE diagnostic OLS
 )
 ```
diff --git a/docs/api/chaisemartin_dhaultfoeuille.rst b/docs/api/chaisemartin_dhaultfoeuille.rst
index cb5b3895..10c3533d 100644
--- a/docs/api/chaisemartin_dhaultfoeuille.rst
+++ b/docs/api/chaisemartin_dhaultfoeuille.rst
@@ -26,7 +26,11 @@ supports binary or integer-coded discrete (D in Z) treatment, and
 composes with ``survey_design`` for analytical Binder TSL SE and
 replicate-weight bootstrap variance (multiplier bootstrap under
 survey + by_path remains gated; no R parity since R
-``did_multiplegt_dyn`` does not support survey weighting).
+``did_multiplegt_dyn`` does not support survey weighting). ``by_path``
+and ``paths_of_interest`` also compose with ``heterogeneity="<col>"``:
+per-path heterogeneity coefficient surfaces on
+``results.path_heterogeneity_effects`` (mirrors R
+``did_multiplegt_dyn(..., by_path, predict_het)`` per-by_level).
 
 The estimator:
 
diff --git a/docs/methodology/REGISTRY.md b/docs/methodology/REGISTRY.md
index 076632d0..596c97df 100644
--- a/docs/methodology/REGISTRY.md
+++ b/docs/methodology/REGISTRY.md
@@ -640,7 +640,9 @@ The guard is fired by `_survey_se_from_group_if` (analytical and replicate) and
 
 - **Note (Phase 3 Design-2 switch-in/switch-out):** Convenience wrapper for Web Appendix Section 1.6 (Assumption 16). Identifies groups with exactly 2 treatment changes (join then leave), reports switch-in and switch-out mean effects. This is a descriptive summary, not a full re-estimation with specialized control pools as described in the paper. **Always uses raw (unadjusted) outcomes** regardless of active `controls`, `trends_linear`, or `trends_nonparam` options - those adjustments apply to the main estimator surface but not to the Design-2 descriptive block. For full adjusted Design-2 estimation with proper control pools, the paper recommends "running the command on a restricted subsample and using `trends_nonparam` for the entry-timing grouping." Activated via `design2=True` in `fit()`, requires `drop_larger_lower=False` to retain 2-switch groups.
 
-- **Note (Phase 3 `by_path` per-path event-study disaggregation):** Per-path disaggregation of the multi-horizon event study, mirroring R `did_multiplegt_dyn(..., by_path=k)`. Activated via `ChaisemartinDHaultfoeuille(by_path=k, drop_larger_lower=False)` where `k` is a positive integer (top-k most common observed paths by switcher-group frequency). **Window convention:** the path tuple for a switcher group `g` is `(D_{g, F_g-1}, D_{g, F_g}, ..., D_{g, F_g-1+L_max})` — length `L_max + 1`, matching R's window `[F_{g-1}, F_{g-1+l}]`. **Ranking:** paths are ranked by descending frequency; ties are broken lexicographically on the path tuple for deterministic ordering, so every selected path has a unique `frequency_rank`. If `by_path` exceeds the number of observed paths, all observed paths are returned with a `UserWarning`. **Per-path SE convention (joiners/leavers precedent):** the per-path influence function follows the joiners-only / leavers-only IF construction at `chaisemartin_dhaultfoeuille.py:5495-5504`: the switcher-side contribution `+S_g * (Y_{g,out} - Y_{g,ref})` is zeroed for groups whose observed trajectory is NOT the selected path; control contributions and the full cohort structure `(D_{g,1}, F_g, S_g)` are unchanged. After applying the singleton-baseline eligible mask and cohort-recentering with the original cohort IDs, the plug-in SE uses the path-specific divisor `N_l_path` (count of path switchers eligible at horizon `l`) — same pattern as `joiners_se` using `joiner_total`. This gives the **within-path mean** estimand `DID_{path,l}` as the within-path average of `DID_{g,l}`. **Degenerate-cohort behavior per path:** when a path's centered IF at some horizon is identically zero (every variance-eligible path switcher forms its own `(D_{g,1}, F_g, S_g)` cohort, or the path has a single contributing group), SE / t_stat / p_value / conf_int are NaN-consistent and a `UserWarning` is emitted scoped to `(path, horizon)`. This mirrors the overall-path degenerate-cohort surface and is common for rare paths with few contributing groups. **Empty-state contract:** `results.path_effects` distinguishes "not requested" (`None`) from "requested but empty" (`{}` — all switchers have windows outside the panel or unobserved cells). The empty-dict case emits a `UserWarning` at fit-time and renders as an explicit "no observed paths" notice in `summary()`; `to_dataframe(level="by_path")` returns an empty DataFrame with the canonical column set (mirrors the `linear_trends` pattern when `trends_linear=True` but no horizons survive). **Requirements:** `drop_larger_lower=False` (multi-switch groups are the object of interest; default `True` filters them out) and `L_max >= 1` (path window depends on the horizon). **Scope:** combinations with `heterogeneity`, `design2`, and `honest_did` remain gated behind explicit `NotImplementedError` (deferred to follow-up wave PRs). `n_bootstrap > 0` is now supported — see the **Bootstrap SE** paragraph below. `survey_design` is supported under analytical Binder TSL and replicate-weight bootstrap — see the **Per-path survey-design SE** paragraph below; multiplier bootstrap (`n_bootstrap > 0`) under `survey_design + by_path/paths_of_interest` remains gated. `placebo=True` is now supported per-path — see the **Per-path placebos** paragraph below. **TWFE diagnostic** remains a sample-level summary (not computed per path) in this release. Results are exposed on `results.path_effects` as `Dict[Tuple[int, ...], Dict[str, Any]]` with nested `horizons` dicts per horizon `l`, and on `results.to_dataframe(level="by_path")` as a long-format table with columns `[path, frequency_rank, n_groups, horizon, effect, se, t_stat, p_value, conf_int_lower, conf_int_upper, n_obs, cband_lower, cband_upper, cumulated_effect, cumulated_se]` (the `cband_*` columns are added by the joint sup-t Note below, populated for positive-horizon rows of paths with a finite sup-t crit and NaN otherwise; the `cumulated_*` columns are added by the per-path linear-trends Note below, populated for positive-horizon rows when `trends_linear=True` is set and NaN otherwise). Gated tests live in `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathGates` / `::TestByPathBehavior` / `::TestByPathEdgeCases`. **R-parity** against `DIDmultiplegtDYN 2.3.3` is confirmed at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPath` via two scenarios: `mixed_single_switch_by_path` (2 paths, `by_path=2`) and `multi_path_reversible_by_path` (4 paths, `by_path=3`; path-assignment deterministic on `F_g` so each `(D_{g,1}, F_g, S_g)` cohort contains switchers from a single path). Per-path point estimates and per-path switcher counts match R exactly; per-path SE matches within the Phase 2 multi-horizon SE envelope (observed rtol ≤ 10.2% on the 2-path mixed scenario, ≤ 4.2% on the 4-path cohort-clean scenario). **Deviation from R (cross-path cohort-sharing SE):** our analytical SE is the marginal variance of the path-contribution estimator cohort-centered on the *full-panel* cohort structure (joiners/leavers precedent — non-path switchers contribute to cohort means via their zeroed switcher row). R's `did_multiplegt_dyn(..., by_path=k)` re-runs the estimator per path, so cohort means are computed over the path's own switchers only. When a cohort `(D_{g,1}, F_g, S_g)` spans multiple observed paths, Python and R SE diverge materially (our empirical probes with random post-window toggling saw rtol > 100%); when every cohort is single-path (scenario 13 by design, scenario 14 by construction), the two approaches coincide up to the documented Phase 2 envelope. Practitioners with cohort structures that mix paths should interpret the per-path SE as a within-full-panel marginal variance, not a per-path conditional variance. **Bootstrap SE:** when `n_bootstrap > 0` is set, the top-k paths are enumerated once on the observed data (R-faithful: matches `did_multiplegt_dyn(..., by_path=k, bootstrap=B)`'s path-stability convention — verified empirically against DIDmultiplegtDYN 2.3.3) and the multiplier bootstrap (`bootstrap_weights ∈ {"rademacher", "mammen", "webb"}`) runs per `(path, horizon)` target via the shared `_bootstrap_one_target` / `compute_effect_bootstrap_stats` helpers. Point estimates are unchanged from the analytical path. Bootstrap SE replaces the analytical SE in `path_effects[path]["horizons"][l]["se"]`, and `p_value` / `conf_int` are taken as the **bootstrap percentile** statistics, matching the Round-10 library convention for overall / joiners / leavers / multi-horizon bootstrap (see the `Note (bootstrap inference surface)` elsewhere in this file and the pinned regression `test_bootstrap_p_value_and_ci_propagated_to_top_level`). `t_stat` is SE-derived via `safe_inference` per the anti-pattern rule. Interpretation: inference is *conditional on the observed path set*. **SE inherits the analytical cross-path cohort-sharing deviation:** the bootstrap input is the exact same full-panel cohort-centered path IF that the analytical path computes (`_collect_path_bootstrap_inputs` reuses the same enumeration / cohort IDs / IF construction), so the bootstrap SE is a Monte Carlo analog of the analytical SE — it inherits the same cross-path cohort-sharing deviation from R's per-path re-run convention documented above. On single-path-cohort panels (scenarios 13 and 14 of the R-parity fixture, and any DGP where `(D_{g,1}, F_g, S_g)` cohorts never span multiple observed paths), bootstrap SE tracks analytical SE up to Monte Carlo noise and both coincide with R up to the Phase 2 envelope. On cross-path cohort panels, bootstrap SE inherits the >100% rtol divergence from R that analytical already has. **Deviation from R (CI method):** R's per-path CI is normal-theory around the bootstrap SE (half-width ≈ `1.96·se`); ours is the bootstrap percentile CI, intentionally diverging from R to keep the dCDH inference surface internally consistent across all bootstrap targets. Practitioners who want *unconditional* inference capturing path-selection uncertainty need a pairs-bootstrap (deferred — no R precedent). Positive regressions live in `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathBootstrap` (gated `@pytest.mark.slow`): point-estimate invariance, finite positive SE on non-degenerate panels, SE-within-30%-rtol of analytical on cohort-clean fixtures, degenerate-cohort NaN propagation, Rademacher/Mammen/Webb parity, seed reproducibility, and percentile-vs-normal-theory CI pinning. **Per-path placebos:** when `placebo=True` (and `L_max >= 1`) is combined with `by_path=k`, per-path backward-horizon placebos `DID^{pl}_{path, l}` for `l = 1..L_max` are computed using the same joiners/leavers IF precedent applied to `_compute_per_group_if_placebo_horizon` (with the new `switcher_subset_mask` parameter): switcher contributions are zeroed for groups not in the path; the control pool and the variance-eligible cohort structure `(D_{g,1}, F_g, S_g)` are unchanged. Plug-in SE uses the path-specific divisor `N^{pl}_{l, path}` (count of path switchers eligible at backward lag `l`). Surfaced on `results.path_placebo_event_study[path][-l]` with the same `{effect, se, t_stat, p_value, conf_int, n_obs}` shape as `placebo_event_study` (negative-int inner keys parallel the existing per-path event-study positive-int keys, so a unified forward+backward view is well-formed). **Inherits the cross-path cohort-sharing SE deviation from R** documented above for `path_effects` (same convention applied backward); tracks R within numerical tolerance on single-path-cohort panels and diverges on cohort-mixed panels. Multiplier bootstrap (when `n_bootstrap > 0`) runs per `(path, lag)` target via the same `_bootstrap_one_target` dispatch used for the per-path event-study, with the canonical NaN-on-invalid contract. The bootstrap SE is a Monte Carlo analog of the analytical placebo SE — same per-path centered IF input — and inherits the same deviation. Surfaced through `summary()` (negative-keyed rows rendered alongside positive-keyed event-study rows under each path block) and `to_dataframe(level="by_path")` (`horizon` column takes negative ints for placebo rows). **Empty-state contract:** `results.path_placebo_event_study` mirrors `path_effects` — `None` when `by_path + placebo` was not requested, `{}` when requested but no observed path has a complete window within the panel (same regime that returns `{}` for `path_effects`, with the same fit-time `UserWarning`). R-parity is confirmed at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPathPlacebo` on the `multi_path_reversible_by_path_placebo` scenario; positive analytical + bootstrap invariants live in `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathPlacebo` (with the gated `::TestByPathPlacebo::TestBootstrap` subclass). **Per-path covariate residualization (DID^X):** when `controls=[...]