diff --git a/CHANGELOG.md b/CHANGELOG.md
index 60e5c940..5d8caeb4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -34,6 +34,20 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
     `survey=`/`weights=` kwargs on the HAD pretest helpers (`stute_test`, `qug_test`,
     `did_had_pretest_workflow`, ...) are unchanged in this release and removed separately.
 
+### Fixed
+- **`HonestDiD` Δ^SD optimal-FLCI center parity with R (SE-audit B2b).** The optimal
+  Fixed-Length CI optimizer was a flat Nelder-Mead over slope weights that landed on a
+  different affine estimator than R `HonestDiD::findOptimalFLCI` at intermediate smoothness
+  `M` — the CI **center** drifted up to ~9% (the width/coverage matched). Replaced it with a
+  faithful port of R's **nested convex program**: an inner minimum-worst-case-bias problem at a
+  fixed estimator SD `h` (a smooth convex QCQP over slope weights, solved with `scipy` SLSQP —
+  no cvxpy) and an outer 1-D search over `h`. Now matches R's optimal FLCI **center +
+  half-length + optimalVec** to ~1e-3 (median ~1e-5) across a stress grid. diff-diff's
+  **analytical** folded-normal critical value is strictly more accurate than R's Monte-Carlo
+  `.qfoldednormal`, so it also solves the deterministic version of R's problem more precisely
+  than stock R. Verified vs R HonestDiD 0.2.6 (`benchmarks/data/honest_flci_golden.json`,
+  `TestHonestFLCIParityR`); the M=0 result and all existing behaviour are unchanged.
+
 ### Testing
 - **CI-locked standard-error parity for flagship and previously-unasserted paths (SE-audit
   coverage batch).** These surfaces computed SEs matching R but had no CI assertion pinning them
diff --git a/TODO.md b/TODO.md
index c35b548f..d721ffd3 100644
--- a/TODO.md
+++ b/TODO.md
@@ -34,7 +34,7 @@ The `Origin` column (Actionable tables) and the `PR` column (Deferred tables) bo
 | `CallawaySantAnna` no-covariate ipw treats the propensity as unconditional (no correction term); R's `did` fits an intercept-only logit whose estimation effect is identically zero in the IF, so values match — decide whether to document-only (current REGISTRY note) or mirror R's code path for structural parity. | `staggered.py::_ipw_estimation` (no-cov branch) | CS-scaling | Quick | Low |
 | Fold the R `did` 2.5.1 ipw aggregation yardsticks (hardcoded with provenance in `test_golden_ipw_aggregation_se_vs_r_did_251`) into `csdid_golden_values.json` on the next fixture regeneration — the generator already emits the ipw `aggte` blocks; switch the test to read the JSON. | `benchmarks/R/generate_csdid_test_values.R`, `tests/test_csdid_ported.py` | CS-scaling | Quick | Low |
 | TWFE's HC2/HC2-BM inline full-dummy build (`twfe.py:280-315`) duplicates the dummy-construction logic in `DifferenceInDifferences(fixed_effects=...)` (`estimators.py:478-486`). Extract a shared helper, or delegate TWFE's HC2/HC2-BM path to DiD's `fixed_effects=` branch (with TWFE-specific cluster-default threading), to reduce drift risk on FE naming / survey behavior / result-surface conventions. Substantive refactor — touches both estimators. | `twfe.py::fit`, `estimators.py::DifferenceInDifferences.fit` | follow-up | Heavy | Low |
-| `HonestDiD` Δ^SD optimal-FLCI affine-estimator optimizer (Nelder-Mead over slope weights) diverges from R `.FLCI.computeFLCI` at intermediate small M (~`[0.005, 0.02]`): the CI **center** shifts up to ~9% on wide pre/post windows while the **width** matches to ~1e-3. Not a local-minimum artifact (multi-start does not move it); the two implementations land on different affine estimators of near-equal length. Coverage is unaffected. Reconcile our FLCI optimization with R's exact algorithm. Exposed when the identified-set NaN gate was removed (finite CIs now surface at all M). | `honest_did.py::_compute_optimal_flci` | SE-audit | Mid | Low |
+| `HonestDiD` Δ^SD optimal-FLCI center parity — **LANDED (SE-audit B2b)**: replaced the flat Nelder-Mead affine-estimator optimizer with a faithful port of R `HonestDiD::findOptimalFLCI`'s nested convex program (inner min-worst-case-bias at fixed estimator SD `h` via SLSQP QCQP; outer grid-zoom over `h`). Matches R's center + half-length + optimalVec to ~1e-3 (median ~1e-5) across a stress grid; the prior ~9% intermediate-M center drift is removed (widths always matched, coverage unaffected). Analytical folded-normal cv is more accurate than R's MC `.qfoldednormal`. Golden `honest_flci_golden.json` + `TestHonestFLCIParityR`. | `honest_did.py::_flci_solve` | SE-audit | Done | Low |
 
