diff --git a/TODO.md b/TODO.md
index 6797e6bc..aa3c4805 100644
--- a/TODO.md
+++ b/TODO.md
@@ -96,13 +96,12 @@ Deferred items from PR reviews that were not addressed before merge.
 | Replicate weight tests use Fay-like BRR perturbations (0.5/1.5), not true half-sample BRR. Add true BRR regressions per estimator family. Existing `test_survey_phase6.py` covers true BRR at the helper level. | `tests/test_replicate_weight_expansion.py` | #253 | Low |
 | WooldridgeDiD: QMLE sandwich uses `aweight` cluster-robust adjustment `(G/(G-1))*(n-1)/(n-k)` vs Stata's `G/(G-1)` only. Conservative (inflates SEs). Add `qmle` weight type if Stata golden values confirm material difference. | `wooldridge.py`, `linalg.py` | #216 | Medium |
 | WooldridgeDiD: aggregation weights use cell-level n_{g,t} counts. Paper (W2025 Eqs. 7.2-7.4) defines cohort-share weights. Add optional `weights="cohort_share"` parameter to `aggregate()`. | `wooldridge_results.py` | #216 | Medium |
-| WooldridgeDiD: canonical link requirement (W2023 Prop 3.1) not enforced — no warning if user applies wrong method to outcome type. Estimator is consistent regardless, but equivalence with imputation breaks. | `wooldridge.py` | #216 | Low |
+| WooldridgeDiD: optional *efficiency hint* (NOT a canonical-link violation per W2023 Prop 3.1) when method/outcome pairing is sub-optimal — e.g., `method="ols"` on binary data is consistent under QMLE, but `method="logit"` is typically more efficient. The original framing in this row as a "canonical link requirement" tied to Prop 3.1 was incorrect: Wooldridge (2023) Table 1 lists Gaussian/OLS for "any response" and logistic-Bernoulli for "binary OR fractional". A useful hint exists (efficiency), but should not be framed as a methodology violation. See PR #453 R1 review for the corrected reading. | `wooldridge.py` | #216 | Low |
 | WooldridgeDiD: Stata `jwdid` golden value tests — add R/Stata reference script and `TestReferenceValues` class. | `tests/test_wooldridge.py` | #216 | Medium |
 | Thread `vcov_type` (classical / hc1 / hc2 / hc2_bm) through the 8 standalone estimators that expose `cluster=`: `CallawaySantAnna`, `SunAbraham`, `ImputationDiD`, `TwoStageDiD`, `TripleDifference`, `StackedDiD`, `WooldridgeDiD`, `EfficientDiD`. Phase 1a added `vcov_type` to the `DifferenceInDifferences` inheritance chain only. | multiple | Phase 1a | Medium |
 | Weighted one-way Bell-McCaffrey (`vcov_type="hc2_bm"` + `weights`, no cluster) currently raises `NotImplementedError`. `_compute_bm_dof_from_contrasts` builds its hat matrix from the unscaled design via `X (X'WX)^{-1} X' W`, but `solve_ols` solves the WLS problem by transforming to `X* = sqrt(w) X`, so the correct symmetric idempotent residual-maker is `M* = I - sqrt(W) X (X'WX)^{-1} X' sqrt(W)`. Rederive the Satterthwaite `(tr G)^2 / tr(G^2)` ratio on the transformed design and add weighted parity tests before lifting the guard. | `linalg.py::_compute_bm_dof_from_contrasts`, `linalg.py::_validate_vcov_args` | Phase 1a | Medium |
 | HC2 / HC2 + Bell-McCaffrey on absorbed-FE fits currently raises `NotImplementedError` in three places: `TwoWayFixedEffects` unconditionally; `DifferenceInDifferences(absorb=..., vcov_type in {"hc2","hc2_bm"})`; `MultiPeriodDiD(absorb=..., vcov_type in {"hc2","hc2_bm"})`. Within-transformation preserves coefficients and residuals under FWL but not the hat matrix, so the reduced-design `h_ii` is not the diagonal of the full FE projection and CR2's block adjustment `A_g = (I - H_gg)^{-1/2}` is likewise wrong on absorbed cluster blocks. Lifting the guard needs HC2/CR2-BM computed from the full absorbed projection (unit/time FE dummies reconstructed internally, or a FE-aware hat-matrix formulation) and a parity harness against a full-dummy OLS run or R `fixest`/`clubSandwich`. HC1/CR1 are unaffected by this because they have no leverage term. | `twfe.py::fit`, `estimators.py::DifferenceInDifferences.fit`, `estimators.py::MultiPeriodDiD.fit` | Phase 1a | Medium |
 | Weighted CR2 Bell-McCaffrey cluster-robust (`vcov_type="hc2_bm"` + `cluster_ids` + `weights`) currently raises `NotImplementedError`. Weighted hat matrix and residual rebalancing need threading per clubSandwich WLS handling. | `linalg.py::_compute_cr2_bm` | Phase 1a | Medium |
-| `honest_did.py:1907` `np.linalg.solve(A_sys, b_sys) / except LinAlgError: continue` is a silent basis-rejection in the vertex-enumeration loop that is algorithmically intentional (try the next basis). Consider surfacing a count of rejected bases as a diagnostic when ARP enumeration exhausts, so users see when the vertex search was heavily constrained. Not a silent failure in the sense of the Phase 2 audit (the algorithm is supposed to skip), but the diagnostic would help debug borderline cases. | `honest_did.py` | #334 | Low |