` is set with `by_path=k`, the per-baseline OLS residualization (Web Appendix Section 1.2) runs once on the first-differenced outcome BEFORE path enumeration. All four downstream surfaces — analytical per-path SE, bootstrap SE, per-path placebos, and per-path joint sup-t bands — consume the residualized `Y_mat` automatically (Frisch-Waugh-Lovell). Per-period effects remain unadjusted, consistent with the existing `controls` + per-period DID contract (per-period DID does not support residualization). Failed-stratum baselines (rank-deficient X) zero out `N_mat` for affected groups, which the path enumeration treats as ineligible per its existing convention. **Deviation from R on multi-baseline switcher panels (point estimates):** R `did_multiplegt_dyn(..., by_path, controls)` re-runs the per-baseline residualization on each path's restricted subsample (`R/R/did_multiplegt_dyn.R` lines 401-405: rows of the path's switchers OR rows where `yet_to_switch=1 AND baseline matches the path's baseline`). The first-stage residualization sample R uses for path B equals: pre-switch rows of all switchers with matching baseline + all rows of never-switchers with matching baseline — bit-identical to our global first-stage sample under single-baseline switcher panels (every switcher shares the same `D_{g,1}`, regardless of how `F_g` or path identity varies across switchers). Per-path point estimates therefore coincide with R on those panels up to the existing **DID^X first-stage cell-weighting deviation** documented above in `Note (Phase 3 DID^X covariate adjustment)` (Python's first-stage OLS uses equal cell weights — one observation per `(g, t)` cell, consistent with the library's cell-aggregated input convention; R weights by `N_gt`). On panels with one observation per `(g, t)` cell (the common case after the cell-aggregation step in `fit()`), Python matches R bit-exactly: the `multi_path_reversible_by_path_controls` parity fixture has 4 paths with switcher `F_g` values spanning [0..6] under `D_{g,1}=0` and Python matches R to rtol ~1e-11. On multi-baseline switcher panels (some switchers have `D_{g,1}=0`, others have `D_{g,1}=1`) R's per-path subset drops switchers whose baseline differs from the path's baseline, so the per-baseline regression coefficients diverge per path under R and point estimates can diverge between Python and R — a `UserWarning` is emitted at fit-time when this configuration is detected so practitioners do not silently consume estimates that disagree with R. The warning filters to switcher groups only; never-switchers (never-treated + always-treated controls) at multiple baseline values do NOT trigger the warning because they don't affect R's per-path subset construction. **Inherits the cross-path cohort-sharing SE deviation from R** documented above for `path_effects` — bootstrap SE, placebo SE, and sup-t crit are Monte Carlo / joint-distribution analogs of the same residualized analytical IF and carry the same deviation. R-parity is confirmed against `did_multiplegt_dyn(..., by_path=3, controls="X1")` at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPathControls` on the `multi_path_reversible_by_path_controls` scenario (single-baseline DGP, exact point-estimate match measured rtol ~1e-11); cross-surface inheritance and the multi-baseline warning are regression-tested at `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathControls` (analytical + bootstrap + placebo + sup-t + `to_dataframe(level="by_path")` cband columns + multi-baseline `UserWarning`). **Per-path linear-trends DID^{fd}:** when `trends_linear=True` is set with `by_path=k`, the first-differencing transform at `chaisemartin_dhaultfoeuille.py:1599-1630` runs once globally BEFORE path enumeration (replaces `Y_mat` with `Z_mat = Y_t - Y_{t-1}` and shrinks the time axis by one), 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)` per the existing parity test pivot at `tests/test_chaisemartin_dhaultfoeuille_parity.py:403-409`) surface on the new `results.path_cumulated_event_study[path][l]` field — a per-group running sum of `DID^{fd}_{g, l'}` averaged over the path's switchers eligible at horizon `l`, mirroring the global `linear_trends_effects` cumulation logic at `chaisemartin_dhaultfoeuille.py:3340-3398`. SE on the cumulated layer is the conservative upper bound (sum of per-horizon component SEs from `path_effects[path]["horizons"][l]["se"]`, NaN-consistent: any non-finite component yields a NaN cumulated SE). **Post-bootstrap recomputation:** the cumulated layer is built AFTER the bootstrap propagation block at `chaisemartin_dhaultfoeuille.py:3034-3081` so it reads the FINAL post-bootstrap per-horizon SEs (mirrors the global `linear_trends_effects` placement). When `n_bootstrap > 0`, cumulated SE / t / p / CI are derived from bootstrap per-horizon SEs; when bootstrap produces non-finite SE (e.g., `n_bootstrap=1` degenerate distribution), the cumulated layer's full inference tuple is NaN per the library-wide NaN-on-invalid bootstrap contract. `to_dataframe(level="by_path")` exposes `cumulated_effect` and `cumulated_se` columns (always present, NaN-when-None — mirrors the `cband_*` always-present convention from PR #374). `summary()` renders a `Cumulated Level Effects (DID^{fd}, trends_linear)` sub-section under each per-path block. **Path enumeration uses 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 at line 1620 surfaces the issue), so a path whose switchers all have `F_g < 3` is silently absent from `path_effects` rather than present-with-NaN. **F_g=3 boundary-case divergence (`by_path + trends_linear`):** `F_g=3` switchers have exactly 2 pre-switch periods, which after first-differencing and the `time==1` filter leaves only 1 valid pre-window Z value. R's per-path full-pipeline call handles this single-pre-period regime differently from Python's global-then-disaggregate architecture, producing 30%+ relative divergence on point estimates for paths whose switchers include `F_g=3` (empirically observed on the parity fixture's earlier `F_g=3` variant). A separate `UserWarning` fires at fit-time when the panel includes any `F_g=3` switcher AND `by_path + trends_linear` is set, mirroring the `F_g < 3` exclusion warning. The shipped parity fixture (`single_baseline_multi_path_by_path_trends_lin`) restricts to `F_g >= 4` exclusively to avoid this regime; per-path R parity is asserted only there. **Placebo under `trends_linear` returns RAW per-horizon values** (no per-path placebo cumulation surface) — verified empirically against the existing `joiners_only_trends_lin` parity fixture: R's per-path Placebo_l matches Python's `path_placebo_event_study[path][-l]` (raw) bit-exactly under non-`by_path` trends_lin. **Deviation from R on multi-baseline switcher panels (point estimates):** R `did_multiplegt_dyn(..., by_path, trends_lin)` re-runs the full pipeline (including first-differencing) on each path's restricted subsample, so it operates on different switcher samples per path when switchers have different baseline values `D_{g,1}`. Python first-differences once globally before path enumeration. On single-baseline switcher panels the two architectures coincide; on multi-baseline switcher panels per-path point estimates can diverge — a `UserWarning` is emitted at fit-time when this configuration is detected so practitioners do not silently consume estimates that disagree with R (mirroring the analogous `by_path + controls` warning). Per-path R parity is confirmed against `did_multiplegt_dyn(..., by_path=3, trends_lin=TRUE, placebo=1)` at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPathTrendsLinear` on the `single_baseline_multi_path_by_path_trends_lin` scenario (single-baseline + cohort-single-path + `F_g >= 4` DGP designed to eliminate the multi-baseline divergence, the cross-path cohort-sharing deviation, and the F_g=3 boundary case under R's per-path full-pipeline call). Per-path cumulated point estimates match R bit-exactly (rtol ~1e-9) on event horizons under those conditions; cumulated SE_RTOL is widened to `0.20` (vs `0.12` used for non-cumulated by_path parity) because the conservative upper-bound SE compounds the cross-path cohort-sharing deviation under summation. **Placebo parity is intentionally skipped for `trends_linear`**: 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, producing a sign-and-magnitude divergence on paths whose switchers have minimal pre-window depth (e.g., `F_g=4` switchers). Placebo under `by_path + trends_linear` is exercised via internal regression in `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathTrendsLinear` (finite values, bootstrap inheritance) but not pinned to R bit-by-bit. Cross-surface invariants (analytical + bootstrap + placebo + sup-t + `path_cumulated_event_study` + `to_dataframe` columns + `summary()` rendering) are regression-tested at `TestByPathTrendsLinear`. **Per-path state-set trends:** when `trends_nonparam="state_col"` is set with `by_path=k`, the set membership column is validated and stored once globally as `set_ids_arr` (time-invariance, NaN rejection, partition-coarseness checks unchanged from the non-by_path path). The `set_ids` parameter is 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. R does NOT first-difference and does NOT cumulate under `trends_nonparam` (unlike `trends_lin`); per-horizon `Effect_l` is a normal DID with set-restricted controls. Per-path R parity is confirmed against `did_multiplegt_dyn(..., by_path=3, trends_nonparam="state", placebo=1)` at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPathTrendsNonparam` on the `multi_path_reversible_by_path_trends_nonparam` scenario; per-path point estimates AND placebos match R bit-exactly (rtol ~1e-9), per-path SE matches within the Phase 2 envelope (~13% rtol observed). Cross-surface invariants are regression-tested at `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathTrendsNonparam`. **Per-path non-binary treatment:** integer-coded discrete treatment (D in Z, e.g. ordinal {0, 1, 2}) is supported under `by_path=k` and `paths_of_interest`. Path tuples become integer-state tuples (`(0, 2, 2, 2)`) keyed bit-for-bit against R's comma-separated path strings (`"0,2,2,2"`) for D in {0..9}. Continuous D (e.g. `1.5`) raises `ValueError` at fit-time per the no-silent-failures contract — the existing `int(round(float(v)))` cast in `_enumerate_treatment_paths` is now defensive (no-op for integer-coded D). **Deviation from R for D >= 10:** R's `did_multiplegt_by_path` derives the per-path baseline via `path_index$baseline_XX <- substr(path_index$path, 1, 1)` (extracted 2026-05-03 via `Rscript -e 'cat(paste(deparse(DIDmultiplegtDYN:::did_multiplegt_by_path), collapse="\n"))'`), capturing only the first character of the comma-separated path string. For D >= 10 this captures `"1"` instead of `"12"` for `path = "12,12,..."