 ### Performance
 
diff --git a/benchmarks/R/generate_honest_flci_golden.R b/benchmarks/R/generate_honest_flci_golden.R
new file mode 100644
index 00000000..7cd85477
--- /dev/null
+++ b/benchmarks/R/generate_honest_flci_golden.R
@@ -0,0 +1,102 @@
+#!/usr/bin/env Rscript
+# Generate R HonestDiD parity goldens for diff-diff's Delta^SD optimal FLCI
+# (`_compute_optimal_flci`, Rambachan & Roth 2023 Section 4.1). SE-audit B2b.
+#
+# Requires: R 4.4+, install.packages(c("HonestDiD", "jsonlite")).  HonestDiD 0.2.6.
+# Run from the REPO ROOT: `Rscript benchmarks/R/generate_honest_flci_golden.R`
+# (the output path below is resolved relative to the working directory).
+# Output: benchmarks/data/honest_flci_golden.json
+#
+# Two tiers, both stored per case:
+#   (1) override-R (PRIMARY): R's Monte-Carlo folded-normal quantile
+#       `.qfoldednormal` (10^6 draws, seed 0) is replaced by an ANALYTICAL
+#       quantile via assignInNamespace, so R solves the SAME deterministic outer
+#       problem as diff-diff (whose `_cv_alpha` is analytical). diff-diff matches
+#       the override-R center + half-length + optimalVec to ~1e-3 (median ~1e-5).
+#   (2) stock-R (REALISM): the unmodified MC `.qfoldednormal`. Because the width
+#       surface is near-flat at the optimum, R's MC noise perturbs R's own
+#       hstar/center by up to a few e-3 -- diff-diff (analytical) is strictly more
+#       accurate, so it matches stock R only to ~1.4e-2 (max observed). Looser tier.
+suppressWarnings(suppressMessages({
+  library(HonestDiD)
+  library(jsonlite)
+}))
+stopifnot(as.character(packageVersion("HonestDiD")) == "0.2.6")
+
+qfold_analytic <- function(p, mu = 0, sd = 1, ...) sapply(mu, function(m) {
+  f <- function(x) (pnorm(x - m, sd = sd) - pnorm(-x - m, sd = sd)) - p
+  uniroot(f, lower = 0, upper = abs(m) + sd * 12 + 5, tol = 1e-12)$root
+})
+
+# --- Curated stress grid (includes a curved [1,0,1,...] pre-trend, kink-prone
+#     for the L1 inner objective) ------------------------------------------------
+set.seed(20260707)
+cases <- list()
+for (npre in c(3, 6, 9)) {
+  for (npost in c(1, 4)) {
+    n <- npre + npost
+    idx <- 0:(n - 1)
+    for (rho in c(0.0, 0.5)) {
+      corr <- rho^abs(outer(idx, idx, "-"))
+      sigma <- corr * 0.01
+      base_pre <- rep(c(1, 0), length.out = npre)
+      beta <- c(base_pre, seq(1.2, 1.7, length.out = npost))
+      lvecs <- list(c(1, rep(0, npost - 1)))
+      if (npost > 1) lvecs <- c(lvecs, list(rep(1 / npost, npost)))
+      for (l in lvecs) {
+        for (M in c(0.0, 0.05, 0.1, 0.2, 0.5)) {
+          cases[[length(cases) + 1]] <- list(
+            beta = beta, sigma = sigma, num_pre = npre, num_post = npost,
+            l_vec = l, M = M, alpha = 0.05
+          )
+        }
+      }
+    }
+  }
+}
+
+run_flci <- function(c) {
+  r <- suppressWarnings(findOptimalFLCI(
+    betahat = c$beta, sigma = matrix(unlist(c$sigma), nrow = length(c$beta)),
+    M = c$M, numPrePeriods = c$num_pre, numPostPeriods = c$num_post,
+    l_vec = c$l_vec, alpha = c$alpha
+  ))
+  list(center = mean(r$FLCI), half_length = (r$FLCI[2] - r$FLCI[1]) / 2,
+       optimal_vec = as.numeric(r$optimalVec))
+}
+
+# stock-R tier first (unmodified MC .qfoldednormal)
+stock <- lapply(cases, function(c) tryCatch(run_flci(c)$center, error = function(e) NA))
+
+# override-R tier (deterministic analytical quantile) -- PRIMARY
+assignInNamespace(".qfoldednormal", qfold_analytic, "HonestDiD")
+out <- vector("list", length(cases))
+for (i in seq_along(cases)) {
+  c <- cases[[i]]
+  ov <- tryCatch(run_flci(c), error = function(e) NULL)
+  out[[i]] <- list(
+    beta = c$beta, sigma = c$sigma, num_pre = c$num_pre, num_post = c$num_post,
+    l_vec = c$l_vec, M = c$M, alpha = c$alpha,
+    center = if (is.null(ov)) NA else ov$center,
+    half_length = if (is.null(ov)) NA else ov$half_length,
+    optimal_vec = if (is.null(ov)) NA else ov$optimal_vec,
+    stock_center = stock[[i]]
+  )
+}
+
+golden <- list(
+  meta = list(
+    did_version = as.character(packageVersion("HonestDiD")),
+    n_cases = length(cases),
+    note = paste0(
+      "Delta^SD optimal FLCI. `center`/`half_length`/`optimal_vec` are override-R ",
+      "(analytical .qfoldednormal -> deterministic outer problem; diff-diff matches ",
+      "to ~1e-3). `stock_center` is unmodified MC-R (diff-diff matches to ~1.4e-2; the ",
+      "gap is R's simulation noise on the near-flat width surface)."
+    )
+  ),
+  cases = out
+)
+out_path <- file.path("benchmarks", "data", "honest_flci_golden.json")
+writeLines(toJSON(golden, auto_unbox = TRUE, digits = 14, pretty = TRUE), out_path)
+cat("Wrote", out_path, "-", length(cases), "cases\n")
diff --git a/benchmarks/data/honest_flci_golden.json b/benchmarks/data/honest_flci_golden.json
new file mode 100644
index 00000000..29f7c973
--- /dev/null
+++ b/benchmarks/data/honest_flci_golden.json
@@ -0,0 +1,2079 @@
+{
+  "meta": {
+    "did_version": "0.2.6",
+    "n_cases": 90,
+    "note": "Delta^SD optimal FLCI. `center`/`half_length`/`optimal_vec` are override-R (analytical .qfoldednormal -> deterministic outer problem; diff-diff matches to ~1e-3). `stock_center` is unmodified MC-R (diff-diff matches to ~1.4e-2; the gap is R's simulation noise on the near-flat width surface)."
+  },
+  "cases": [
+    {
+      "beta": [1, 0, 1, 1.2],
+      "sigma": [
+        [0.01, 0, 0, 0],
+        [0, 0.01, 0, 0],
+        [0, 0, 0.01, 0],
+        [0, 0, 0, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 1,
+      "l_vec": 1,
+      "M": 0,
+      "alpha": 0.05,
+      "center": 1.48575528987607,
+      "half_length": 0.202875546401568,
+      "optimal_vec": [0.214101056232411, 0.143021320229767, 0.0716542336436621, 1],
+      "stock_center": 1.48575528987607
+    },
+    {
+      "beta": [1, 0, 1, 1.2],
+      "sigma": [
+        [0.01, 0, 0, 0],
+        [0, 0.01, 0, 0],
+        [0, 0, 0.01, 0],
+        [0, 0, 0, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 1,
+      "l_vec": 1,
+      "M": 0.05,
+      "alpha": 0.05,
+      "center": 1.52634895987866,
+      "half_length": 0.250459332503154,
+      "optimal_vec": [0.0314153336190004, 0.305410186411428, 0.294933626259655, 1],
+      "stock_center": 1.53269987482138
+    },
+    {
+      "beta": [1, 0, 1, 1.2],
+      "sigma": [
+        [0.01, 0, 0, 0],
+        [0, 0.01, 0, 0],
+        [0, 0, 0.01, 0],
+        [0, 0, 0, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 1,
+      "l_vec": 1,
+      "M": 0.1,
+      "alpha": 0.05,
+      "center": 1.67452641383249,
+      "half_length": 0.313458657958823,
+      "optimal_vec": [1.4015842980875e-10, 0.262736792932774, 0.474526413692334, 1],
+      "stock_center": 1.6769901069974
+    },
+    {
+      "beta": [1, 0, 1, 1.2],
+      "sigma": [
+        [0.01, 0, 0, 0],
+        [0, 0.01, 0, 0],
+        [0, 0, 0.01, 0],
+        [0, 0, 0, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 1,
+      "l_vec": 1,
+      "M": 0.2,
+      "alpha": 0.05,
+      "center": 2.03478246906161,
+      "half_length": 0.431217243166294,
+      "optimal_vec": [-5.22063031086743e-12, 0.0826087654750007, 0.834782469066833, 1],
+      "stock_center": 2.03568602943555
+    },
+    {
+      "beta": [1, 0, 1, 1.2],
+      "sigma": [
+        [0.01, 0, 0, 0],
+        [0, 0.01, 0, 0],
+        [0, 0, 0.01, 0],
+        [0, 0, 0, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 1,
+      "l_vec": 1,
+      "M": 0.5,
+      "alpha": 0.05,
+      "center": 2.19999999993086,
+      "half_length": 0.732617430726547,
+      "optimal_vec": [-1.0773491809276e-11, 4.53342779325044e-11, 0.999999999941632, 1],
+      "stock_center": 2.19999999993086
+    },
+    {
+      "beta": [1, 0, 1, 1.2],
+      "sigma": [
+        [0.01, 0.005, 0.0025, 0.00125],
+        [0.005, 0.01, 0.005, 0.0025],
+        [0.0025, 0.005, 0.01, 0.005],
+        [0.00125, 0.0025, 0.005, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 1,
+      "l_vec": 1,
+      "M": 0,
+      "alpha": 0.05,
+      "center": 1.12853523123463,
+      "half_length": 0.195119452680227,
+      "optimal_vec": [0.42841075193424, 0.107321653181894, -0.49987552069961, 1],
+      "stock_center": 1.12853523123463
+    },
+    {
+      "beta": [1, 0, 1, 1.2],
+      "sigma": [
+        [0.01, 0.005, 0.0025, 0.00125],
+        [0.005, 0.01, 0.005, 0.0025],
+        [0.0025, 0.005, 0.01, 0.005],
+        [0.00125, 0.0025, 0.005, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 1,
+      "l_vec": 1,
+      "M": 0.05,
+      "alpha": 0.05,
+      "center": 1.06873476216774,
+      "half_length": 0.271013845132539,
+      "optimal_vec": [0.159478512980705, 0.406154105932635, -0.290743750812968, 1],
+      "stock_center": 1.06624599124562
+    },
+    {
+      "beta": [1, 0, 1, 1.2],
+      "sigma": [
+        [0.01, 0.005, 0.0025, 0.00125],
+        [0.005, 0.01, 0.005, 0.0025],
+        [0.0025, 0.005, 0.01, 0.005],
+        [0.00125, 0.0025, 0.005, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 1,
+      "l_vec": 1,
+      "M": 0.1,
+      "alpha": 0.05,
+      "center": 1.19412747799138,
+      "half_length": 0.351476184950717,
+      "optimal_vec": [1.08604539783501e-10, 0.502936260894609, -0.00587252211722639, 1],
+      "stock_center": 1.19632983187625
+    },
+    {
+      "beta": [1, 0, 1, 1.2],
+      "sigma": [
+        [0.01, 0.005, 0.0025, 0.00125],
+        [0.005, 0.01, 0.005, 0.0025],
+        [0.0025, 0.005, 0.01, 0.005],
+        [0.00125, 0.0025, 0.005, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 1,
+      "l_vec": 1,
+      "M": 0.2,
+      "alpha": 0.05,
+      "center": 2.00143608768822,
+      "half_length": 0.484211636465734,
+      "optimal_vec": [-2.26527210459502e-11, 0.0992819561786276, 0.801436087710874, 1],
+      "stock_center": 2.00635347859419
+    },
+    {
+      "beta": [1, 0, 1, 1.2],
+      "sigma": [
+        [0.01, 0.005, 0.0025, 0.00125],
+        [0.005, 0.01, 0.005, 0.0025],
+        [0.0025, 0.005, 0.01, 0.005],
+        [0.00125, 0.0025, 0.005, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 1,
+      "l_vec": 1,
+      "M": 0.5,
+      "alpha": 0.05,
+      "center": 2.19999999985492,
+      "half_length": 0.784897005287011,
+      "optimal_vec": [-8.57140210135209e-12, 8.12690573363712e-11, 0.999999999863488, 1],
+      "stock_center": 2.19999999985492
+    },
+    {
+      "beta": [1, 0, 1, 1.2, 1.36666666666667, 1.53333333333333, 1.7],
+      "sigma": [
+        [0.01, 0, 0, 0, 0, 0, 0],
+        [0, 0.01, 0, 0, 0, 0, 0],
+        [0, 0, 0.01, 0, 0, 0, 0],
+        [0, 0, 0, 0.01, 0, 0, 0],
+        [0, 0, 0, 0, 0.01, 0, 0],
+        [0, 0, 0, 0, 0, 0.01, 0],
+        [0, 0, 0, 0, 0, 0, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 4,
+      "l_vec": [1, 0, 0, 0],
+      "M": 0,
+      "alpha": 0.05,
+      "center": 1.48575528987607,
+      "half_length": 0.202875546401568,
+      "optimal_vec": [0.214101056232411, 0.143021320229767, 0.0716542336436621, 1, 0, 0, 0],
+      "stock_center": 1.48575528987607
+    },
+    {
+      "beta": [1, 0, 1, 1.2, 1.36666666666667, 1.53333333333333, 1.7],
+      "sigma": [
+        [0.01, 0, 0, 0, 0, 0, 0],
+        [0, 0.01, 0, 0, 0, 0, 0],
+        [0, 0, 0.01, 0, 0, 0, 0],
+        [0, 0, 0, 0.01, 0, 0, 0],
+        [0, 0, 0, 0, 0.01, 0, 0],
+        [0, 0, 0, 0, 0, 0.01, 0],
+        [0, 0, 0, 0, 0, 0, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 4,
+      "l_vec": [1, 0, 0, 0],
+      "M": 0.05,
+      "alpha": 0.05,
+      "center": 1.52634895987866,
+      "half_length": 0.250459332503154,
+      "optimal_vec": [0.0314153336190004, 0.305410186411428, 0.294933626259655, 1, 0, 0, 0],
+      "stock_center": 1.53269987471633
+    },
+    {
+      "beta": [1, 0, 1, 1.2, 1.36666666666667, 1.53333333333333, 1.7],
+      "sigma": [
+        [0.01, 0, 0, 0, 0, 0, 0],
+        [0, 0.01, 0, 0, 0, 0, 0],
+        [0, 0, 0.01, 0, 0, 0, 0],
+        [0, 0, 0, 0.01, 0, 0, 0],
+        [0, 0, 0, 0, 0.01, 0, 0],
+        [0, 0, 0, 0, 0, 0.01, 0],
+        [0, 0, 0, 0, 0, 0, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 4,
+      "l_vec": [1, 0, 0, 0],
+      "M": 0.1,
+      "alpha": 0.05,
+      "center": 1.67452641471952,
+      "half_length": 0.313458657958824,
+      "optimal_vec": [1.4015842310939e-10, 0.262736792489259, 0.474526414579359, 1, 0, 0, 0],
+      "stock_center": 1.6769901069974
+    },
+    {
+      "beta": [1, 0, 1, 1.2, 1.36666666666667, 1.53333333333333, 1.7],
+      "sigma": [
+        [0.01, 0, 0, 0, 0, 0, 0],
+        [0, 0.01, 0, 0, 0, 0, 0],
+        [0, 0, 0.01, 0, 0, 0, 0],
+        [0, 0, 0, 0.01, 0, 0, 0],
+        [0, 0, 0, 0, 0.01, 0, 0],
+        [0, 0, 0, 0, 0, 0.01, 0],
+        [0, 0, 0, 0, 0, 0, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 4,
+      "l_vec": [1, 0, 0, 0],
+      "M": 0.2,
+      "alpha": 0.05,
+      "center": 2.03478246906161,
+      "half_length": 0.431217243166294,
+      "optimal_vec": [-5.22063031086743e-12, 0.0826087654750007, 0.834782469066833, 1, 0, 0, 0],
+      "stock_center": 2.03568602943555
+    },
+    {
+      "beta": [1, 0, 1, 1.2, 1.36666666666667, 1.53333333333333, 1.7],
+      "sigma": [
+        [0.01, 0, 0, 0, 0, 0, 0],
+        [0, 0.01, 0, 0, 0, 0, 0],
+        [0, 0, 0.01, 0, 0, 0, 0],
+        [0, 0, 0, 0.01, 0, 0, 0],
+        [0, 0, 0, 0, 0.01, 0, 0],
+        [0, 0, 0, 0, 0, 0.01, 0],
+        [0, 0, 0, 0, 0, 0, 0.01]
+      ],
+      "num_pre": 3,
+      "num_post": 4,
+      "l_vec": [1, 0, 0, 0],
+      "M": 0.5,
+      "alpha": 0.05,
+      "center": 2.19999999993086,
+      "half_length": 0.732617430726547,
+      "optimal_vec": [-1.0773491809276e-11, 4.53342779325044e-11, 0.999999999941632, 1, 0, 0, 0],
+      "stock_center": 2.19999999993086
+    },
+    {
+      "beta": [1, 0, 1, 1.2, 1.36666666666667, 1.53333333333333, 1.7],
+      "sigma": [
+        [0.01, 0, 0, 0, 0, 0, 0],
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+        [0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625],
+        [7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125],
+        [3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625],
+        [1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125],
+        [9.765625e-06, 1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025],
+        [4.8828125e-06, 9.765625e-06, 1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005],
+        [2.44140625e-06, 4.8828125e-06, 9.765625e-06, 1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01]
+      ],
+      "num_pre": 9,
+      "num_post": 4,
+      "l_vec": [0.25, 0.25, 0.25, 0.25],
+      "M": 0.1,
+      "alpha": 0.05,
+      "center": 1.8763090766382,
+      "half_length": 0.871814486784312,
+      "optimal_vec": [-9.17276889406284e-13, 6.52872075756517e-15, -9.17790798084749e-13, -1.8649564535257e-12, -4.08519336820438e-12, -1.10294242823093e-11, 3.44955403845706e-10, 1.03684546137868, 0.426309076299168, 0.25, 0.25, 0.25, 0.25],
+      "stock_center": 1.87704548356434
+    },
+    {
+      "beta": [1, 0, 1, 0, 1, 0, 1, 0, 1, 1.2, 1.36666666666667, 1.53333333333333, 1.7],
+      "sigma": [
+        [0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05, 3.90625e-05, 1.953125e-05, 9.765625e-06, 4.8828125e-06, 2.44140625e-06],
+        [0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05, 3.90625e-05, 1.953125e-05, 9.765625e-06, 4.8828125e-06],
+        [0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05, 3.90625e-05, 1.953125e-05, 9.765625e-06],
+        [0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05, 3.90625e-05, 1.953125e-05],
+        [0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05, 3.90625e-05],
+        [0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05],
+        [0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625],
+        [7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125],
+        [3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625],
+        [1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125],
+        [9.765625e-06, 1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025],
+        [4.8828125e-06, 9.765625e-06, 1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005],
+        [2.44140625e-06, 4.8828125e-06, 9.765625e-06, 1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01]
+      ],
+      "num_pre": 9,
+      "num_post": 4,
+      "l_vec": [0.25, 0.25, 0.25, 0.25],
+      "M": 0.2,
+      "alpha": 0.05,
+      "center": 2.95301862473338,
+      "half_length": 1.45224201688975,
+      "optimal_vec": [-1.10683183776666e-13, 1.87932698050233e-16, -1.10746414514918e-13, -2.21633627632278e-13, -4.46896286918287e-13, -1.02544050290325e-12, 5.04240750554483e-12, 0.498490687632721, 1.50301862472901, 0.25, 0.25, 0.25, 0.25],
+      "stock_center": 2.95620098482395
+    },
+    {
+      "beta": [1, 0, 1, 0, 1, 0, 1, 0, 1, 1.2, 1.36666666666667, 1.53333333333333, 1.7],
+      "sigma": [
+        [0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05, 3.90625e-05, 1.953125e-05, 9.765625e-06, 4.8828125e-06, 2.44140625e-06],
+        [0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05, 3.90625e-05, 1.953125e-05, 9.765625e-06, 4.8828125e-06],
+        [0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05, 3.90625e-05, 1.953125e-05, 9.765625e-06],
+        [0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05, 3.90625e-05, 1.953125e-05],
+        [0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05, 3.90625e-05],
+        [0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625, 7.8125e-05],
+        [0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125, 0.00015625],
+        [7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625, 0.0003125],
+        [3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125, 0.000625],
+        [1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025, 0.00125],
+        [9.765625e-06, 1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005, 0.0025],
+        [4.8828125e-06, 9.765625e-06, 1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01, 0.005],
+        [2.44140625e-06, 4.8828125e-06, 9.765625e-06, 1.953125e-05, 3.90625e-05, 7.8125e-05, 0.00015625, 0.0003125, 0.000625, 0.00125, 0.0025, 0.005, 0.01]
+      ],
+      "num_pre": 9,
+      "num_post": 4,
+      "l_vec": [0.25, 0.25, 0.25, 0.25],
+      "M": 0.5,
+      "alpha": 0.05,
+      "center": 3.9499999999979,
+      "half_length": 2.96341397439769,
+      "optimal_vec": [-2.9437718098552e-15, 5.09993128640104e-18, -2.94060794802578e-15, -5.8762387686928e-15, -1.17533429253264e-14, -2.35778666615341e-14, -4.96997605132596e-14, 1.40615553048958e-12, 2.49999999999796, 0.25, 0.25, 0.25, 0.25],
+      "stock_center": 3.9499999999979
+    }
+  ]
+}
diff --git a/diff_diff/honest_did.py b/diff_diff/honest_did.py
index bf6da448..9308a71f 100644
--- a/diff_diff/honest_did.py
+++ b/diff_diff/honest_did.py
@@ -1709,7 +1709,181 @@ def _compute_worst_case_bias(
         return np.inf
 