 | Unify Rust local-method `estimate_model` solver path to `solve_wls_svd` (the same SVD helper used by the global-method since PR #348) for sub-1e-14 bootstrap SE parity. Current local-method bootstrap parity test (`tests/test_rust_backend.py::TestTROPRustEdgeCaseParity::test_bootstrap_seed_reproducibility_local`) passes at `atol=1e-5` — the residual ~1e-7 gap is roundoff between Rust's `estimate_model` matrix factorization and numpy's `lstsq`, which accumulates differently across per-replicate bootstrap fits. Main-fit ATT parity is regime-dependent (`atol=1e-14` for `lambda_nn=inf`, `atol=1e-10` for finite `lambda_nn` — see `test_local_method_main_fit_parity`); the bootstrap gap is a same-solver-path roundoff concern and not a user-visible correctness bug. | `rust/src/trop.rs::estimate_model`, `rust/src/linalg.rs::solve_wls_svd` | follow-up | Low |
 | Rust multiplier-bootstrap weight RNG (`generate_bootstrap_weights_batch` in `rust/src/bootstrap.rs:9-10, 57-75`) uses `Xoshiro256PlusPlus::seed_from_u64(seed + i)` per row for Rademacher/Mammen/Webb generation. If any Python caller (SDID / efficient-DiD multiplier bootstrap) has a numpy-canonical equivalent, the two backends likely diverge under the same seed. Audit Python callers (`diff_diff/sdid.py`, `diff_diff/efficient_did_bootstrap.py`, `diff_diff/bootstrap_utils.py::generate_bootstrap_weights_batch_numpy`) for parity-test gaps. Same fix shape as TROP RNG parity (PR #354): pre-generate weights in Python via numpy and pass them to Rust through PyO3. | `rust/src/bootstrap.rs`, `diff_diff/bootstrap_utils.py` | follow-up | Medium |
 | `bias_corrected_local_linear`: extend golden parity to `kernel="triangular"` and `kernel="uniform"` (currently epa-only; all three kernels share `kernel_W` and the `lprobust` math, so parity is expected but not separately asserted). | `benchmarks/R/generate_nprobust_lprobust_golden.R`, `tests/test_bias_corrected_lprobust.py` | Phase 1c | Low |
@@ -160,7 +159,6 @@ Deferred items from PR reviews that were not addressed before merge.
 | CS R helpers hard-code `xformla = ~ 1`; no covariate-adjusted R benchmark for IRLS path | `tests/test_methodology_callaway.py` | #202 | Low |
 | Doc-snippet smoke tests only cover `.rst` files; `.txt` AI guides outside CI validation | `tests/test_doc_snippets.py` | #239 | Low |
 | Add CI validation for `docs/doc-deps.yaml` integrity (stale paths, unmapped source files) | `docs/doc-deps.yaml` | #269 | Low |
-| HonestDiD `test_m0_short_circuit` uses wall-clock `elapsed < 0.5s` as a proxy for "short-circuit path taken" instead of calling the full optimizer. Replace with a direct correctness signal (mock/spy the optimizer or check a state flag) so the test doesn't depend on CI timing. Not flaky today at 500ms, but load-bearing correctness on a timing proxy is brittle. | `tests/test_methodology_honest_did.py:246` | — | Low |
 | SyntheticDiD: rename internal `placebo_effects` variable to `variance_effects` (or `resampled_effects`). Misleading name across the placebo/bootstrap/jackknife dispatch paths — holds three different contents depending on variance method. Low-risk refactor; user-facing field rename should preserve `placebo_effects` as a deprecated alias for one release. | `synthetic_did.py`, `results.py` | follow-up | Medium |
 | AI review CI: pin workflow contract via test (uses `openai/codex-action@v1`, passes `prompt-file`, reads `steps.run_codex.outputs.final-message`, preserves diff-exclude paths and comment markers). Currently only the wrapper-tag and closing-tag-escape strings are asserted. | `tests/test_openai_review.py`, `.github/workflows/ai_pr_review.yml` | #416 | Low |
 | `TestWorkflowDoesNotExecutePRHeadCode` (CodeQL #14 dismissal guard) does not model: `bash <script>` / `sh <script>` / `./<script>` / `source <script>` / `. <script>` direct shell-script execution; multi-line `python3 -c` bodies (line-by-line shlex can't reassemble across newlines — the workflow's 5 sanitizer bodies are exempt by invisibility); shell-variable-expansion indirection (`SCRIPT="$X"; python3 "$SCRIPT"`); `eval`; `find -exec`; `xargs -I {}`. Each represents a path by which PR-head bytes COULD execute without the test failing. The guard catches accidental regressions of common forms (16 tests covering pip/npm/cargo/maturin/etc. installs, python file exec, bash -c indirection with compound flags, env-var prefixes, line continuations, subshells/brace groups, single-line python -c, write-overwrites of allowlisted /tmp paths). Closing the residuals would require multi-line shell parsing with command-substitution awareness + script-execution allowlists — significant work for diminishing return given the dismissal's primary defense is the documented threat model on the alert and in `.github/workflows/ai_pr_review.yml` comment block. | `tests/test_openai_review.py`, `.github/workflows/ai_pr_review.yml` | #436 | Low |
@@ -174,12 +172,10 @@ Ordered paydown view across the tables above. Tier A → D is by effort × risk,
 