`, mis-allocating R's per-path control-pool subset. Python's tuple-key matching is correct in this regime; the per-path point estimates we compute are correct, R's per-path subset for the same path is buggy. The shipped parity scenario stays in `D in {0, 1, 2}` to avoid the R bug; R-parity for D in {0..9} is asserted at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPathNonBinary` on the `multi_path_reversible_by_path_non_binary` scenario (78 switchers, 3 paths, single-baseline custom DGP, F_g >= 4) — per-path point estimates match R bit-exactly (rtol ~1e-9 events; rtol+atol envelope for placebo near-zero values), SE inherits the documented cross-path cohort-sharing deviation (~5% rtol observed; SE_RTOL=0.15 envelope). Cross-surface invariants regression-tested at `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathNonBinary`. **Per-path survey-design SE** (analytical Binder TSL + replicate-weight bootstrap): under `by_path` / `paths_of_interest` + `survey_design`, the per-path per-horizon SE routes through `_survey_se_from_group_if` using the cell-period allocator. The per-path influence function `U_pp_l_path` is the per-period IF with non-path switcher-side contributions skipped — control contributions remain unchanged, matching the joiners/leavers IF convention from the **Per-path SE convention** paragraph above (the `switcher_subset_mask` zeroes the switcher row of the per-group IF, which trivially zeroes the corresponding row of the per-cell IF, preserving the row-sum identity `U_pp.sum(axis=1) == U`). The IF is cohort-recentered via `_cohort_recenter_per_period` and expanded to observations as `psi_i = U_pp[g_i, t_i] · (w_i / W_{g_i, t_i})`. Replicate-weight designs unconditionally route through the cell allocator (Class A contract, PR #323). Multiplier bootstrap (`n_bootstrap > 0`) under `survey_design + by_path/paths_of_interest` raises `NotImplementedError` at fit-time — the survey-aware perturbation pivot for path-restricted IFs is methodologically underived and deferred to a future wave; the global non-by_path TSL multiplier bootstrap is unaffected and continues to ship. **Path-enumeration ranking is unweighted** under `survey_design`: top-k selection uses group cardinality (`path_to_count[p]` = number of groups), not population-weight mass — survey weights do not affect which paths are selected as "top-k". A weighted-ranking variant (sum of survey weights per path) is deferred until concrete demand. **`df_survey` propagation:** under replicate weights, every per-path per-horizon fit contributes an `n_valid` count to the shared `_replicate_n_valid_list` accumulator and the final `_effective_df_survey = min(...) - 1` reflects all per-path replicate fits. A post-call `_refresh_path_inference` helper re-runs `safe_inference` on every populated entry so `multi_horizon_inference`, `placebo_horizon_inference`, `path_effects`, and `path_placebos` all use the same final df after per-path appends complete. **Lonely-PSU policy is sample-wide, not per-path** — the `lonely_psu` policy (`remove`/`certainty`/`adjust`) operates on the full design-level PSU/strata structure, not on path-restricted subsamples. **Telescope invariant:** on a single-path panel where every switcher follows the same trajectory and `eligible_groups` matches between by_path and non-by_path, per-path SE equals the global non-by_path survey SE bit-exactly — pinned at `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathSurveyDesignTelescope::test_telescope_analytical_TSL`. **Deviation from R:** none — R `did_multiplegt_dyn` does not support survey weighting, so this is a Python-only methodology extension (no R parity available; no R parity test class). Regression test anchor: `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathSurveyDesignAnalytical` covering analytical SE, replicate-weight SE, the `n_bootstrap` gate, the global anti-regression, per-path placebos, `trends_linear` composition, and unobserved-path warnings under survey. **Per-path user-specified path selection (`paths_of_interest`):** Python-only API extension — R's `did_multiplegt_dyn(..., by_path=k)` only accepts a positive int (top-k automatic ranking) or `-1` (all observed paths) and provides no list-based selection. Activated via `ChaisemartinDHaultfoeuille(paths_of_interest=[(0, 1, 1, 1), (0, 1, 0, 0)], drop_larger_lower=False)` as an alternative to `by_path=k`; the two are **mutually exclusive** (setting both raises `ValueError` at `__init__` and `set_params` time). Each path tuple must have length `L_max + 1`; the type / element / non-empty / length-uniformity checks fire at `__init__`, the length-vs-L_max check fires at fit-time. `bool` and `np.bool_` are explicitly rejected; `np.integer` is accepted and canonicalized to Python `int` for tuple-key consistency. Duplicates emit a `UserWarning` and are deduplicated; paths not observed in the panel emit a `UserWarning` and are omitted from `path_effects`. Paths appear in `results.path_effects` in the user-specified order, modulo deduplication and unobserved-path filtering. Composes with non-binary D and all downstream `by_path` surfaces (bootstrap, per-path placebos, per-path joint sup-t bands, `controls`, `trends_linear`, `trends_nonparam`) — mechanical filter on observed paths, no methodology change. Behavior + cross-feature regressions live at `tests/test_chaisemartin_dhaultfoeuille.py::TestPathsOfInterest`.
+- **Note (Phase 3 `by_path` per-path event-study disaggregation):** Per-path disaggregation of the multi-horizon event study, mirroring R `did_multiplegt_dyn(..., by_path=k)`. Activated via `ChaisemartinDHaultfoeuille(by_path=k, drop_larger_lower=False)` where `k` is a positive integer (top-k most common observed paths by switcher-group frequency). **Window convention:** the path tuple for a switcher group `g` is `(D_{g, F_g-1}, D_{g, F_g}, ..., D_{g, F_g-1+L_max})` — length `L_max + 1`, matching R's window `[F_{g-1}, F_{g-1+l}]`. **Ranking:** paths are ranked by descending frequency; ties are broken lexicographically on the path tuple for deterministic ordering, so every selected path has a unique `frequency_rank`. If `by_path` exceeds the number of observed paths, all observed paths are returned with a `UserWarning`. **Per-path SE convention (joiners/leavers precedent):** the per-path influence function follows the joiners-only / leavers-only IF construction at `chaisemartin_dhaultfoeuille.py:5495-5504`: the switcher-side contribution `+S_g * (Y_{g,out} - Y_{g,ref})` is zeroed for groups whose observed trajectory is NOT the selected path; control contributions and the full cohort structure `(D_{g,1}, F_g, S_g)` are unchanged. After applying the singleton-baseline eligible mask and cohort-recentering with the original cohort IDs, the plug-in SE uses the path-specific divisor `N_l_path` (count of path switchers eligible at horizon `l`) — same pattern as `joiners_se` using `joiner_total`. This gives the **within-path mean** estimand `DID_{path,l}` as the within-path average of `DID_{g,l}`. **Degenerate-cohort behavior per path:** when a path's centered IF at some horizon is identically zero (every variance-eligible path switcher forms its own `(D_{g,1}, F_g, S_g)` cohort, or the path has a single contributing group), SE / t_stat / p_value / conf_int are NaN-consistent and a `UserWarning` is emitted scoped to `(path, horizon)`. This mirrors the overall-path degenerate-cohort surface and is common for rare paths with few contributing groups. **Empty-state contract:** `results.path_effects` distinguishes "not requested" (`None`) from "requested but empty" (`{}` — all switchers have windows outside the panel or unobserved cells). The empty-dict case emits a `UserWarning` at fit-time and renders as an explicit "no observed paths" notice in `summary()`; `to_dataframe(level="by_path")` returns an empty DataFrame with the canonical column set (mirrors the `linear_trends` pattern when `trends_linear=True` but no horizons survive). **Requirements:** `drop_larger_lower=False` (multi-switch groups are the object of interest; default `True` filters them out) and `L_max >= 1` (path window depends on the horizon). **Scope:** combinations with `design2` and `honest_did` remain gated behind explicit `NotImplementedError` (deferred to follow-up wave PRs); `heterogeneity` is supported per-path — see the **Per-path heterogeneity testing** paragraph below. `n_bootstrap > 0` is now supported — see the **Bootstrap SE** paragraph below. `survey_design` is supported under analytical Binder TSL and replicate-weight bootstrap — see the **Per-path survey-design SE** paragraph below; multiplier bootstrap (`n_bootstrap > 0`) under `survey_design + by_path/paths_of_interest` remains gated. `placebo=True` is now supported per-path — see the **Per-path placebos** paragraph below. **TWFE diagnostic** remains a sample-level summary (not computed per path) in this release. Results are exposed on `results.path_effects` as `Dict[Tuple[int, ...], Dict[str, Any]]` with nested `horizons` dicts per horizon `l`, and on `results.to_dataframe(level="by_path")` as a long-format table with columns `[path, frequency_rank, n_groups, horizon, effect, se, t_stat, p_value, conf_int_lower, conf_int_upper, n_obs, cband_lower, cband_upper, cumulated_effect, cumulated_se]` (the `cband_*` columns are added by the joint sup-t Note below, populated for positive-horizon rows of paths with a finite sup-t crit and NaN otherwise; the `cumulated_*` columns are added by the per-path linear-trends Note below, populated for positive-horizon rows when `trends_linear=True` is set and NaN otherwise). Gated tests live in `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathGates` / `::TestByPathBehavior` / `::TestByPathEdgeCases`. **R-parity** against `DIDmultiplegtDYN 2.3.3` is confirmed at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPath` via two scenarios: `mixed_single_switch_by_path` (2 paths, `by_path=2`) and `multi_path_reversible_by_path` (4 paths, `by_path=3`; path-assignment deterministic on `F_g` so each `(D_{g,1}, F_g, S_g)` cohort contains switchers from a single path). Per-path point estimates and per-path switcher counts match R exactly; per-path SE matches within the Phase 2 multi-horizon SE envelope (observed rtol ≤ 10.2% on the 2-path mixed scenario, ≤ 4.2% on the 4-path cohort-clean scenario). **Deviation from R (cross-path cohort-sharing SE):** our analytical SE is the marginal variance of the path-contribution estimator cohort-centered on the *full-panel* cohort structure (joiners/leavers precedent — non-path switchers contribute to cohort means via their zeroed switcher row). R's `did_multiplegt_dyn(..., by_path=k)` re-runs the estimator per path, so cohort means are computed over the path's own switchers only. When a cohort `(D_{g,1}, F_g, S_g)` spans multiple observed paths, Python and R SE diverge materially (our empirical probes with random post-window toggling saw rtol > 100%); when every cohort is single-path (scenario 13 by design, scenario 14 by construction), the two approaches coincide up to the documented Phase 2 envelope. Practitioners with cohort structures that mix paths should interpret the per-path SE as a within-full-panel marginal variance, not a per-path conditional variance. **Bootstrap SE:** when `n_bootstrap > 0` is set, the top-k paths are enumerated once on the observed data (R-faithful: matches `did_multiplegt_dyn(..., by_path=k, bootstrap=B)`'s path-stability convention — verified empirically against DIDmultiplegtDYN 2.3.3) and the multiplier bootstrap (`bootstrap_weights ∈ {"rademacher", "mammen", "webb"}`) runs per `(path, horizon)` target via the shared `_bootstrap_one_target` / `compute_effect_bootstrap_stats` helpers. Point estimates are unchanged from the analytical path. Bootstrap SE replaces the analytical SE in `path_effects[path]["horizons"][l]["se"]`, and `p_value` / `conf_int` are taken as the **bootstrap percentile** statistics, matching the Round-10 library convention for overall / joiners / leavers / multi-horizon bootstrap (see the `Note (bootstrap inference surface)` elsewhere in this file and the pinned regression `test_bootstrap_p_value_and_ci_propagated_to_top_level`). `t_stat` is SE-derived via `safe_inference` per the anti-pattern rule. Interpretation: inference is *conditional on the observed path set*. **SE inherits the analytical cross-path cohort-sharing deviation:** the bootstrap input is the exact same full-panel cohort-centered path IF that the analytical path computes (`_collect_path_bootstrap_inputs` reuses the same enumeration / cohort IDs / IF construction), so the bootstrap SE is a Monte Carlo analog of the analytical SE — it inherits the same cross-path cohort-sharing deviation from R's per-path re-run convention documented above. On single-path-cohort panels (scenarios 13 and 14 of the R-parity fixture, and any DGP where `(D_{g,1}, F_g, S_g)` cohorts never span multiple observed paths), bootstrap SE tracks analytical SE up to Monte Carlo noise and both coincide with R up to the Phase 2 envelope. On cross-path cohort panels, bootstrap SE inherits the >100% rtol divergence from R that analytical already has. **Deviation from R (CI method):** R's per-path CI is normal-theory around the bootstrap SE (half-width ≈ `1.96·se`); ours is the bootstrap percentile CI, intentionally diverging from R to keep the dCDH inference surface internally consistent across all bootstrap targets. Practitioners who want *unconditional* inference capturing path-selection uncertainty need a pairs-bootstrap (deferred — no R precedent). Positive regressions live in `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathBootstrap` (gated `@pytest.mark.slow`): point-estimate invariance, finite positive SE on non-degenerate panels, SE-within-30%-rtol of analytical on cohort-clean fixtures, degenerate-cohort NaN propagation, Rademacher/Mammen/Webb parity, seed reproducibility, and percentile-vs-normal-theory CI pinning. **Per-path placebos:** when `placebo=True` (and `L_max >= 1`) is combined with `by_path=k`, per-path backward-horizon placebos `DID^{pl}_{path, l}` for `l = 1..L_max` are computed using the same joiners/leavers IF precedent applied to `_compute_per_group_if_placebo_horizon` (with the new `switcher_subset_mask` parameter): switcher contributions are zeroed for groups not in the path; the control pool and the variance-eligible cohort structure `(D_{g,1}, F_g, S_g)` are unchanged. Plug-in SE uses the path-specific divisor `N^{pl}_{l, path}` (count of path switchers eligible at backward lag `l`). Surfaced on `results.path_placebo_event_study[path][-l]` with the same `{effect, se, t_stat, p_value, conf_int, n_obs}` shape as `placebo_event_study` (negative-int inner keys parallel the existing per-path event-study positive-int keys, so a unified forward+backward view is well-formed). **Inherits the cross-path cohort-sharing SE deviation from R** documented above for `path_effects` (same convention applied backward); tracks R within numerical tolerance on single-path-cohort panels and diverges on cohort-mixed panels. Multiplier bootstrap (when `n_bootstrap > 0`) runs per `(path, lag)` target via the same `_bootstrap_one_target` dispatch used for the per-path event-study, with the canonical NaN-on-invalid contract. The bootstrap SE is a Monte Carlo analog of the analytical placebo SE — same per-path centered IF input — and inherits the same deviation. Surfaced through `summary()` (negative-keyed rows rendered alongside positive-keyed event-study rows under each path block) and `to_dataframe(level="by_path")` (`horizon` column takes negative ints for placebo rows). **Empty-state contract:** `results.path_placebo_event_study` mirrors `path_effects` — `None` when `by_path + placebo` was not requested, `{}` when requested but no observed path has a complete window within the panel (same regime that returns `{}` for `path_effects`, with the same fit-time `UserWarning`). R-parity is confirmed at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPathPlacebo` on the `multi_path_reversible_by_path_placebo` scenario; positive analytical + bootstrap invariants live in `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathPlacebo` (with the gated `::TestByPathPlacebo::TestBootstrap` subclass). **Per-path covariate residualization (DID^X):** when `controls=[...]` is set with `by_path=k`, the per-baseline OLS residualization (Web Appendix Section 1.2) runs once on the first-differenced outcome BEFORE path enumeration. All four downstream surfaces — analytical per-path SE, bootstrap SE, per-path placebos, and per-path joint sup-t bands — consume the residualized `Y_mat` automatically (Frisch-Waugh-Lovell). Per-period effects remain unadjusted, consistent with the existing `controls` + per-period DID contract (per-period DID does not support residualization). Failed-stratum baselines (rank-deficient X) zero out `N_mat` for affected groups, which the path enumeration treats as ineligible per its existing convention. **Deviation from R on multi-baseline switcher panels (point estimates):** R `did_multiplegt_dyn(..., by_path, controls)` re-runs the per-baseline residualization on each path's restricted subsample (`R/R/did_multiplegt_dyn.R` lines 401-405: rows of the path's switchers OR rows where `yet_to_switch=1 AND baseline matches the path's baseline`). The first-stage residualization sample R uses for path B equals: pre-switch rows of all switchers with matching baseline + all rows of never-switchers with matching baseline — bit-identical to our global first-stage sample under single-baseline switcher panels (every switcher shares the same `D_{g,1}`, regardless of how `F_g` or path identity varies across switchers). Per-path point estimates therefore coincide with R on those panels up to the existing **DID^X first-stage cell-weighting deviation** documented above in `Note (Phase 3 DID^X covariate adjustment)` (Python's first-stage OLS uses equal cell weights — one observation per `(g, t)` cell, consistent with the library's cell-aggregated input convention; R weights by `N_gt`). On panels with one observation per `(g, t)` cell (the common case after the cell-aggregation step in `fit()`), Python matches R bit-exactly: the `multi_path_reversible_by_path_controls` parity fixture has 4 paths with switcher `F_g` values spanning [0..6] under `D_{g,1}=0` and Python matches R to rtol ~1e-11. On multi-baseline switcher panels (some switchers have `D_{g,1}=0`, others have `D_{g,1}=1`) R's per-path subset drops switchers whose baseline differs from the path's baseline, so the per-baseline regression coefficients diverge per path under R and point estimates can diverge between Python and R — a `UserWarning` is emitted at fit-time when this configuration is detected so practitioners do not silently consume estimates that disagree with R. The warning filters to switcher groups only; never-switchers (never-treated + always-treated controls) at multiple baseline values do NOT trigger the warning because they don't affect R's per-path subset construction. **Inherits the cross-path cohort-sharing SE deviation from R** documented above for `path_effects` — bootstrap SE, placebo SE, and sup-t crit are Monte Carlo / joint-distribution analogs of the same residualized analytical IF and carry the same deviation. R-parity is confirmed against `did_multiplegt_dyn(..., by_path=3, controls="X1")` at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPathControls` on the `multi_path_reversible_by_path_controls` scenario (single-baseline DGP, exact point-estimate match measured rtol ~1e-11); cross-surface inheritance and the multi-baseline warning are regression-tested at `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathControls` (analytical + bootstrap + placebo + sup-t + `to_dataframe(level="by_path")` cband columns + multi-baseline `UserWarning`). **Per-path linear-trends DID^{fd}:** when `trends_linear=True` is set with `by_path=k`, the first-differencing transform at `chaisemartin_dhaultfoeuille.py:1599-1630` runs once globally BEFORE path enumeration (replaces `Y_mat` with `Z_mat = Y_t - Y_{t-1}` and shrinks the time axis by one), 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)` per the existing parity test pivot at `tests/test_chaisemartin_dhaultfoeuille_parity.py:403-409`) surface on the new `results.path_cumulated_event_study[path][l]` field — a per-group running sum of `DID^{fd}_{g, l'}` averaged over the path's switchers eligible at horizon `l`, mirroring the global `linear_trends_effects` cumulation logic at `chaisemartin_dhaultfoeuille.py:3340-3398`. SE on the cumulated layer is the conservative upper bound (sum of per-horizon component SEs from `path_effects[path]["horizons"][l]["se"]`, NaN-consistent: any non-finite component yields a NaN cumulated SE). **Post-bootstrap recomputation:** the cumulated layer is built AFTER the bootstrap propagation block at `chaisemartin_dhaultfoeuille.py:3034-3081` so it reads the FINAL post-bootstrap per-horizon SEs (mirrors the global `linear_trends_effects` placement). When `n_bootstrap > 0`, cumulated SE / t / p / CI are derived from bootstrap per-horizon SEs; when bootstrap produces non-finite SE (e.g., `n_bootstrap=1` degenerate distribution), the cumulated layer's full inference tuple is NaN per the library-wide NaN-on-invalid bootstrap contract. `to_dataframe(level="by_path")` exposes `cumulated_effect` and `cumulated_se` columns (always present, NaN-when-None — mirrors the `cband_*` always-present convention from PR #374). `summary()` renders a `Cumulated Level Effects (DID^{fd}, trends_linear)` sub-section under each per-path block. **Path enumeration uses 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 at line 1620 surfaces the issue), so a path whose switchers all have `F_g < 3` is silently absent from `path_effects` rather than present-with-NaN. **F_g=3 boundary-case divergence (`by_path + trends_linear`):** `F_g=3` switchers have exactly 2 pre-switch periods, which after first-differencing and the `time==1` filter leaves only 1 valid pre-window Z value. R's per-path full-pipeline call handles this single-pre-period regime differently from Python's global-then-disaggregate architecture, producing 30%+ relative divergence on point estimates for paths whose switchers include `F_g=3` (empirically observed on the parity fixture's earlier `F_g=3` variant). A separate `UserWarning` fires at fit-time when the panel includes any `F_g=3` switcher AND `by_path + trends_linear` is set, mirroring the `F_g < 3` exclusion warning. The shipped parity fixture (`single_baseline_multi_path_by_path_trends_lin`) restricts to `F_g >= 4` exclusively to avoid this regime; per-path R parity is asserted only there. **Placebo under `trends_linear` returns RAW per-horizon values** (no per-path placebo cumulation surface) — verified empirically against the existing `joiners_only_trends_lin` parity fixture: R's per-path Placebo_l matches Python's `path_placebo_event_study[path][-l]` (raw) bit-exactly under non-`by_path` trends_lin. **Deviation from R on multi-baseline switcher panels (point estimates):** R `did_multiplegt_dyn(..., by_path, trends_lin)` re-runs the full pipeline (including first-differencing) on each path's restricted subsample, so it operates on different switcher samples per path when switchers have different baseline values `D_{g,1}`. Python first-differences once globally before path enumeration. On single-baseline switcher panels the two architectures coincide; on multi-baseline switcher panels per-path point estimates can diverge — a `UserWarning` is emitted at fit-time when this configuration is detected so practitioners do not silently consume estimates that disagree with R (mirroring the analogous `by_path + controls` warning). Per-path R parity is confirmed against `did_multiplegt_dyn(..., by_path=3, trends_lin=TRUE, placebo=1)` at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPathTrendsLinear` on the `single_baseline_multi_path_by_path_trends_lin` scenario (single-baseline + cohort-single-path + `F_g >= 4` DGP designed to eliminate the multi-baseline divergence, the cross-path cohort-sharing deviation, and the F_g=3 boundary case under R's per-path full-pipeline call). Per-path cumulated point estimates match R bit-exactly (rtol ~1e-9) on event horizons under those conditions; cumulated SE_RTOL is widened to `0.20` (vs `0.12` used for non-cumulated by_path parity) because the conservative upper-bound SE compounds the cross-path cohort-sharing deviation under summation. **Placebo parity is intentionally skipped for `trends_linear`**: 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, producing a sign-and-magnitude divergence on paths whose switchers have minimal pre-window depth (e.g., `F_g=4` switchers). Placebo under `by_path + trends_linear` is exercised via internal regression in `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathTrendsLinear` (finite values, bootstrap inheritance) but not pinned to R bit-by-bit. Cross-surface invariants (analytical + bootstrap + placebo + sup-t + `path_cumulated_event_study` + `to_dataframe` columns + `summary()` rendering) are regression-tested at `TestByPathTrendsLinear`. **Per-path state-set trends:** when `trends_nonparam="state_col"` is set with `by_path=k`, the set membership column is validated and stored once globally as `set_ids_arr` (time-invariance, NaN rejection, partition-coarseness checks unchanged from the non-by_path path). The `set_ids` parameter is 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. R does NOT first-difference and does NOT cumulate under `trends_nonparam` (unlike `trends_lin`); per-horizon `Effect_l` is a normal DID with set-restricted controls. Per-path R parity is confirmed against `did_multiplegt_dyn(..., by_path=3, trends_nonparam="state", placebo=1)` at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPathTrendsNonparam` on the `multi_path_reversible_by_path_trends_nonparam` scenario; per-path point estimates AND placebos match R bit-exactly (rtol ~1e-9), per-path SE matches within the Phase 2 envelope (~13% rtol observed). Cross-surface invariants are regression-tested at `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathTrendsNonparam`. **Per-path non-binary treatment:** integer-coded discrete treatment (D in Z, e.g. ordinal {0, 1, 2}) is supported under `by_path=k` and `paths_of_interest`. Path tuples become integer-state tuples (`(0, 2, 2, 2)`) keyed bit-for-bit against R's comma-separated path strings (`"0,2,2,2"`) for D in {0..9}. Continuous D (e.g. `1.5`) raises `ValueError` at fit-time per the no-silent-failures contract — the existing `int(round(float(v)))` cast in `_enumerate_treatment_paths` is now defensive (no-op for integer-coded D). **Deviation from R for D >= 10:** R's `did_multiplegt_by_path` derives the per-path baseline via `path_index$baseline_XX <- substr(path_index$path, 1, 1)` (extracted 2026-05-03 via `Rscript -e 'cat(paste(deparse(DIDmultiplegtDYN:::did_multiplegt_by_path), collapse="\n"))'`), capturing only the first character of the comma-separated path string. For D >= 10 this captures `"1"` instead of `"12"` for `path = "12,12,..."