 
-def _compute_optimal_flci(
+def _flci_bias_constant(l_vec: np.ndarray, num_post: int) -> float:
+    """Constant term of the worst-case-bias objective (R's
+    ``.createObjectiveObjectForBias``): ``sum_s |sum_{k=1..s} k*l[Tbar-s+k]| -
+    sum_s s*l[s]``. For NONNEGATIVE (averaging) ``l_vec`` the closed form
+    ``M*(constant + sum_i |cumsum(w)_i|)`` equals ``_compute_worst_case_bias(w,
+    ..., M)`` (the LP oracle) to machine precision; for signed/contrast ``l_vec``
+    it intentionally follows R's conservative closed form (the FLCI still matches
+    R). See REGISTRY.md Delta^SD FLCI note.
+    """
+    c = 0.0
+    for s in range(1, num_post + 1):
+        seg = l_vec[num_post - s : num_post]
+        c += abs(float(np.dot(np.arange(1, s + 1), seg)))
+    c -= float(np.dot(np.arange(1, num_post + 1), l_vec))
+    return c
+
+
+def _flci_precompute(sigma: np.ndarray, l_vec: np.ndarray, num_pre: int, num_post: int) -> dict:
+    """Precompute the FLCI inner problem's quadratic-variance and bias pieces
+    (``sigma`` ordered ``[pre; post]``). ``D`` is the first-difference operator
+    (identical to the pre-block of ``_w_to_v``), ``L`` the cumsum operator, so the
+    estimator variance is ``var(w) = w'Qw + q'w + c0`` and the linear-trend
+    neutrality target is ``sum(w) = sum_s s*l[s]`` (R & R 2023 Eq. 17)."""
+    s_pre = sigma[:num_pre, :num_pre]
+    s_pp = sigma[:num_pre, num_pre:]
+    s_post = float(l_vec @ sigma[num_pre:, num_pre:] @ l_vec)
+    d_mat = np.eye(num_pre)
+    for col in range(num_pre - 1):
+        d_mat[col + 1, col] = -1.0
+    return {
+        "Q": d_mat.T @ s_pre @ d_mat,
+        "q": 2.0 * (d_mat.T @ s_pp @ l_vec),
+        "c0": s_post,
+        "L": np.tril(np.ones((num_pre, num_pre))),
+        "target": float(np.dot(np.arange(1, num_post + 1), l_vec)),
+        "constant": _flci_bias_constant(l_vec, num_post),
+        "num_pre": num_pre,
+    }
+
+
+def _flci_var(w: np.ndarray, P: dict) -> float:
+    return float(w @ P["Q"] @ w + P["q"] @ w + P["c0"])
+
+
+def _flci_w_min(P: dict) -> np.ndarray:
+    """Minimum-variance weights subject to ``sum(w)=target`` via the
+    equality-constrained KKT system (the abs-value constraints are non-binding for
+    the min-variance objective; verified against R's ``.findLowestH``)."""
+    k = P["num_pre"]
+    kkt = np.zeros((k + 1, k + 1))
+    kkt[:k, :k] = 2.0 * P["Q"]
+    kkt[:k, k] = 1.0
+    kkt[k, :k] = 1.0
+    rhs = np.concatenate([-P["q"], [P["target"]]])
+    try:
+        sol = np.linalg.solve(kkt, rhs)
+    except np.linalg.LinAlgError:
+        sol = np.linalg.lstsq(kkt, rhs, rcond=None)[0]
+    return sol[:k]
+
+
+def _flci_h_bounds(P: dict):
+    """FLCI bracket: ``hmin`` = minimum estimator SD (R ``.findLowestH``), ``h0`` =
+    SD at the minimum-bias weights (all mass on the boundary slope, R
+    ``.findHForMinimumBias``). Both match R's closed forms to ~1e-8."""
+    w_min = _flci_w_min(P)
+    hmin = float(np.sqrt(max(_flci_var(w_min, P), 0.0)))
+    w_hi = np.zeros(P["num_pre"])
+    w_hi[-1] = P["target"]
+    h0 = float(np.sqrt(max(_flci_var(w_hi, P), 0.0)))
+    return hmin, h0, w_min
+
+
+def _flci_min_bias_given_h(P: dict, h: float, x0_w: Optional[np.ndarray] = None):
+    """Inner solve (R's ``.findWorstCaseBiasGivenH``): minimize the worst-case bias
+    ``constant + sum_i|cumsum(w)_i|`` subject to ``sum(w)=target`` and the
+    second-order-cone ``var(w) <= h^2``, as a smooth convex QCQP over ``x=[U; w]``
+    (``U >= |Lw|``) via SLSQP. Returns ``(w, bias_unit, feasible)``.
+
+    Gating is on FEASIBILITY (``var<=h^2`` and ``sum=target``), NOT ``res.success``
+    -- SLSQP frequently reports ``success=False`` on a correct convex optimum.
+    """
+    from scipy.optimize import minimize as _sp_minimize
+
+    k = P["num_pre"]
+    L = P["L"]
+    if k == 1:
+        w = np.array([P["target"]])
+        return w, P["constant"] + float(np.abs(L @ w).sum()), True
+    if x0_w is None:
+        x0_w = _flci_w_min(P)
+    x0 = np.concatenate([np.abs(L @ x0_w), x0_w])
+    c = np.concatenate([np.ones(k), np.zeros(k)])
+    cons = [
+        {
+            "type": "ineq",
+            "fun": lambda x: x[:k] - L @ x[k:],
+            "jac": lambda x: np.hstack([np.eye(k), -L]),
+        },
+        {
+            "type": "ineq",
+            "fun": lambda x: x[:k] + L @ x[k:],
+            "jac": lambda x: np.hstack([np.eye(k), L]),
+        },
+        {
+            "type": "eq",
+            "fun": lambda x: float(np.sum(x[k:]) - P["target"]),
+            "jac": lambda x: np.concatenate([np.zeros(k), np.ones(k)]),
+        },
+        {
+            "type": "ineq",
+            "fun": lambda x: h * h - _flci_var(x[k:], P),
+            "jac": lambda x: np.concatenate([np.zeros(k), -(2.0 * P["Q"] @ x[k:] + P["q"])]),
+        },
+    ]
+    res = _sp_minimize(
+        lambda x: float(c @ x),
+        x0,
+        jac=lambda x: c,
+        constraints=cons,
+        method="SLSQP",
+        options={"ftol": 1e-12, "maxiter": 500},
+    )
+    w = res.x[k:]
+    feasible = (_flci_var(w, P) <= h * h + 1e-7) and (abs(float(np.sum(w)) - P["target"]) < 1e-6)
+    return w, P["constant"] + float(np.abs(L @ w).sum()), bool(feasible)
+
+
+def _flci_optimal_h(
+    P: dict,
+    hmin: float,
+    h0: float,
+    M: float,
+    alpha: float,
+    df: Optional[int],
+    levels=(40, 120, 120),
+) -> float:
+    """Argmin over the estimator SD ``h`` of the half-length
+    ``W(h)=cv(M*bias(h)/h)*h`` (R's ``.findOptimalCIDerivativeBisection``), by a
+    multi-level GRID ZOOM. Each level restarts from ``w_min`` and warm-starts the
+    inner solve within the level (``h`` ascending), which keeps the objective
+    smooth despite ~1e-6 SLSQP noise; zooming refines resolution.
+
+    A grid zoom (not R's derivative-bisection or an envelope-theorem derivative) is
+    used deliberately: the width surface is near-flat at the optimum AND the
+    min-bias inner solutions are degenerate (most ``cumsum(w)`` components sit at
+    the abs-value kink), so ``mu`` is not recoverable from ``sign(Lw)`` and
+    finite-difference derivatives are swamped by solver noise. Matches R's
+    (deterministic) center to <3e-4 across the validated stress grid.
+    """
+    if h0 - hmin < 1e-12:
+        return h0
+    lo, hi = hmin, h0
+    gi, grid = 0, np.array([hmin])
+    for npts in levels:
+        grid = np.linspace(lo, hi, npts)
+        seed = _flci_w_min(P)
+        vals = np.full(npts, np.inf)
+        for i, h in enumerate(grid):
+            if h <= 0.0:  # rank-deficient covariance -> hmin=0; skip (M*bias/h undefined)
+                continue
+            w, bias_unit, ok = _flci_min_bias_given_h(P, h, x0_w=seed)
+            if ok and np.isfinite(bias_unit):
+                vals[i] = _cv_alpha(M * bias_unit / h, alpha, df=df) * h
+                seed = w
+        gi = int(np.argmin(vals))
+        if not np.isfinite(vals[gi]):
+            return float("nan")
+        step = (hi - lo) / (npts - 1)
+        lo = max(grid[gi] - 2 * step, hmin)
+        hi = min(grid[gi] + 2 * step, h0)
+    return float(grid[gi])
+
+
+def _flci_solve(
     beta_pre: np.ndarray,
     beta_post: np.ndarray,
     sigma: np.ndarray,
@@ -1719,7 +1893,7 @@ def _compute_optimal_flci(
     M: float,
     alpha: float = 0.05,
     df: Optional[int] = None,
-) -> Tuple[float, float]:
+) -> Tuple[float, float, Optional[np.ndarray]]:
     """
     Compute the optimal Fixed Length Confidence Interval for Delta^SD.
 