 #### Tier A — Quick wins (≤1 day, ≤3 CI rounds expected)
 
-- HonestDiD `test_m0_short_circuit`: replace wall-clock `elapsed < 0.5s` proxy with a state flag (`tests/test_methodology_honest_did.py:246`)
 - EfficientDiD `control_group="last_cohort"` REGISTRY-vs-code alignment with `anticipation>0` (`efficient_did.py`, one design decision)
 - TripleDifference: add `generate_ddd_panel_data` for panel DDD power analysis (`prep_dgp.py`, `power.py`)
 - TROP: extract shared data-setup helper between `fit()` and `_fit_global()` (~150 LoC dedup; `trop.py`, `trop_global.py`, `trop_local.py`)
-- WooldridgeDiD: emit warning when canonical-link is violated (`wooldridge.py`; W2023 Prop 3.1)
-- HonestDiD vertex-rejection diagnostic counter on ARP enumeration exhaust (`honest_did.py:1907`)
+- WooldridgeDiD: optional efficiency hint when method/outcome pairing is sub-optimal (NOT a canonical-link violation per W2023 Prop 3.1 — see Methodology/Correctness row for the corrected framing)
 
 (SyntheticDiD `placebo_effects` → `variance_effects` rename moved to Tier B — the user-facing field rename + one-release deprecation alias is too large for ≤1 day / ≤3 CI rounds.)
 
diff --git a/diff_diff/honest_did.py b/diff_diff/honest_did.py
index 110e0261..714285e3 100644
--- a/diff_diff/honest_did.py
+++ b/diff_diff/honest_did.py
@@ -18,6 +18,7 @@
 """
 
 from dataclasses import dataclass, field
+import warnings
 from typing import Any, Dict, List, Literal, Optional, Tuple, Union
 
 import numpy as np
@@ -1890,11 +1891,15 @@ def _enumerate_vertices(
     if n_eq > n_moments:
         return []
 
-    vertices = []
+    vertices: List[np.ndarray] = []
+    n_total = 0
+    n_linalg_error = 0
+    n_infeasible = 0
 
     # Each vertex has exactly n_eq non-zero (basic) variables
     for basis_idx in itertools.combinations(range(n_moments), n_eq):
         basis_idx = list(basis_idx)
+        n_total += 1
 
         # Build the system for basic variables
         # gamma[basis_idx]' @ X_tilde[basis_idx, :] = 0
@@ -1913,6 +1918,7 @@ def _enumerate_vertices(
         try:
             gamma_basic = np.linalg.solve(A_sys, b_sys)
         except np.linalg.LinAlgError:
+            n_linalg_error += 1
             continue
 