`, mis-allocating R's per-path control-pool subset. Python's tuple-key matching is correct in this regime; the per-path point estimates we compute are correct, R's per-path subset for the same path is buggy. The shipped parity scenario stays in `D in {0, 1, 2}` to avoid the R bug; R-parity for D in {0..9} is asserted at `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityByPathNonBinary` on the `multi_path_reversible_by_path_non_binary` scenario (78 switchers, 3 paths, single-baseline custom DGP, F_g >= 4) — per-path point estimates match R bit-exactly (rtol ~1e-9 events; rtol+atol envelope for placebo near-zero values), SE inherits the documented cross-path cohort-sharing deviation (~5% rtol observed; SE_RTOL=0.15 envelope). Cross-surface invariants regression-tested at `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathNonBinary`. **Per-path survey-design SE** (analytical Binder TSL + replicate-weight bootstrap): under `by_path` / `paths_of_interest` + `survey_design`, the per-path per-horizon SE routes through `_survey_se_from_group_if` using the cell-period allocator. The per-path influence function `U_pp_l_path` is the per-period IF with non-path switcher-side contributions skipped — control contributions remain unchanged, matching the joiners/leavers IF convention from the **Per-path SE convention** paragraph above (the `switcher_subset_mask` zeroes the switcher row of the per-group IF, which trivially zeroes the corresponding row of the per-cell IF, preserving the row-sum identity `U_pp.sum(axis=1) == U`). The IF is cohort-recentered via `_cohort_recenter_per_period` and expanded to observations as `psi_i = U_pp[g_i, t_i] · (w_i / W_{g_i, t_i})`. Replicate-weight designs unconditionally route through the cell allocator (Class A contract, PR #323). Multiplier bootstrap (`n_bootstrap > 0`) under `survey_design + by_path/paths_of_interest` raises `NotImplementedError` at fit-time — the survey-aware perturbation pivot for path-restricted IFs is methodologically underived and deferred to a future wave; the global non-by_path TSL multiplier bootstrap is unaffected and continues to ship. **Path-enumeration ranking is unweighted** under `survey_design`: top-k selection uses group cardinality (`path_to_count[p]` = number of groups), not population-weight mass — survey weights do not affect which paths are selected as "top-k". A weighted-ranking variant (sum of survey weights per path) is deferred until concrete demand. **`df_survey` propagation:** under replicate weights, every per-path per-horizon fit contributes an `n_valid` count to the shared `_replicate_n_valid_list` accumulator and the final `_effective_df_survey = min(...) - 1` reflects all per-path replicate fits. A post-call `_refresh_path_inference` helper re-runs `safe_inference` on every populated entry so `multi_horizon_inference`, `placebo_horizon_inference`, `path_effects`, and `path_placebos` all use the same final df after per-path appends complete. **Lonely-PSU policy is sample-wide, not per-path** — the `lonely_psu` policy (`remove`/`certainty`/`adjust`) operates on the full design-level PSU/strata structure, not on path-restricted subsamples. **Telescope invariant:** on a single-path panel where every switcher follows the same trajectory and `eligible_groups` matches between by_path and non-by_path, per-path SE equals the global non-by_path survey SE bit-exactly — pinned at `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathSurveyDesignTelescope::test_telescope_analytical_TSL`. **Deviation from R:** none — R `did_multiplegt_dyn` does not support survey weighting, so this is a Python-only methodology extension (no R parity available; no R parity test class). Regression test anchor: `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathSurveyDesignAnalytical` covering analytical SE, replicate-weight SE, the `n_bootstrap` gate, the global anti-regression, per-path placebos, `trends_linear` composition, and unobserved-path warnings under survey. **Per-path heterogeneity testing** (analytical OLS / WLS + survey-aware Binder TSL + replicate-weight): under `by_path` / `paths_of_interest` + `heterogeneity="<col>"`, the per-path per-horizon coefficient `beta_X^path_l` is computed by re-running `_compute_heterogeneity_test` on the path-restricted switcher subsample. The path filter (`path_groups: Optional[Set[int]]`) restricts eligibility to switchers ON path `p` inside the inner regression; the variance machinery (standard WLS vcov for non-survey, cell-period IF allocator for Binder TSL, group-level allocator for Rao-Wu replicate) is unchanged from the global heterogeneity path. **Cohort dummies absorb baseline by construction** — the cohort key `(D_{g,1}, F_g, S_g)` includes baseline, so multi-baseline switcher panels do not produce R-divergence (unlike `controls` / `trends_linear`); no parallel `UserWarning` is emitted. **R parity:** matches `did_multiplegt_dyn(..., by_path, predict_het)` per-by_level on the `multi_path_reversible_by_path_predict_het` scenario (rtol ~1e-6 on point estimates AND SE), inheriting the SAME tolerance as the new global `multi_path_reversible_predict_het` scenario (`TestDCDHDynRParityHeterogeneity`) since the per-path R call is `did_multiplegt_main(..., predict_het=...)` per path-restricted subsample with no additional numerical loss. R's `dont_drop_larger_lower=TRUE` is set in both fixture scenarios to match the Python `drop_larger_lower=False` requirement. **Survey composition:** inherits from the **Per-path survey-design SE** paragraph above — analytical Binder TSL routes through `_survey_se_from_group_if`'s cell-period allocator on the post-period of the transition; replicate-weights route through the group-level allocator. Multiplier bootstrap (`n_bootstrap > 0`) under `by_path + heterogeneity + survey_design` inherits the existing per-path multiplier-bootstrap-survey gate. **`df_survey` propagation:** every per-(path, horizon) replicate-weight fit appends `n_valid` to the shared `_replicate_n_valid_list` accumulator; per-path heterogeneity inference is refreshed with the FINAL `_effective_df_survey(...)` in the R2 P1b refresh block (separate dedicated loop because the schema shape is `{path: {l: {...}}}` rather than `{path: {"horizons": {l: {...}}}}`). **Result schema:** `results.path_heterogeneity_effects: Dict[Tuple[int, ...], Dict[int, Dict[str, Any]]]` keyed `{path: {l: {beta, se, t_stat, p_value, conf_int, n_obs}}}`. Empty-state contract mirrors `path_effects`: `None` when not requested, `{}` when requested but no path has eligible switchers. **DataFrame integration:** `to_dataframe(level="by_path")` adds always-present `het_*` columns (`het_beta`, `het_se`, `het_t_stat`, `het_p_value`, `het_conf_int_lower`, `het_conf_int_upper`), populated for positive-horizon rows when `heterogeneity` is set and NaN otherwise (mirrors the `cband_*` and `cumulated_*` always-present convention). Placebo rows (negative `horizon`) have NaN in `het_*` columns: per-path placebo heterogeneity is not exposed in this release (R does not ship per-path predict_het on placebos either, so parity is preserved by deferral). Regression test anchors: `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathHeterogeneity` (gate dispatch, behavior, telescope-to-global on single-path panel, zero-signal anti-regression, multi-baseline UserWarning anti-regression, DataFrame integration, edge cases) + `tests/test_chaisemartin_dhaultfoeuille_parity.py::TestDCDHDynRParityHeterogeneity` (global anchor, FIRST `predict_het` parity baseline) + `::TestDCDHDynRParityByPathHeterogeneity` (per-path).
+
+**Per-path user-specified path selection (`paths_of_interest`):** Python-only API extension — R's `did_multiplegt_dyn(..., by_path=k)` only accepts a positive int (top-k automatic ranking) or `-1` (all observed paths) and provides no list-based selection. Activated via `ChaisemartinDHaultfoeuille(paths_of_interest=[(0, 1, 1, 1), (0, 1, 0, 0)], drop_larger_lower=False)` as an alternative to `by_path=k`; the two are **mutually exclusive** (setting both raises `ValueError` at `__init__` and `set_params` time). Each path tuple must have length `L_max + 1`; the type / element / non-empty / length-uniformity checks fire at `__init__`, the length-vs-L_max check fires at fit-time. `bool` and `np.bool_` are explicitly rejected; `np.integer` is accepted and canonicalized to Python `int` for tuple-key consistency. Duplicates emit a `UserWarning` and are deduplicated; paths not observed in the panel emit a `UserWarning` and are omitted from `path_effects`. Paths appear in `results.path_effects` in the user-specified order, modulo deduplication and unobserved-path filtering. Composes with non-binary D and all downstream `by_path` surfaces (bootstrap, per-path placebos, per-path joint sup-t bands, `controls`, `trends_linear`, `trends_nonparam`) — mechanical filter on observed paths, no methodology change. Behavior + cross-feature regressions live at `tests/test_chaisemartin_dhaultfoeuille.py::TestPathsOfInterest`.
 
 - **Note (Phase 3 `by_path` per-path joint sup-t bands):** When `n_bootstrap > 0` is set with `by_path=k`, per-path joint sup-t simultaneous confidence bands are computed across horizons `1..L_max` within each path. **Methodology:** a single `(n_bootstrap, n_eligible)` multiplier weight matrix (using the estimator's configured `bootstrap_weights` — Rademacher / Mammen / Webb) is drawn per path and broadcast across all horizons of that path, producing correlated bootstrap distributions across horizons within the path. The path-specific critical value `c_p = quantile(max_l |t_l|, 1 - α)` is then used to construct symmetric joint bands `effect_l ± c_p · se_l` per horizon, surfaced in `path_effects[path]["horizons"][l]["cband_conf_int"]` and at top-level `results.path_sup_t_bands[path] = {"crit_value", "alpha", "n_bootstrap", "method", "n_valid_horizons"}`. **Gates:** a path must have `>= 2` valid horizons (finite bootstrap SE > 0) AND a strict majority (more than 50%) of finite sup-t draws to receive a band; otherwise the path is absent from `path_sup_t_bands`. Both gates mirror the OVERALL `event_study_sup_t_bands` semantics at `chaisemartin_dhaultfoeuille_bootstrap.py:605,612`: `len(valid_horizons) >= 2` AND `finite_mask.sum() > 0.5 * n_bootstrap`. Exactly half-finite draws are NOT enough — the gate is strictly greater than half. **Empty-state contract:** `path_sup_t_bands is None` when not requested (no bootstrap, or both `by_path` and `paths_of_interest` are `None`); `{}` when requested but no path passes both gates. **`to_dataframe(level="by_path")` integration:** the table now includes `cband_lower` / `cband_upper` columns for parity with OVERALL `level="event_study"`; populated for positive-horizon rows of paths with a finite sup-t crit, NaN for placebo rows / unbanded paths / the requested-but-empty fallback DataFrame. **Methodology asymmetry vs OVERALL:** OVERALL sup-t reuses the same multi-horizon shared-draw distribution for both the SE in the t-stat denominator and the bootstrap distribution in the numerator. The per-path sup-t draws a fresh shared weight matrix per path AFTER the per-path SE bootstrap block has already populated `results.path_ses` via independent per-(path, horizon) draws — numerator: fresh shared draws, denominator: bootstrap SEs from the earlier independent draws. Asymptotically equivalent to OVERALL's self-consistent reuse, but NOT bit-identical. The fresh draw is intentional: it preserves RNG-state isolation and keeps every existing per-path SE seed-reproducibility test bit-stable post-implementation. **Inherited deviation from R:** the bootstrap SE used as the t-stat denominator carries the cross-path cohort-sharing SE deviation from R documented for `path_effects` above; the per-path sup-t crit therefore inherits the same deviation. **Interpretation:** the band covers joint inference *within a single path across horizons*; it does NOT provide simultaneous coverage *across paths* (a different inference target requiring a `path × horizon` re-derivation, deferred to a future wave). **Deviation from R:** `did_multiplegt_dyn` provides no joint / sup-t / simultaneous bands at any surface — this is a Python-only methodology extension, consistent with the existing OVERALL `event_study_sup_t_bands` (also Python-only). Regression test anchor: `tests/test_chaisemartin_dhaultfoeuille.py::TestByPathSupTBands`.