@@ -1765,72 +1939,68 @@ def _compute_optimal_flci(
         Lower bound of FLCI.
     ci_ub : float
         Upper bound of FLCI.
+    optimal_vec : np.ndarray or None
+        The optimal affine-estimator direction ``v`` (``theta_hat = v'beta``), for
+        parity testing; ``None`` when the CI is NaN.
     """
-    T = num_pre
-    Tbar = num_post
-
-    # Survey df gating: df<=0 sentinel → NaN inference
+    # Negative smoothness is invalid (cv_alpha's abs() would silently treat it as
+    # +|M|); guard the direct helper path too (fit()/sensitivity_analysis() also
+    # validate, but tests call this directly).
+    if M < 0:
+        raise ValueError(f"M must be non-negative, got M={M}")
+    # Survey df<=0 sentinel -> NaN inference.
     if df is not None and df <= 0:
-        return np.nan, np.nan
-
-    # T slopes total (s = -T+1, ..., 0), including boundary slope s=0.
-    # Linear-trend neutrality requires sum(w) = sum_j j*l_j (Eq. 17).
-    n_slopes = T
-    target_sum = float(np.dot(np.arange(1, Tbar + 1), l_vec))
-
-    def flci_half_length(w_free):
-        """Compute FLCI half-length for given free slope weights."""
-        # Reconstruct full w with constraint sum(w) = target_sum
-        if n_slopes == 1:
-            w = np.array([target_sum])
-        elif len(w_free) == n_slopes - 1:
-            w = np.concatenate([w_free, [target_sum - np.sum(w_free)]])
-        else:
-            w = w_free
-
-        # Map w -> v for variance
-        v = _w_to_v(w, l_vec, T)
-        sigma_v = np.sqrt(float(v @ sigma @ v))
-        if sigma_v <= 0:
-            return np.inf
-
-        # Compute bias in fd-space
-        bias = _compute_worst_case_bias(w, l_vec, T, Tbar, M)
-        if not np.isfinite(bias):
-            return np.inf
-
-        t = float(bias / sigma_v)
-        cv = _cv_alpha(t, alpha, df=df)
-        return float(sigma_v * cv)
-
-    from scipy.optimize import minimize as scipy_minimize
+        return np.nan, np.nan, None
 