         # Check feasibility: gamma >= 0
@@ -1920,6 +1926,35 @@ def _enumerate_vertices(
             gamma = np.zeros(n_moments)
             gamma[basis_idx] = np.maximum(gamma_basic, 0)
             vertices.append(gamma)
+        else:
+            n_infeasible += 1
+
+    # Diagnostic warnings — surface vertex-search pathologies that would
+    # otherwise hide behind `_compute_arp_test` returning False
+    # (conservative non-rejection).
+    if n_total > 0 and len(vertices) == 0:
+        warnings.warn(
+            f"ARP vertex enumeration exhausted without feasible vertices: "
+            f"tried {n_total} bases, {n_linalg_error} rejected for "
+            f"LinAlgError, {n_infeasible} infeasible (negative basic "
+            f"variables). The caller (_compute_arp_test) will return False "
+            f"(conservative non-rejection). This may indicate near-singular "
+            f"nuisance constraints (X_tilde) or a degenerate "
+            f"moment-inequality system.",
+            RuntimeWarning,
+            stacklevel=3,
+        )
+    elif n_total > 0 and n_linalg_error / n_total >= 0.5:
+        warnings.warn(
+            f"ARP vertex enumeration heavily constrained: "
+            f"{n_linalg_error} of {n_total} bases ({100 * n_linalg_error / n_total:.0f}%) "
+            f"rejected for LinAlgError, {n_infeasible} infeasible. "
+            f"{len(vertices)} feasible vertex(es) recovered. Results may be "
+            f"numerically fragile; consider regularizing the moment-inequality "
+            f"system or reviewing the nuisance constraints (X_tilde).",
+            RuntimeWarning,
+            stacklevel=3,
+        )
 
     return vertices
 
diff --git a/tests/test_methodology_honest_did.py b/tests/test_methodology_honest_did.py
index f2a63017..2f378a31 100644
--- a/tests/test_methodology_honest_did.py
+++ b/tests/test_methodology_honest_did.py
@@ -5,7 +5,8 @@
 equations, known analytical cases, and expected mathematical properties.
 """
 
-import os
+
+import warnings
 
 import numpy as np
 import pytest
@@ -245,34 +246,37 @@ def test_optimal_flci_is_finite_and_valid(self):
         assert ci_lb_opt <= lb, "CI lower should be <= identified set lower"
         assert ci_ub_opt >= ub, "CI upper should be >= identified set upper"
 
-    @pytest.mark.skipif(
-        os.environ.get("CI") == "true",
-        reason="wall-clock timing is flaky on shared CI runners; short-circuit "
-        "correctness signal will be replaced with a mock/spy per TODO.md "
-        "(see PR #330 follow-up note)",
-    )
     def test_m0_short_circuit(self):
-        """M=0 should use standard CI without optimization.
-
-        Uses wall-clock elapsed time as a proxy for "short-circuit path
-        taken" — fast path is ``<0.5s``, slow optimization would be ``>>
-        0.5s``. Skipped on CI because neighbor-VM contention on shared
-        runners can push even the short-circuit path past the threshold.
-        Run locally to validate the fast-path invariant; the TODO.md entry
-        added by PR #330 tracks replacing this with a mock/spy so the
-        correctness signal becomes CI-safe.
+        """M=0 takes the bias=0 fast path and never invokes the LP solver.
+
+        ``_compute_worst_case_bias`` returns ``0.0`` immediately when ``M=0``
+        (diff_diff/honest_did.py:1650), so ``scipy.optimize.linprog`` is
+        never reached. Patching the LP solver and asserting ``call_count
+        == 0`` is a direct correctness signal — CI-safe (no wall-clock
+        dependency) and faster than the prior timing-based proxy.
         """
+        from unittest.mock import patch
+
         beta_pre = np.array([0.3, 0.2, 0.1])
         beta_post = np.array([2.0])
         sigma = np.eye(4) * 0.01
         l_vec = np.array([1.0])
 
-        import time
-        t0 = time.time()
-        _compute_optimal_flci(beta_pre, beta_post, sigma, l_vec, 3, 1, M=0.0)
-        elapsed = time.time() - t0
+        with patch("diff_diff.honest_did.optimize.linprog") as mock_linprog:
+            ci_lb, ci_ub = _compute_optimal_flci(
+                beta_pre, beta_post, sigma, l_vec, 3, 1, M=0.0
+            )
 