 
diff --git a/tests/test_chaisemartin_dhaultfoeuille.py b/tests/test_chaisemartin_dhaultfoeuille.py
index ccaba2e9..f7d496f6 100644
--- a/tests/test_chaisemartin_dhaultfoeuille.py
+++ b/tests/test_chaisemartin_dhaultfoeuille.py
@@ -3828,19 +3828,17 @@ def test_requires_lmax(self):
     @pytest.mark.parametrize(
         "fit_kwargs, msg",
         [
-            # NB: prior `controls` (Wave 3 #5), `trends_linear`, and
-            # `trends_nonparam` (Wave 3 #6+#7) entries were removed
-            # when their gates were lifted. After gate removal, those
-            # combinations either fit successfully (controls passes
-            # column-validation; trends_linear/trends_nonparam route
-            # to their respective code paths) or raise a non-
-            # NotImplementedError specific to the parameter (e.g.,
-            # trends_nonparam=group raises a partition-coarseness
-            # ValueError because the set partition equals the group
-            # partition). Coverage for those combinations now lives
-            # in `TestByPathControls`, `TestByPathTrendsLinear`, and
-            # `TestByPathTrendsNonparam`.
-            ({"heterogeneity": "group"}, "heterogeneity"),
+            # NB: prior `controls` (Wave 3 #5), `trends_linear` /
+            # `trends_nonparam` (Wave 3 #6+#7), and `heterogeneity`
+            # (Wave 5 #11) entries were removed when their gates were
+            # lifted. After gate removal, those combinations either fit
+            # successfully (heterogeneity routes to
+            # path_heterogeneity_effects; controls passes column-
+            # validation; trends_linear/trends_nonparam route to their
+            # respective code paths) or raise a non-NotImplementedError
+            # specific to the parameter. Coverage for those combinations
+            # now lives in `TestByPathControls`, `TestByPathTrendsLinear`,
+            # `TestByPathTrendsNonparam`, and `TestByPathHeterogeneity`.
             ({"design2": True}, "design2"),
             ({"honest_did": True}, "honest_did"),
         ],
@@ -9924,3 +9922,681 @@ def test_telescope_analytical_TSL(self):
                 res_g.event_study_effects[l_h]["se"],
                 atol=1e-12,
             )
+
+
+# ===========================================================================
+# Wave 5 #11: by_path / paths_of_interest + heterogeneity testing
+# ===========================================================================
+
+
+def _by_path_het_data(seed=44, n_switchers=90, n_controls=30, n_periods=10):
+    """Multi-path panel with binary `het_x` covariate.
+
+    Layered on `TestHeterogeneityTesting._make_panel_with_het` shape
+    (binary het_x, half each) plus multi-path structure (3 paths, F_g
+    independent of path so each path has multiple cohorts). Includes
+    never-treated controls so the heterogeneity regression has cohort
+    variation at every horizon under the reversal-path eligibility
+    filter (cf. PR #408 R parity preflight: without controls, R drops
+    reversal paths past horizon 1 leaving a single cohort and triggering
+    empty-cohort-dummy errors). Outcome: 0.5*t + (5 + 3*het_x) * D + N(0, 0.5).
+    """
+    rng = np.random.RandomState(seed)
+    rows = []
+    paths = [(0, 1, 1, 1), (0, 1, 0, 0), (0, 1, 1, 0)]
+    for g in range(n_switchers):
+        F_g = 3 + ((g // 3) % 3)  # F_g in {3,4,5}
+        path = paths[g % 3]
+        het_x = 1 if g < n_switchers // 2 else 0
+        effect = 5.0 + 3.0 * het_x
+        for t in range(n_periods):
+            if F_g - 1 <= t < F_g - 1 + len(path):
+                d = path[t - (F_g - 1)]
+            elif t >= F_g - 1 + len(path):
+                d = path[-1]
+            else:
+                d = 0
+            y = 0.5 * t + effect * d + rng.normal(0, 0.5)
+            rows.append({
+                "group": g, "period": t, "treatment": d,
+                "outcome": y, "het_x": het_x,
+            })
+    # Never-treated controls (D=0 throughout), het_x balanced
+    for k in range(n_controls):
+        het_x = 1 if k < n_controls // 2 else 0
+        g = n_switchers + k
+        for t in range(n_periods):
+            y = 0.5 * t + rng.normal(0, 0.5)
+            rows.append({
+                "group": g, "period": t, "treatment": 0,
+                "outcome": y, "het_x": het_x,
+            })
+    return pd.DataFrame(rows)
+
+
+class TestByPathHeterogeneity:
+    """Per-path heterogeneity (Wave 5 #11) — composes ``by_path`` /
+    ``paths_of_interest`` with ``heterogeneity="<col>"``.
+
+    R parity coverage in
+    ``tests/test_chaisemartin_dhaultfoeuille_parity.py::
+    TestDCDHDynRParityByPathHeterogeneity``.
+    """
+
+    # Gate dispatch: lifts no longer raise
+
+    def test_no_longer_raises_on_heterogeneity(self):
+        """``by_path=k`` + ``heterogeneity`` no longer raises."""
+        df = _by_path_het_data()
+        est = ChaisemartinDHaultfoeuille(drop_larger_lower=False, by_path=2)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            res = est.fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3, heterogeneity="het_x",
+            )
+        assert res.path_heterogeneity_effects is not None
+
+    def test_paths_of_interest_with_heterogeneity_no_longer_raises(self):
+        """``paths_of_interest`` + ``heterogeneity`` no longer raises."""
+        df = _by_path_het_data()
+        est = ChaisemartinDHaultfoeuille(
+            drop_larger_lower=False,
+            paths_of_interest=[(0, 1, 1, 1), (0, 1, 0, 0)],
+        )
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            res = est.fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3, heterogeneity="het_x",
+            )
+        assert res.path_heterogeneity_effects is not None
+
+    def test_heterogeneity_still_rejects_controls_under_by_path(self):
+        """``heterogeneity + controls`` mutex still fires under by_path."""
+        df = _by_path_het_data()
+        df["X1"] = np.random.RandomState(42).normal(0, 1, len(df))
+        with pytest.raises(ValueError, match="cannot be combined with controls"):
+            ChaisemartinDHaultfoeuille(
+                drop_larger_lower=False, by_path=2
+            ).fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3,
+                heterogeneity="het_x", controls=["X1"],
+            )
+
+    def test_heterogeneity_still_rejects_trends_linear_under_by_path(self):
+        """``heterogeneity + trends_linear`` mutex still fires under by_path."""
+        df = _by_path_het_data()
+        with pytest.raises(
+            ValueError, match="cannot be combined with trends_linear"
+        ):
+            ChaisemartinDHaultfoeuille(
+                drop_larger_lower=False, by_path=2
+            ).fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3,
+                heterogeneity="het_x", trends_linear=True,
+            )
+
+    def test_heterogeneity_still_rejects_trends_nonparam_under_by_path(self):
+        """``heterogeneity + trends_nonparam`` mutex still fires under by_path."""
+        df = _by_path_het_data()
+        df["state"] = df["group"] % 3
+        with pytest.raises(
+            ValueError, match="cannot be combined with trends_nonparam"
+        ):
+            ChaisemartinDHaultfoeuille(
+                drop_larger_lower=False, by_path=2
+            ).fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3,
+                heterogeneity="het_x", trends_nonparam="state",
+            )
+
+    # Behavior
+
+    def test_per_path_heterogeneity_finite_under_known_signal(self):
+        """Detects positive heterogeneity on the path that contains the
+        effect-varying switchers."""
+        df = _by_path_het_data()
+        est = ChaisemartinDHaultfoeuille(drop_larger_lower=False, by_path=3)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            res = est.fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3, heterogeneity="het_x",
+            )
+        assert res.path_heterogeneity_effects
+        # At horizon 1 every path has switchers; heterogeneity beta should
+        # be positive (DGP: effect = 5 + 3*het_x).
+        for path, horizons in res.path_heterogeneity_effects.items():
+            assert 1 in horizons
+            assert np.isfinite(horizons[1]["beta"])
+            assert np.isfinite(horizons[1]["se"])
+            assert horizons[1]["beta"] > 0, (
+                f"path={path} l=1: expected positive het beta "
+                f"(DGP: 5 + 3*het_x), got {horizons[1]['beta']}"
+            )
+
+    def test_per_path_heterogeneity_telescope_to_global_on_single_path(self):
+        """On a single-path panel, per-path == global heterogeneity.
+        Plain OLS path: bit-exact via path_groups identity."""
+        # Single-path DGP: all switchers follow (0,1,1,1)
+        rng = np.random.RandomState(44)
+        rows = []
+        n_switchers = 60
+        n_controls = 20
+        for g in range(n_switchers):
+            F_g = 3 + ((g // 3) % 3)
+            path = (0, 1, 1, 1)
+            het_x = 1 if g < n_switchers // 2 else 0
+            effect = 5.0 + 3.0 * het_x
+            for t in range(10):
+                if F_g - 1 <= t < F_g - 1 + len(path):
+                    d = path[t - (F_g - 1)]
+                elif t >= F_g - 1 + len(path):
+                    d = path[-1]
+                else:
+                    d = 0
+                rows.append({
+                    "group": g, "period": t, "treatment": d,
+                    "outcome": 0.5 * t + effect * d + rng.normal(0, 0.5),
+                    "het_x": het_x,
+                })
+        for k in range(n_controls):
+            het_x = 1 if k < n_controls // 2 else 0
+            for t in range(10):
+                rows.append({
+                    "group": n_switchers + k, "period": t, "treatment": 0,
+                    "outcome": 0.5 * t + rng.normal(0, 0.5),
+                    "het_x": het_x,
+                })
+        df = pd.DataFrame(rows)
+        # Run with by_path=1 (path is observed)
+        est_p = ChaisemartinDHaultfoeuille(drop_larger_lower=False, by_path=1)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            res_p = est_p.fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3, heterogeneity="het_x",
+            )
+        # Run global (no by_path)
+        est_g = ChaisemartinDHaultfoeuille(drop_larger_lower=False)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            res_g = est_g.fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3, heterogeneity="het_x",
+            )
+        assert res_p.path_heterogeneity_effects
+        path_key = (0, 1, 1, 1)
+        assert path_key in res_p.path_heterogeneity_effects
+        for l_h in range(1, 4):
+            py_path = res_p.path_heterogeneity_effects[path_key][l_h]
+            py_global = res_g.heterogeneity_effects[l_h]
+            if not np.isfinite(py_path["beta"]):
+                assert not np.isfinite(py_global["beta"])
+                continue
+            np.testing.assert_allclose(
+                py_path["beta"], py_global["beta"], atol=1e-14, rtol=1e-14,
+                err_msg=f"l={l_h}: per-path beta != global beta (telescope failed)",
+            )
+            np.testing.assert_allclose(
+                py_path["se"], py_global["se"], atol=1e-14, rtol=1e-14,
+                err_msg=f"l={l_h}: per-path se != global se (telescope failed)",
+            )
+
+    def test_per_path_heterogeneity_zero_signal_yields_small_beta(self):
+        """Uncorrelated covariate yields beta near zero per (path, l)."""