-    if n_slopes == 1:
-        # Only one slope weight, determined by constraint.
-        w_opt = np.array([target_sum])
-        chi = flci_half_length(w_opt)
-    else:
-        # Optimize over T-1 free parameters (last w determined by sum constraint)
-        x0 = np.full(n_slopes - 1, target_sum / n_slopes)
-
-        result = scipy_minimize(
-            flci_half_length,
-            x0=x0,
-            method="Nelder-Mead",
-            options={"maxiter": 500, "xatol": 1e-5, "fatol": 1e-6},
-        )
-        w_opt = np.concatenate([result.x, [target_sum - np.sum(result.x)]])
-        chi = flci_half_length(result.x)
-
-    # Build the estimator value: theta_hat = v'beta
+    P = _flci_precompute(sigma, l_vec, num_pre, num_post)
     beta_full = np.concatenate([beta_pre, beta_post])
-    v_opt = _w_to_v(w_opt, l_vec, T)
-    theta_hat = float(v_opt @ beta_full)
 
+    with np.errstate(divide="ignore", invalid="ignore", over="ignore"):
+        if M == 0.0:
+            # Zero worst-case bias (linear trends): the FLCI estimator is simply the
+            # minimum-variance affine estimator, so this branch is unchanged from the
+            # prior optimizer's M=0 behaviour (min variance -> half-length z*sd).
+            w_opt = _flci_w_min(P)
+            hstar = float(np.sqrt(max(_flci_var(w_opt, P), 0.0)))
+            if hstar <= 0.0:
+                # Zero estimator SD (degenerate covariance) -> undefined inference.
+                return np.nan, np.nan, None
+            chi = _cv_alpha(0.0, alpha, df=df) * hstar
+        else:
+            hmin, h0, _ = _flci_h_bounds(P)
+            hstar = _flci_optimal_h(P, hmin, h0, M, alpha, df)
+            # hstar<=0 (zero SD, e.g. degenerate covariance) would divide by zero in
+            # M*bias/hstar; NaN the inference per the zero-SE convention.
+            if not np.isfinite(hstar) or hstar <= 0.0:
+                return np.nan, np.nan, None
+            w_opt, bias_unit, feasible = _flci_min_bias_given_h(P, hstar)
+            if not feasible:
+                return np.nan, np.nan, None
+            chi = _cv_alpha(M * bias_unit / hstar, alpha, df=df) * hstar
+
+    v_opt = _w_to_v(w_opt, l_vec, num_pre)
+    theta_hat = float(v_opt @ beta_full)
     if not np.isfinite(chi):
-        return np.nan, np.nan
+        return np.nan, np.nan, None
+    return theta_hat - chi, theta_hat + chi, v_opt
+
 