-        assert elapsed < 0.5, f"M=0 should be fast, took {elapsed:.2f}s"
+        assert mock_linprog.call_count == 0, (
+            f"M=0 must skip the LP solver (fast path at "
+            f"_compute_worst_case_bias:1650); got "
+            f"{mock_linprog.call_count} linprog call(s)."
+        )
+        # End-to-end correctness: M=0 CI is still well-defined.
+        assert np.isfinite(ci_lb) and np.isfinite(ci_ub), (
+            f"M=0 CI must be finite; got [{ci_lb}, {ci_ub}]"
+        )
+        assert ci_lb <= ci_ub, f"M=0 CI must be ordered; got [{ci_lb}, {ci_ub}]"
 
     def test_smoothness_flci_with_survey_df(self):
         """Survey df should widen the smoothness FLCI (folded t vs folded normal)."""
@@ -493,3 +497,64 @@ def test_breakdown_monotonicity(self):
         # The optimal FLCI is efficient, so need large M for a weak effect.
         r_large = honest.fit(results, M=20.0)
         assert r_large.ci_lb <= 0 <= r_large.ci_ub, "Should lose significance at large M"
+
+
+class TestARPVertexEnumeration:
+    """Diagnostic warnings on `_enumerate_vertices` vertex-search pathologies."""
+
+    def test_enumerate_vertices_warns_on_exhausted_search(self):
+        """All-LinAlgError path: fully-zero nuisance column makes A_sys
+        singular on every basis, so the enumeration exhausts without
+        feasible vertices and the user should see a RuntimeWarning rather
+        than a silent empty-list return."""
+        from diff_diff.honest_did import _enumerate_vertices
+
+        # 4 moments, 1 nuisance column (all zeros) → A_sys singular on every basis
+        X_tilde = np.zeros((4, 1))
+        sigma_tilde_diag = np.array([1.0, 1.0, 1.0, 1.0])
+        with pytest.warns(RuntimeWarning, match="exhausted"):
+            vertices = _enumerate_vertices(X_tilde, sigma_tilde_diag, n_moments=4)
+        assert vertices == []
+
+    def test_enumerate_vertices_warns_on_heavy_rejection(self):
+        """Mixed-basis path: 5 moments, 1 nuisance column. C(5, 2) = 10
+        bases. By design, 6 bases hit LinAlgError (the singular pairs
+        among indices {0,1,2,3} that share aligned nuisance/sigma values)
+        and 4 bases produce feasible vertices (the (i, 4) pairs that pair
+        a positive-X_tilde row with the unique negative-X_tilde row at
+        index 4). 60% rejection rate trips the `heavily constrained`
+        branch specifically, not the exhausted branch."""
+        from diff_diff.honest_did import _enumerate_vertices
+
+        X_tilde = np.array([[1.0], [1.0], [1.0], [2.0], [-1.0]])
+        sigma_tilde_diag = np.array([1.0, 1.0, 1.0, 2.0, 1.0])
+        with pytest.warns(RuntimeWarning, match="heavily constrained"):
+            vertices = _enumerate_vertices(X_tilde, sigma_tilde_diag, n_moments=5)
+        assert len(vertices) >= 1, (
+            f"Heavy-rejection construction must still produce some feasible "
+            f"vertices (otherwise the exhausted branch fires); got "
+            f"{len(vertices)} vertices."
+        )
+
+    def test_enumerate_vertices_quiet_on_healthy_enumeration(self):
+        """Well-conditioned X_tilde: most bases solve cleanly and feasible
+        vertices are recovered. No RuntimeWarning should fire."""
+        from diff_diff.honest_did import _enumerate_vertices
+
+        rng = np.random.default_rng(0)
+        # 4 moments, 1 nuisance — small and well-conditioned
+        X_tilde = rng.normal(size=(4, 1))
+        sigma_tilde_diag = np.array([1.0, 1.0, 1.0, 1.0])
+        with warnings.catch_warnings(record=True) as caught:
+            warnings.simplefilter("always", RuntimeWarning)
+            vertices = _enumerate_vertices(X_tilde, sigma_tilde_diag, n_moments=4)
+        diag_warnings = [
+            w for w in caught
+            if "exhausted" in str(w.message) or "heavily constrained" in str(w.message)
+        ]
+        assert not diag_warnings, (
+            f"Healthy enumeration must not emit ARP diagnostics; got "
+            f"{[str(w.message) for w in diag_warnings]}"
+        )
+        # Sanity: we expect some feasible vertices on a well-conditioned input
+        assert isinstance(vertices, list)