+        rng = np.random.RandomState(123)
+        rows = []
+        n_switchers = 90
+        n_controls = 30
+        paths = [(0, 1, 1, 1), (0, 1, 0, 0), (0, 1, 1, 0)]
+        for g in range(n_switchers):
+            F_g = 3 + ((g // 3) % 3)
+            path = paths[g % 3]
+            # het_x is random and uncorrelated with anything
+            het_x = rng.normal(0, 1)
+            for t in range(10):
+                if F_g - 1 <= t < F_g - 1 + len(path):
+                    d = path[t - (F_g - 1)]
+                elif t >= F_g - 1 + len(path):
+                    d = path[-1]
+                else:
+                    d = 0
+                # Effect is constant 5.0 — no heterogeneity by het_x
+                rows.append({
+                    "group": g, "period": t, "treatment": d,
+                    "outcome": 0.5 * t + 5.0 * d + rng.normal(0, 0.5),
+                    "het_x": het_x,
+                })
+        for k in range(n_controls):
+            # Draw het_x ONCE per group (must be time-invariant)
+            het_x = rng.normal(0, 1)
+            for t in range(10):
+                rows.append({
+                    "group": n_switchers + k, "period": t, "treatment": 0,
+                    "outcome": 0.5 * t + rng.normal(0, 0.5),
+                    "het_x": het_x,
+                })
+        df = pd.DataFrame(rows)
+        est = ChaisemartinDHaultfoeuille(drop_larger_lower=False, by_path=3)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            res = est.fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3, heterogeneity="het_x",
+            )
+        assert res.path_heterogeneity_effects
+        for path, horizons in res.path_heterogeneity_effects.items():
+            for l_h, vals in horizons.items():
+                if np.isfinite(vals["beta"]):
+                    # |beta| should be small (well within 3 standard
+                    # errors of zero) under the null
+                    assert abs(vals["beta"]) < 5.0, (
+                        f"path={path} l={l_h}: |beta|={abs(vals['beta']):.3f} "
+                        f"too large for zero-signal DGP"
+                    )
+
+    def test_path_with_too_few_eligible_yields_nan(self):
+        """A path with <3 eligible switchers per horizon emits NaN."""
+        # Construct a panel where one path has only 2 switchers — the
+        # n_obs >= 3 guard should fire. Use paths_of_interest to ensure
+        # the rare path is selected.
+        rng = np.random.RandomState(45)
+        rows = []
+        # 30 switchers on path (0,1,1,1), 2 switchers on (0,1,0,0)
+        for g in range(30):
+            F_g = 3 + (g % 3)
+            path = (0, 1, 1, 1)
+            het_x = 1 if g < 15 else 0
+            for t in range(10):
+                if F_g - 1 <= t < F_g - 1 + len(path):
+                    d = path[t - (F_g - 1)]
+                elif t >= F_g - 1 + len(path):
+                    d = path[-1]
+                else:
+                    d = 0
+                rows.append({
+                    "group": g, "period": t, "treatment": d,
+                    "outcome": 0.5 * t + 5.0 * d + rng.normal(0, 0.5),
+                    "het_x": het_x,
+                })
+        # 2 switchers on the rare path — under-eligible
+        for g in range(30, 32):
+            F_g = 3
+            path = (0, 1, 0, 0)
+            het_x = 1
+            for t in range(10):
+                if F_g - 1 <= t < F_g - 1 + len(path):
+                    d = path[t - (F_g - 1)]
+                elif t >= F_g - 1 + len(path):
+                    d = path[-1]
+                else:
+                    d = 0
+                rows.append({
+                    "group": g, "period": t, "treatment": d,
+                    "outcome": 0.5 * t + 5.0 * d + rng.normal(0, 0.5),
+                    "het_x": het_x,
+                })
+        # Controls
+        for k in range(15):
+            for t in range(10):
+                rows.append({
+                    "group": 32 + k, "period": t, "treatment": 0,
+                    "outcome": 0.5 * t + rng.normal(0, 0.5), "het_x": 0,
+                })
+        df = pd.DataFrame(rows)
+        est = ChaisemartinDHaultfoeuille(
+            drop_larger_lower=False,
+            paths_of_interest=[(0, 1, 1, 1), (0, 1, 0, 0)],
+        )
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            res = est.fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3, heterogeneity="het_x",
+            )
+        assert res.path_heterogeneity_effects
+        rare = res.path_heterogeneity_effects[(0, 1, 0, 0)]
+        # All horizons for the rare path should have NaN inference (n_obs < 3)
+        for l_h, vals in rare.items():
+            assert vals["n_obs"] < 3, (
+                f"rare path l={l_h}: expected n_obs < 3, got {vals['n_obs']}"
+            )
+            assert not np.isfinite(vals["beta"])
+            assert not np.isfinite(vals["se"])
+            assert not np.isfinite(vals["t_stat"])
+            assert not np.isfinite(vals["p_value"])
+            assert not np.isfinite(vals["conf_int"][0])
+            assert not np.isfinite(vals["conf_int"][1])
+
+    def test_per_path_heterogeneity_no_multi_baseline_warning(self):
+        """Anti-regression: heterogeneity + by_path does NOT emit the
+        multi-baseline UserWarning that controls/trends_linear emit.
+        Cohort dummies absorb baseline by construction (REGISTRY)."""
+        df = _by_path_het_data()
+        with warnings.catch_warnings(record=True) as caught:
+            warnings.simplefilter("always")
+            res = ChaisemartinDHaultfoeuille(
+                drop_larger_lower=False, by_path=3
+            ).fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3, heterogeneity="het_x",
+            )
+        assert res.path_heterogeneity_effects
+        # Filter for any multi-baseline-style warning
+        multi_baseline = [
+            w for w in caught
+            if "baseline" in str(w.message).lower()
+            and "multi" in str(w.message).lower()
+        ]
+        assert not multi_baseline, (
+            f"Unexpected multi-baseline warning(s): "
+            f"{[str(w.message) for w in multi_baseline]}"
+        )
+
+    # Survey composition (slow)
+
+    @staticmethod
+    def _by_path_het_data_with_survey(seed=44, n_replicates=0):
+        """Extends `_by_path_het_data` with survey columns (weights /
+        strata / PSU). When ``n_replicates > 0``, also attaches BRR
+        replicate-weight columns ``rep_0..rep_{n_replicates-1}``.
+
+        Strata are coarser than groups (3 strata) and PSU=group for the
+        analytical Binder TSL path. Replicate weights are mutually
+        exclusive with strata/PSU/FPC at the SurveyDesign level (see
+        survey.py validation), so the caller picks one mode by passing
+        the appropriate kwargs to SurveyDesign.
+        """
+        rng = np.random.RandomState(seed)
+        n_switchers, n_controls, n_periods = 90, 30, 10
+        n_groups_total = n_switchers + n_controls
+        H = (
+            rng.choice([-1, 1], size=(n_groups_total, n_replicates))
+            if n_replicates > 0
+            else None
+        )
+        rows = []
+        paths = [(0, 1, 1, 1), (0, 1, 0, 0), (0, 1, 1, 0)]
+        for g in range(n_switchers):
+            F_g = 3 + ((g // 3) % 3)
+            path = paths[g % 3]
+            het_x = 1 if g < n_switchers // 2 else 0
+            effect = 5.0 + 3.0 * het_x
+            stratum = g // 30
+            psu = g // 3
+            weight = 1.0 + 0.1 * (g % 5)
+            for t in range(n_periods):
+                if F_g - 1 <= t < F_g - 1 + len(path):
+                    d = path[t - (F_g - 1)]
+                elif t >= F_g - 1 + len(path):
+                    d = path[-1]
+                else:
+                    d = 0
+                y = 0.5 * t + effect * d + rng.normal(0, 0.5)
+                row = {
+                    "group": g,
+                    "period": t,
+                    "treatment": d,
+                    "outcome": y,
+                    "het_x": het_x,
+                    "survey_weights": weight,
+                    "strata": stratum,
+                    "psu": psu,
+                }
+                if H is not None:
+                    for r in range(n_replicates):
+                        row[f"rep_{r}"] = float(weight) * (1 + 0.5 * H[g, r])
+                rows.append(row)
+        for k in range(n_controls):
+            het_x = 1 if k < n_controls // 2 else 0
+            g = n_switchers + k
+            stratum = g // 30
+            psu = g // 3
+            weight = 1.0 + 0.1 * (k % 5)
+            for t in range(n_periods):
+                row = {
+                    "group": g,
+                    "period": t,
+                    "treatment": 0,
+                    "outcome": 0.5 * t + rng.normal(0, 0.5),
+                    "het_x": het_x,
+                    "survey_weights": weight,
+                    "strata": stratum,
+                    "psu": psu,
+                }
+                if H is not None:
+                    for r in range(n_replicates):
+                        row[f"rep_{r}"] = float(weight) * (1 + 0.5 * H[g, r])
+                rows.append(row)
+        return pd.DataFrame(rows)
+
+    @pytest.mark.slow
+    def test_per_path_heterogeneity_under_survey_finite(self):
+        """Analytical Binder TSL SE finite per (path, l) under
+        ``by_path + heterogeneity + survey_design``. Wave 5 #11 plan
+        regression coverage for the documented survey composition
+        (REGISTRY: "Per-path heterogeneity testing" → "Survey
+        composition")."""
+        from diff_diff.survey import SurveyDesign
+
+        df = self._by_path_het_data_with_survey()
+        sd = SurveyDesign(weights="survey_weights", strata="strata", psu="psu")
+        est = ChaisemartinDHaultfoeuille(drop_larger_lower=False, by_path=2)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            res = est.fit(
+                df,
+                outcome="outcome",
+                group="group",
+                time="period",
+                treatment="treatment",
+                L_max=3,
+                heterogeneity="het_x",
+                survey_design=sd,
+            )
+        assert res.path_heterogeneity_effects
+        finite_count = 0
+        for path, horizons in res.path_heterogeneity_effects.items():
+            for l_h, vals in horizons.items():
+                if vals["n_obs"] >= 3:
+                    assert np.isfinite(vals["beta"]), (
+                        f"path={path} l={l_h}: beta is NaN under survey TSL"
+                    )
+                    assert np.isfinite(vals["se"]) and vals["se"] > 0, (
+                        f"path={path} l={l_h}: se non-positive under survey TSL"
+                    )
+                    finite_count += 1
+        assert finite_count >= 4, (
+            f"Expected ≥4 finite (path, l) entries, got {finite_count}"
+        )
+
+    @pytest.mark.slow
+    def test_per_path_heterogeneity_replicate_weights_propagates_n_valid(self):
+        """Under replicate weights, every per-(path, l) replicate fit
+        appends ``n_valid`` to the shared accumulator and the final
+        ``survey_metadata.df_survey`` reflects ``min(n_valid) - 1``.
+
+        For BRR with ``n_replicates=8`` and well-formed data, the
+        expected df_survey is ``n_replicates - 1 = 7`` (every replicate
+        produces a finite SE on this DGP). Anti-regression: drives the
+        end-to-end `_replicate_n_valid_list` accumulator through per-
+        (path, l) heterogeneity calls.
+        """
+        from diff_diff.survey import SurveyDesign
+
+        n_replicates = 8
+        df = self._by_path_het_data_with_survey(n_replicates=n_replicates)
+        sd = SurveyDesign(
+            weights="survey_weights",
+            replicate_weights=[f"rep_{r}" for r in range(n_replicates)],
+            replicate_method="BRR",
+        )
+        est = ChaisemartinDHaultfoeuille(drop_larger_lower=False, by_path=2)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            res = est.fit(
+                df,
+                outcome="outcome",
+                group="group",
+                time="period",
+                treatment="treatment",
+                L_max=3,
+                heterogeneity="het_x",
+                survey_design=sd,
+            )
+        assert res.path_heterogeneity_effects
+        assert res.survey_metadata is not None
+        # df_survey ≤ n_replicates - 1 per Rao-Wu replicate convention.
+        # With well-formed BRR weights and n_obs >= 3 per (path, l), we
+        # expect every replicate fit to produce finite SE → df = 7.
+        assert res.survey_metadata.df_survey is not None, (
+            "df_survey must be populated under replicate-weight survey"
+        )
+        assert res.survey_metadata.df_survey == n_replicates - 1, (
+            f"df_survey={res.survey_metadata.df_survey}, "
+            f"expected {n_replicates - 1}"
+        )
+        # Every populated (path, l) should have finite inference under
+        # replicate weights too.