-    return theta_hat - chi, theta_hat + chi
+def _compute_optimal_flci(
+    beta_pre: np.ndarray,
+    beta_post: np.ndarray,
+    sigma: np.ndarray,
+    l_vec: np.ndarray,
+    num_pre: int,
+    num_post: int,
+    M: float,
+    alpha: float = 0.05,
+    df: Optional[int] = None,
+) -> Tuple[float, float]:
+    """Optimal Delta^SD FLCI ``(ci_lb, ci_ub)`` (Rambachan & Roth 2023 §4.1).
+    Thin wrapper over :func:`_flci_solve` (which also returns the optimal affine
+    estimator direction ``v`` for parity testing)."""
+    lb, ub, _ = _flci_solve(beta_pre, beta_post, sigma, l_vec, num_pre, num_post, M, alpha, df)
+    return lb, ub
 
 
 def _setup_moment_inequalities(
@@ -2315,6 +2485,10 @@ def fit(
             Results containing bounds and robust confidence intervals.
         """
         M = M if M is not None else self.M
+        # The fit()-time M override bypasses constructor validation; re-check here
+        # (a negative M would be silently treated as +|M| via cv_alpha's abs()).
+        if M < 0:
+            raise ValueError(f"M must be non-negative, got M={M}")
 
         # Extract event study parameters
         beta_hat, sigma, num_pre, num_post, pre_periods, post_periods, df_survey = (
@@ -2690,6 +2864,8 @@ def sensitivity_analysis(
                 M_grid = [0, 0.1, 0.2, 0.3, 0.5, 0.75, 1.0]
 
         M_values = np.array(M_grid)
+        if np.any(M_values < 0):
+            raise ValueError(f"M must be non-negative; M_grid has a negative value: {M_grid}")
         bounds_list = []
         ci_list = []
 
diff --git a/docs/methodology/REGISTRY.md b/docs/methodology/REGISTRY.md
index 98fb462d..c351896e 100644
--- a/docs/methodology/REGISTRY.md
+++ b/docs/methodology/REGISTRY.md
@@ -3614,7 +3614,7 @@ Post-treatment consecutive first differences bounded by M̄ × max pre-treatment
 CRITICAL: δ_pre = β_pre pins pre-treatment violations to observed coefficients. Solved via LP (scipy.optimize.linprog).
 
 *Inference (Sections 3.2, 4.1):*
-- Delta^SD: Optimal FLCI — jointly optimizes affine estimator direction and half-length via folded normal quantile cv_α(bias/se) (Equation 18). When `df_survey` is present, uses folded non-central t (`scipy.stats.nct`) instead of folded normal; `df_survey=0` → NaN inference. For M=0, uses `_get_critical_value(alpha, df)` (standard t/z).
+- Delta^SD: Optimal FLCI — a nested convex program (inner: minimize worst-case bias at a fixed estimator SD `h`; outer: minimize the half-length over `h`) that matches R `HonestDiD::findOptimalFLCI`'s optimal affine estimator, using the folded-normal quantile cv_α(bias/se) (Equation 18). See the "Δ^SD FLCI optimizer" note below for the algorithm + R parity. When `df_survey` is present, uses folded non-central t (`scipy.stats.nct`) instead of folded normal; `df_survey=0` → NaN inference. For M=0, uses `_get_critical_value(alpha, df)` (standard t/z).
 - Delta^RM: Paper recommends ARP conditional/hybrid confidence sets (Equations 14-15, κ = α/10). Currently uses **naive FLCI** unconditionally (conservative — wider CIs, valid coverage). ARP infrastructure exists but is disabled.
 - **Note (deviation from R):** Delta^RM CIs use naive FLCI (`lb - z*se, ub + z*se`) instead of the paper's ARP hybrid. R's `HonestDiD` package implements full ARP conditional/hybrid. Our naive FLCI is conservative (wider, valid coverage) but does not adapt to the length of the identified set. ARP implementation deferred (see TODO.md).
 - **Note:** `method="combined"` (Delta^SDRM) uses naive FLCI on the intersection of Delta^SD and Delta^RM bounds. The paper proves FLCI is NOT consistent for Delta^SDRM (Proposition 4.2). The paper recommends ARP hybrid for non-SD restriction classes. This is a known conservative approximation; a runtime UserWarning is emitted.
@@ -3629,7 +3629,37 @@ CRITICAL: δ_pre = β_pre pins pre-treatment violations to observed coefficients
 - Breakdown point: smallest M where CI includes zero
 - Negative M: not valid (constraints become infeasible)
 - **Note:** Δ^SD **empty estimated identified set** (the observed pre-trend's curvature exceeds M, so the `δ_pre = β_pre`-pinned identified-set LP is infeasible → `lb`/`ub` = NaN) does **not** suppress the FLCI. The optimal FLCI is an affine estimator whose worst-case bias is taken over `δ ∈ Δ^SD(M)` treating β as random, so it is well-defined given (Σ, M) regardless of whether the realized `β_pre` lies in Δ; R's `HonestDiD::createSensitivityResults` returns it in exactly this case. `_compute_smoothness_bounds` therefore returns the finite FLCI with `lb`/`ub` = NaN (empty id-set), matching R (prior behavior NaN-propagated the whole result, silently yielding no inference on high-curvature pre-trends). The naive fallback FLCI (diagonal Σ only) still requires finite id-set bounds and returns NaN CI when infeasible. Guarded by `test_infeasible_smoothness_fit_returns_flci_with_empty_idset`.
-- **Note (deviation from R — Δ^SD FLCI optimizer at intermediate M):** The optimal-FLCI affine-estimator optimization (Nelder-Mead over slope weights) agrees with R `createSensitivityResults` to ~1e-3 at M=0 and at larger M, but diverges at **intermediate small M** (roughly `M ∈ [0.005, 0.02]` on wide pre/post windows): the CI **width** matches R to ~1e-3 while the **center** shifts by up to ~9% (npre=6/npost=4 event study). Not a local-minimum artifact (multi-start does not move it); the two implementations land on different affine estimators of near-equal length. Reconciliation with R's `.FLCI.computeFLCI` algorithm is deferred (see TODO.md). Coverage is unaffected (widths match); the shift is in the reported CI location.
+- **Note (Δ^SD FLCI optimizer — R-faithful nested algorithm; B2b resolved):** The optimal
+  FLCI is a faithful port of R `HonestDiD::findOptimalFLCI`'s **nested convex program**. For a
+  fixed estimator standard deviation `h`, an inner problem minimizes the worst-case bias over
+  `Δ^SD(M)` subject to `sd(estimator) ≤ h` — a smooth convex QCQP over the slope weights `w`
+  (variables `[U; w]`, `U ≥ |cumsum(w)|`, one second-order-cone `var(w) ≤ h²`, linear-trend
+  neutrality `Σw = Σ_s s·l_s`), solved with `scipy.optimize` SLSQP (no cvxpy). An outer 1-D
+  search over `h ∈ [hMin, h0]` (a warm-started grid zoom) minimizes the half-length
+  `cv_α(M·bias(h)/h)·h`. The worst-case bias uses R's exact **closed form**
+  `M·(constant + Σ_i |cumsum(w)_i|)` (a direct port of R's `.createObjectiveObjectForBias`), so
+  the inner objective is linear in the abs-linearized weights; `hMin`/`h0` are the min-variance
+  and min-bias SDs (R's `.findLowestH` / `.findHForMinimumBias`). For **nonnegative (averaging)**
+  `l_vec` — the standard case, including the default first-post-period basis vector and equal
+  weights — this closed form equals the general LP oracle `_compute_worst_case_bias` (max |v'δ|
+  over Δ^SD) to machine precision. For a **signed / contrast** `l_vec` (e.g. `[1, -1]`) R's closed
+  form is *conservative* relative to the exact LP-oracle bias (a shared R property, not a
+  diff-diff bug); the FLCI still matches R (verified to ~1e-6 for `l_vec=[1,-1]`,
+  `test_signed_contrast_lvec_matches_r`), because we port R's objective exactly. This matches R's
+  optimal FLCI **center + half-length + optimalVec** to ~1e-3 (median ~1e-5) across a stress grid
+  (`num_pre × num_post × AR(1) ρ × M`); `TestHonestFLCIParityR`, golden
+  `benchmarks/data/honest_flci_golden.json`. The prior flat Nelder-Mead optimizer drifted from
+  R's center by up to ~9% at intermediate M (widths matched, coverage unaffected); the nested
+  structure removes that drift (SE-audit B2b). A derivative-based outer solve is not viable: the
+  min-bias inner solutions are degenerate (most `cumsum(w)` components sit at the abs-value
+  kink), so the SD-constraint multiplier is not recoverable from `sign(Lw)`, and the width
+  surface is near-flat at the optimum.
+- **Deviation from R:** diff-diff uses an **analytical** folded-normal critical value
+  (`_cv_alpha`, `scipy.stats`) in place of R's Monte-Carlo `.qfoldednormal` (10⁶ draws, seed 0)
+  — strictly more accurate (noise-free). Against **override-R** (R with the MC quantile replaced
+  by the analytical one, so both solve the same deterministic outer problem) the center matches
+  to ~1e-3; against **stock** MC-R the center matches to ~1.4e-2, the residual being R's own
+  simulation noise on the near-flat width surface. The committed golden stores both tiers.
 - **Note:** Phase 7d: survey variance support. When input results carry `survey_metadata` with `df_survey`, Delta^SD smoothness uses folded non-central t critical values (`scipy.stats.nct`); Delta^RM and naive FLCI paths use `_get_critical_value(alpha, df)` (standard t-distribution). `df_survey=0` → NaN inference. CallawaySantAnnaResults stores `event_study_vcov` (full cross-event-time VCV from IF vectors), which HonestDiD uses instead of the diagonal fallback. For replicate-weight designs, the event-study VCV falls back to diagonal (multivariate replicate VCV deferred).
 - **Note (deviation from R):** When HonestDiD receives bootstrap-fitted CallawaySantAnna results (`n_bootstrap > 0`), the full event-study covariance is unavailable (cleared to prevent mixing analytical VCV with bootstrap SEs). HonestDiD falls back to `diag(se^2)` from the bootstrap SEs with a UserWarning. R's `honest_did.AGGTEobj` computes a full covariance from the influence function matrix; implementing bootstrap event-study covariance is deferred. For full covariance structure in HonestDiD, use analytical SEs (`n_bootstrap=0`).
 - **Note (deviation from R):** When CallawaySantAnna results are passed to HonestDiD, `base_period != "universal"` emits a warning but does not error. R's `honest_did::honest_did.AGGTEobj` requires universal base period. Our implementation warns because the varying-base pre-treatment coefficients use consecutive comparisons (not a common reference), which changes the parallel-trends restriction interpretation.
diff --git a/tests/test_honest_did.py b/tests/test_honest_did.py
index 8fa1441d..f5229a2e 100644
--- a/tests/test_honest_did.py
+++ b/tests/test_honest_did.py
@@ -389,6 +389,19 @@ def test_fit_returns_results(self, mock_multiperiod_results):
         assert results.M == 1.0
         assert results.method == "relative_magnitude"
 
+    def test_fit_negative_M_override_raises(self, mock_multiperiod_results):
+        """A negative M passed to fit() (bypassing constructor validation) must
+        raise, not be silently treated as +|M| by the FLCI cv abs()."""
+        honest = HonestDiD(method="smoothness", M=0.0)
+        with pytest.raises(ValueError, match="non-negative"):
+            honest.fit(mock_multiperiod_results, M=-0.1)
+
+    def test_sensitivity_analysis_negative_M_grid_raises(self, mock_multiperiod_results):
+        """A negative value in M_grid must raise (bypasses constructor validation)."""
+        honest = HonestDiD(method="smoothness")
+        with pytest.raises(ValueError, match="non-negative"):
+            honest.sensitivity_analysis(mock_multiperiod_results, M_grid=[0.0, -0.1])
+
     def test_fit_smoothness(self, mock_multiperiod_results):
         """Test fit with smoothness method."""
         honest = HonestDiD(method="smoothness", M=0.0)
diff --git a/tests/test_methodology_honest_did.py b/tests/test_methodology_honest_did.py
index efdfb1d7..1fdcae87 100644
--- a/tests/test_methodology_honest_did.py
+++ b/tests/test_methodology_honest_did.py
@@ -6,6 +6,8 @@
 """
 
 
+import json
+import os
 import warnings
 
 import numpy as np
@@ -24,7 +26,6 @@
     _solve_rm_bounds_union,
 )
 
-
 # =============================================================================
 # TestDeltaSDConstraintMatrix
 # =============================================================================
@@ -472,16 +473,16 @@ def test_smoothness_df_survey_zero_returns_nan(self):
         )
         assert np.isnan(ci_lb) and np.isnan(ci_ub), "df=0 should give NaN CI"
 
-    def test_smoothness_flci_finite_across_M_grid_and_matches_r_at_zero(self):
-        """Smoothness FLCI is finite across an M grid; tight R parity at M=0.
+    def test_smoothness_flci_finite_and_matches_r_across_M_grid(self):
+        """Smoothness FLCI is finite AND matches R across the M grid (not just M=0).
 
-        Regression guard for the identified-set NaN-gate bug: an empty estimated
-        identified set must not suppress the FLCI (previously it did). The FLCI must
-        stay finite for every M. At M=0 the affine-estimator optimum is unambiguous
-        and matches R ``createSensitivityResults`` to <1e-3; at intermediate M there
-        is a known optimizer/center divergence from R (up to ~9% on wide pre/post
-        windows, CI width unaffected; see REGISTRY.md and TODO.md), so this test only
-        pins finiteness there.
+        Regression guard for the identified-set NaN-gate bug (an empty estimated
+        identified set must not suppress the FLCI). Also the B2b center-parity lock:
+        the nested optimizer now matches R HonestDiD's optimal FLCI CENTER at
+        intermediate M (previously the flat Nelder-Mead drifted up to ~9%). This
+        ``[1, 0, 1]`` curved pre-trend is the kink-prone case; R centers are the
+        deterministic (analytical-quantile) values, matching R's own MC output to its
+        simulation noise. See ``TestHonestFLCIParityR`` for the full stress grid.
         """
         from diff_diff.honest_did import _compute_optimal_flci
 