+        for path, horizons in res.path_heterogeneity_effects.items():
+            for l_h, vals in horizons.items():
+                if vals["n_obs"] >= 3:
+                    assert np.isfinite(vals["se"]), (
+                        f"path={path} l={l_h}: replicate SE non-finite"
+                    )
+
+    @pytest.mark.slow
+    def test_survey_design_plus_n_bootstrap_with_heterogeneity_still_raises(
+        self,
+    ):
+        """The existing ``by_path + survey_design + n_bootstrap > 0``
+        gate (PR #408) must still fire when ``heterogeneity`` is also
+        set. Anti-regression: confirms heterogeneity composition does
+        not accidentally re-route around the multiplier-bootstrap
+        gate.
+        """
+        from diff_diff.survey import SurveyDesign
+
+        df = self._by_path_het_data_with_survey()
+        sd = SurveyDesign(weights="survey_weights", strata="strata", psu="psu")
+        est = ChaisemartinDHaultfoeuille(
+            drop_larger_lower=False, by_path=2, n_bootstrap=10, seed=1
+        )
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            with pytest.raises(NotImplementedError, match="multiplier"):
+                est.fit(
+                    df,
+                    outcome="outcome",
+                    group="group",
+                    time="period",
+                    treatment="treatment",
+                    L_max=3,
+                    heterogeneity="het_x",
+                    survey_design=sd,
+                )
+
+    # DataFrame integration
+
+    def test_to_dataframe_by_path_includes_heterogeneity_columns(self):
+        """``to_dataframe(level='by_path')`` includes het_* columns;
+        populated for positive horizons and NaN for placebo rows."""
+        df = _by_path_het_data()
+        est = ChaisemartinDHaultfoeuille(
+            drop_larger_lower=False, by_path=2, placebo=True
+        )
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            res = est.fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3, heterogeneity="het_x",
+            )
+        out = res.to_dataframe(level="by_path")
+        assert "het_beta" in out.columns
+        assert "het_se" in out.columns
+        assert "het_t_stat" in out.columns
+        assert "het_p_value" in out.columns
+        assert "het_conf_int_lower" in out.columns
+        assert "het_conf_int_upper" in out.columns
+        # Placebo rows: het_* must be NaN
+        if (out.horizon < 0).any():
+            placebo_rows = out[out.horizon < 0]
+            assert placebo_rows["het_beta"].isna().all()
+        # Positive horizons: at least some entries are populated
+        positive_rows = out[out.horizon > 0]
+        assert positive_rows["het_beta"].notna().any()
+
+    def test_per_path_heterogeneity_renders_in_summary(self):
+        """``summary()`` includes per-path heterogeneity sub-block.
+
+        Sibling-surface mirror of `_render_heterogeneity_section`
+        (global) and `path_cumulated_event_study` rendering. Anti-
+        regression: ensures `path_heterogeneity_effects` is not
+        silently omitted from the user-facing report.
+        """
+        df = _by_path_het_data()
+        est = ChaisemartinDHaultfoeuille(drop_larger_lower=False, by_path=2)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            res = est.fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3, heterogeneity="het_x",
+            )
+        report = res.summary()
+        assert "Heterogeneity Test (Section 1.5, partial)" in report, (
+            "summary() must render the per-path heterogeneity sub-block"
+        )
+        # The header appears in BOTH the global and per-path blocks; check
+        # that at least one populated path's beta value is rendered. We
+        # use a small float comparison rather than a full string match
+        # because `_format_inference_row` formats with 4 decimal places.
+        assert res.path_heterogeneity_effects
+        rendered_any = False
+        for path, horizons in res.path_heterogeneity_effects.items():
+            for l_h, vals in horizons.items():
+                if not np.isfinite(vals["beta"]):
+                    continue
+                fragment = f"{vals['beta']:.4f}"
+                if fragment in report:
+                    rendered_any = True
+                    break
+            if rendered_any:
+                break
+        assert rendered_any, (
+            "summary() must contain at least one per-path heterogeneity "
+            "beta value rounded to 4 decimal places"
+        )
+
+    # Edge cases
+
+    def test_path_unobserved_under_heterogeneity_warns_omits(self):
+        """POI with unobserved path emits unobserved-path warning and
+        omits the path from path_heterogeneity_effects."""
+        df = _by_path_het_data()
+        # (1, 1, 1, 0) is not in the DGP (all paths start with 0)
+        est = ChaisemartinDHaultfoeuille(
+            drop_larger_lower=False,
+            paths_of_interest=[(0, 1, 1, 1), (1, 1, 1, 0)],
+        )
+        with warnings.catch_warnings(record=True) as caught:
+            warnings.simplefilter("always")
+            res = est.fit(
+                df, outcome="outcome", group="group", time="period",
+                treatment="treatment", L_max=3, heterogeneity="het_x",
+            )
+        # Unobserved path warning should have fired (at least once;
+        # may fire from path_effects + path_heterogeneity_effects)
+        unobs = [
+            w for w in caught
+            if "(1, 1, 1, 0)" in str(w.message)
+            and "zero observed groups" in str(w.message)
+        ]
+        assert unobs, "expected unobserved-path UserWarning"
+        assert res.path_heterogeneity_effects is not None
+        assert (1, 1, 1, 0) not in res.path_heterogeneity_effects
+        assert (0, 1, 1, 1) in res.path_heterogeneity_effects
diff --git a/tests/test_chaisemartin_dhaultfoeuille_parity.py b/tests/test_chaisemartin_dhaultfoeuille_parity.py
index ef1fbe4b..dd0bae4e 100644
--- a/tests/test_chaisemartin_dhaultfoeuille_parity.py
+++ b/tests/test_chaisemartin_dhaultfoeuille_parity.py
@@ -1319,3 +1319,154 @@ def test_parity_multi_path_reversible_by_path_non_binary(
                         f"path={path_key} h={h} SE: "
                         f"py={py_se:.4f} vs r={r_se:.4f}"
                     )
+
+
+class TestDCDHDynRParityHeterogeneity:
+    """Parity tests for global ``predict_het`` against R DIDmultiplegtDYN.
+
+    Wave 5 #11 introduces this as the FIRST ``predict_het`` parity
+    baseline in the repo. Anchors the per-path tolerance for
+    ``TestDCDHDynRParityByPathHeterogeneity`` since the per-path R call
+    is ``did_multiplegt_main(..., predict_het=...)`` per path-restricted
+    subsample with no additional numerical loss.
+
+    Fixture: scenario 20 (``multi_path_reversible_predict_het``) — 90
+    switchers across 3 reversal paths + 30 never-treated controls,
+    binary ``het_x`` with effect = 5.0 + 3.0 * het_x. R is invoked with
+    ``dont_drop_larger_lower=TRUE`` so the reversal-path eligibility
+    matches Python's ``drop_larger_lower=False`` requirement.
+    """
+
+    BETA_RTOL = 1e-6
+    BETA_ATOL = 1e-9
+    SE_RTOL = 1e-5
+
+    def test_parity_multi_path_reversible_predict_het(self, golden_values):
+        """Global heterogeneity coefficient parity per horizon."""
+        import warnings
+
+        scenario = golden_values.get("multi_path_reversible_predict_het")
+        if scenario is None:
+            pytest.skip(
+                "scenario 'multi_path_reversible_predict_het' not in "
+                "golden values"
+            )
+
+        df = _golden_to_df_with_extra(scenario["data"], extra_cols=["het_x"])
+        est = ChaisemartinDHaultfoeuille(drop_larger_lower=False)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            results = est.fit(
+                df,
+                outcome="outcome",
+                group="group",
+                time="period",
+                treatment="treatment",
+                L_max=3,
+                heterogeneity="het_x",
+            )
+
+        assert results.heterogeneity_effects is not None
+        r_predict_het = scenario["results"]["predict_het"]
+
+        for h_str, r_h in r_predict_het.items():
+            h = int(h_str)
+            assert h in results.heterogeneity_effects, (
+                f"horizon {h} missing from Python heterogeneity_effects"
+            )
+            py_h = results.heterogeneity_effects[h]
+            assert py_h["beta"] == pytest.approx(
+                r_h["beta"], rel=self.BETA_RTOL, abs=self.BETA_ATOL
+            ), f"h={h} beta: py={py_h['beta']:.6f} vs r={r_h['beta']:.6f}"
+            assert py_h["se"] == pytest.approx(r_h["se"], rel=self.SE_RTOL), (
+                f"h={h} se: py={py_h['se']:.6f} vs r={r_h['se']:.6f}"
+            )
+
+
+class TestDCDHDynRParityByPathHeterogeneity:
+    """Parity tests for ``by_path`` + ``predict_het`` against R DIDmultiplegtDYN.
+
+    Wave 5 #11 lift. R's per-path dispatcher
+    (``did_multiplegt_dyn.R:226-257``) re-runs
+    ``did_multiplegt_main(..., predict_het=...)`` on each path-restricted
+    subsample. Python mirrors via ``_compute_path_heterogeneity_test``,
+    which loops ``_compute_heterogeneity_test`` over selected paths
+    with a ``path_groups`` filter restricting eligibility to the path's
+    switchers. Cohort dummies absorb baseline by construction, so
+    multi-baseline switcher panels do not produce R-divergence.
+
+    Fixture: scenario 21 (``multi_path_reversible_by_path_predict_het``)
+    — same DGP as scenario 20 so per-path tolerances inherit from
+    ``TestDCDHDynRParityHeterogeneity``.
+    """
+
+    BETA_RTOL = 1e-6
+    BETA_ATOL = 1e-9
+    SE_RTOL = 1e-5
+
+    def _path_key_from_r_label(self, r_label: str):
+        return tuple(int(x) for x in r_label.split(","))
+
+    def test_parity_multi_path_reversible_by_path_predict_het(
+        self, golden_values
+    ):
+        """Per-path heterogeneity coefficient parity per (path, horizon)."""
+        import warnings
+
+        scenario = golden_values.get(
+            "multi_path_reversible_by_path_predict_het"
+        )
+        if scenario is None:
+            pytest.skip(
+                "scenario 'multi_path_reversible_by_path_predict_het' "
+                "not in golden values"
+            )
+
+        df = _golden_to_df_with_extra(scenario["data"], extra_cols=["het_x"])
+        est = ChaisemartinDHaultfoeuille(drop_larger_lower=False, by_path=3)
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore", UserWarning)
+            results = est.fit(
+                df,
+                outcome="outcome",
+                group="group",
+                time="period",
+                treatment="treatment",
+                L_max=3,
+                heterogeneity="het_x",
+            )
+
+        assert results.path_heterogeneity_effects is not None
+        r_by_path = scenario["results"]["by_path_predict_het"]
+
+        py_keys = set(results.path_heterogeneity_effects.keys())
+        r_keys = {self._path_key_from_r_label(e["path"]) for e in r_by_path}
+        assert py_keys == r_keys, (
+            f"Path-set mismatch.\n"
+            f"  Python only: {py_keys - r_keys}\n"
+            f"  R only:      {r_keys - py_keys}"
+        )
+
+        for r_path_entry in r_by_path:
+            path_key = self._path_key_from_r_label(r_path_entry["path"])
+            py_horizons = results.path_heterogeneity_effects[path_key]
+
+            for h_str, r_h in r_path_entry["horizons"].items():
+                h = int(h_str)
+                assert h in py_horizons, (
+                    f"path={path_key}: horizon {h} missing from Python "
+                    f"path_heterogeneity_effects"
+                )
+                py_h = py_horizons[h]
+                assert py_h["beta"] == pytest.approx(
+                    r_h["beta"], rel=self.BETA_RTOL, abs=self.BETA_ATOL
+                ), (
+                    f"path={path_key} h={h} beta: "
+                    f"py={py_h['beta']:.6f} vs r={r_h['beta']:.6f}"
+                )
+                assert py_h["se"] == pytest.approx(
+                    r_h["se"], rel=self.SE_RTOL
+                ), (
+                    f"path={path_key} h={h} se: "
+                    f"py={py_h['se']:.6f} vs r={r_h['se']:.6f}"
+                )