@@ -489,18 +490,163 @@ def test_smoothness_flci_finite_across_M_grid_and_matches_r_at_zero(self):
         beta_post = np.array([2.0])
         sigma = np.eye(4) * 0.01
         lvec = np.array([1.0])
-        for M in [0.0, 0.01, 0.02, 0.05, 0.1]:
+        # R HonestDiD 0.2.6, deterministic (analytical .qfoldednormal) centers.
+        r_center = {0.0: 2.285755, 0.02: 2.295042, 0.05: 2.326349, 0.10: 2.474526}
+        for M in [0.0, 0.02, 0.05, 0.1]:
             ci_lb, ci_ub = _compute_optimal_flci(
                 beta_pre, beta_post, sigma, lvec, 3, 1, M=M, df=None
             )
             assert np.isfinite(ci_lb) and np.isfinite(ci_ub), f"M={M}: non-finite FLCI"
             assert ci_ub > ci_lb, f"M={M}: degenerate CI"
-        # M=0: tight R parity (R HonestDiD 0.2.6: [2.082644, 2.488866]).
+            center = (ci_lb + ci_ub) / 2
+            assert abs(center - r_center[M]) < 1e-3, (
+                f"M={M} center={center:.6f} vs R {r_center[M]:.6f}"
+            )
+        # M=0: tight R parity on the endpoints too (R 0.2.6: [2.082880, 2.488631]).
         ci_lb, ci_ub = _compute_optimal_flci(
             beta_pre, beta_post, sigma, lvec, 3, 1, M=0.0, df=None
         )
-        assert abs(ci_lb - 2.082644) < 1e-3, f"M=0 ci_lb={ci_lb:.6f} vs R 2.082644"
-        assert abs(ci_ub - 2.488866) < 1e-3, f"M=0 ci_ub={ci_ub:.6f} vs R 2.488866"
+        assert abs(ci_lb - 2.082880) < 1e-3, f"M=0 ci_lb={ci_lb:.6f} vs R 2.082880"
+        assert abs(ci_ub - 2.488631) < 1e-3, f"M=0 ci_ub={ci_ub:.6f} vs R 2.488631"
+
+    def test_zero_sd_covariance_returns_nan(self):
+        """Degenerate (zero) covariance -> zero estimator SD -> NaN inference (no
+        ZeroDivisionError in M*bias/h), for M=0 and M>0 (zero-SE convention)."""
+        from diff_diff.honest_did import _compute_optimal_flci
+
+        beta_pre = np.array([0.1, -0.05, 0.1])
+        beta_post = np.array([1.0])
+        sigma = np.zeros((4, 4))
+        lvec = np.array([1.0])
+        for M in [0.0, 0.1, 0.5]:
+            ci_lb, ci_ub = _compute_optimal_flci(beta_pre, beta_post, sigma, lvec, 3, 1, M=M)
+            assert np.isnan(ci_lb) and np.isnan(ci_ub), f"M={M}: expected NaN CI on zero SD"
+
+    def test_signed_contrast_lvec_matches_r(self):
+        """A signed contrast target (l_vec=[1, -1], a difference of post-period
+        effects) matches R HonestDiD's optimal FLCI. Our worst-case-bias objective
+        is a faithful port of R's ``.createObjectiveObjectForBias``; for signed
+        (non-averaging) l_vec that closed form is CONSERVATIVE relative to the exact
+        LP-oracle bias ``_compute_worst_case_bias`` (the two coincide only for
+        nonnegative l_vec) -- we match R either way. R HonestDiD 0.2.6 (deterministic
+        quantile): center 0.200000, half-length 4.637049.
+        """
+        from diff_diff.honest_did import _compute_optimal_flci
+
+        lb, ub = _compute_optimal_flci(
+            np.array([0.1, 0.0, 0.1]), np.array([1.2, 0.9]),
+            np.eye(5) * 0.05, np.array([1.0, -1.0]), 3, 2, M=1.0,
+        )
+        assert abs((lb + ub) / 2 - 0.200000) < 1e-3, f"center={(lb + ub) / 2:.6f} vs R 0.200000"
+        assert abs((ub - lb) / 2 - 4.637049) < 1e-3, f"half={(ub - lb) / 2:.6f} vs R 4.637049"
+
+    def test_negative_M_raises(self):
+        """Negative smoothness in the direct FLCI helper raises (cv_alpha's abs()
+        would otherwise silently treat M=-0.1 like M=0.1)."""
+        from diff_diff.honest_did import _compute_optimal_flci
+
+        with pytest.raises(ValueError, match="non-negative"):
+            _compute_optimal_flci(
+                np.array([0.1, 0.0, 0.1]), np.array([1.0]),
+                np.eye(4) * 0.01, np.array([1.0]), 3, 1, M=-0.1,
+            )
+
+
+# =============================================================================
+# TestHonestFLCIParityR - B2b optimal-FLCI parity vs R HonestDiD 0.2.6
+# =============================================================================
+
+_FLCI_GOLDEN = os.path.join(
+    os.path.dirname(os.path.dirname(os.path.abspath(__file__))),
+    "benchmarks",
+    "data",
+    "honest_flci_golden.json",
+)
+
+
+@pytest.mark.skipif(
+    not os.path.exists(_FLCI_GOLDEN),
+    reason="HonestDiD FLCI golden absent (partial checkout); "
+    "run benchmarks/R/generate_honest_flci_golden.R",
+)
+class TestHonestFLCIParityR:
+    """B2b: the nested optimal-FLCI optimizer matches R HonestDiD 0.2.6 across a
+    stress grid (num_pre x num_post x AR(1) rho x M x l_vec).
+
+    ``center``/``half_length``/``optimal_vec`` in the golden are override-R
+    (R's Monte-Carlo ``.qfoldednormal`` replaced by an analytical quantile, so R
+    solves the same deterministic outer problem as diff-diff's analytical
+    ``_cv_alpha``) -> parity to 1e-3. The same diff-diff values also match stock
+    (MC) R (``stock_center``) to ~1e-2, the residual being R's simulation noise on
+    the near-flat width surface (diff-diff is strictly more accurate).
+    """
+
+    @staticmethod
+    def _cases():
+        with open(_FLCI_GOLDEN) as fh:
+            return json.load(fh)["cases"]
+
+    @staticmethod
+    def _unpack(c):
+        npre, npost = c["num_pre"], c["num_post"]
+        beta = np.asarray(c["beta"], float)
+        sigma = np.asarray(c["sigma"], float)
+        l_vec = np.atleast_1d(np.asarray(c["l_vec"], float))  # npost==1 auto-unboxed
+        return beta[:npre], beta[npre:], sigma, l_vec, npre, npost
+
+    def test_center_and_halflength_match_override_r(self):
+        max_dc = max_dw = 0.0
+        for c in self._cases():
+            if c["center"] is None:
+                continue
+            bp, bq, sigma, l_vec, npre, npost = self._unpack(c)
+            lb, ub = _compute_optimal_flci(bp, bq, sigma, l_vec, npre, npost, c["M"], c["alpha"])
+            center, half = (lb + ub) / 2, (ub - lb) / 2
+            tag = f"npre={npre} npost={npost} M={c['M']}"
+            assert abs(center - c["center"]) < 1e-3, f"{tag}: center {center:.6f} vs R {c['center']:.6f}"
+            assert abs(half - c["half_length"]) < 1e-3, f"{tag}: half {half:.6f} vs R {c['half_length']:.6f}"
+            max_dc = max(max_dc, abs(center - c["center"]))
+            max_dw = max(max_dw, abs(half - c["half_length"]))
+        assert max_dc < 1e-3 and max_dw < 1e-3
+
+    def test_optimal_vec_matches_override_r(self):
+        from diff_diff.honest_did import _flci_solve
+
+        for c in self._cases():
+            if c["optimal_vec"] is None:
+                continue
+            bp, bq, sigma, l_vec, npre, npost = self._unpack(c)
+            _, _, v = _flci_solve(bp, bq, sigma, l_vec, npre, npost, c["M"], c["alpha"])
+            r_v = np.atleast_1d(np.asarray(c["optimal_vec"], float))
+            assert v is not None and np.max(np.abs(v - r_v)) < 3e-3, (
+                f"npre={npre} M={c['M']}: optvec gap {np.max(np.abs(v - r_v)):.2e}"
+            )
+
+    def test_center_matches_stock_r_within_mc_noise(self):
+        for c in self._cases():
+            if c["stock_center"] is None:
+                continue
+            bp, bq, sigma, l_vec, npre, npost = self._unpack(c)
+            lb, ub = _compute_optimal_flci(bp, bq, sigma, l_vec, npre, npost, c["M"], c["alpha"])
+            # Loose tier: R's MC .qfoldednormal noise reaches ~1.4e-2 on flat-surface
+            # cases (max observed 1.39e-2); the tight parity is vs override-R (1e-3).
+            assert abs((lb + ub) / 2 - c["stock_center"]) < 1.5e-2, (
+                f"npre={npre} M={c['M']}: vs stock-R {abs((lb + ub) / 2 - c['stock_center']):.2e}"
+            )
+
+    def test_inner_solve_failure_nan_consistent(self, monkeypatch):
+        """A failed / infeasible inner solve NaN-propagates the full FLCI (no silent
+        fallback to a wrong estimator), distinct from R's legitimate Inf-bias branch."""
+        import diff_diff.honest_did as hd
+
+        monkeypatch.setattr(
+            hd, "_flci_min_bias_given_h",
+            lambda P, h, x0_w=None: (np.zeros(P["num_pre"]), np.nan, False),
+        )
+        lb, ub = _compute_optimal_flci(
+            np.array([0.1, -0.05, 0.1]), np.array([1.2]), np.eye(4) * 0.01, np.array([1.0]), 3, 1, M=0.1
+        )
+        assert np.isnan(lb) and np.isnan(ub)
 
 
 # =============================================================================