diff --git a/docs/experiment_round31_adaptive_cap.json b/docs/experiment_round31_adaptive_cap.json
new file mode 100644
index 0000000..43c6c22
--- /dev/null
+++ b/docs/experiment_round31_adaptive_cap.json
@@ -0,0 +1,1988 @@
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+}
\ No newline at end of file
diff --git a/docs/experiment_round31_cert_cost_model.json b/docs/experiment_round31_cert_cost_model.json
new file mode 100644
index 0000000..c4df0fd
--- /dev/null
+++ b/docs/experiment_round31_cert_cost_model.json
@@ -0,0 +1,658 @@
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+}
\ No newline at end of file
diff --git a/docs/experiment_round31_certificates.json b/docs/experiment_round31_certificates.json
new file mode 100644
index 0000000..535ea4a
--- /dev/null
+++ b/docs/experiment_round31_certificates.json
@@ -0,0 +1,2909 @@
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+}
\ No newline at end of file
diff --git a/docs/experiment_round31_distance.json b/docs/experiment_round31_distance.json
new file mode 100644
index 0000000..70028fa
--- /dev/null
+++ b/docs/experiment_round31_distance.json
@@ -0,0 +1,24 @@
+{
+  "baseline_commit": "95da491",
+  "poses": "first 64 existing parity poses",
+  "n_poses": 64,
+  "kin_fp": "2ebcbf17",
+  "dtype": "float64",
+  "degenerate_capsules": [
+    686
+  ],
+  "pairs_with_second_degenerate": 670,
+  "evaluated_pairs": 42880,
+  "changed_pairs_over_1e_8": 20661,
+  "old_minus_new_min_mm": 0.0,
+  "old_minus_new_max_mm": 86.00309853133399,
+  "new_reverse_max_abs_mm": 0.0,
+  "worst": {
+    "pose": 29,
+    "first_capsule": 430,
+    "second_capsule": 686,
+    "old_distance_mm": 493.354753665718,
+    "new_distance_mm": 407.35165513438403
+  },
+  "scope": "Raw capsule distances; does not imply these pairs win the group minimum."
+}
\ No newline at end of file
diff --git a/docs/experiment_round31_kernel_replay.json b/docs/experiment_round31_kernel_replay.json
new file mode 100644
index 0000000..201e908
--- /dev/null
+++ b/docs/experiment_round31_kernel_replay.json
@@ -0,0 +1,16 @@
+{
+  "baseline_commit": "95da491",
+  "sample_source": "docs/experiment_round31_certificates.json",
+  "segments": 48,
+  "dense_points": 7586,
+  "max_step_deg": 0.01,
+  "cap_mm": 0.5,
+  "dtype": "float64",
+  "device": "cuda",
+  "kin_fp": "2ebcbf17",
+  "max_group_gap_difference_mm": 0.0,
+  "group_gaps_changed_over_1e_8": 0,
+  "minimum_gaps_changed_over_1e_8": 0,
+  "collision_bool_mismatches": 0,
+  "wall_s": 4.18259759999637
+}
\ No newline at end of file
diff --git a/docs/experiment_round31_parity.json b/docs/experiment_round31_parity.json
new file mode 100644
index 0000000..50de293
--- /dev/null
+++ b/docs/experiment_round31_parity.json
@@ -0,0 +1,10 @@
+{
+ "n": 2000,
+ "fk_max_abs_mm": 4.547473508864641e-13,
+ "orient_max_abs": 3.3306690738754696e-16,
+ "gap_max_abs_mm": 2.5224267119483557e-13,
+ "collide_bool_mismatch": 0,
+ "feat_max_abs": 5.960463655974024e-08,
+ "grad_rel_err_max": 1.8474076070450906e-06,
+ "PASS": true
+}
diff --git a/docs/探索日志.md b/docs/探索日志.md
index 87e055b..87b5a44 100644
--- a/docs/探索日志.md
+++ b/docs/探索日志.md
@@ -582,6 +582,27 @@
 - **新增硬约束证据**：before/after 两组256题实际轨迹都出现超速，最大 **1.660004×VMAX**（来源是动作限幅后叠加0.3×gain2.2反馈）。实际各轴最大速度约 `[99.600,99.600,149.400,149.400,199.200,298.800]°/s`，并非只看原始指令推测。行程仍约参考2.425倍；速度、加速度和真实控制时延均未达部署验收。历史 `travel` 累积的是指令而非夹紧后位移，本轮已同时列出实际轨迹重算值，不悄悄换分母。
 - **结论与下一步**：逐步限位一致性修复有效，未牺牲本批到达率；但加密审计仍检出段内碰撞，**不能部署、不能宣称零碰撞或50 Hz合格**。下一轮先验证更强的段内认证，再单独评估反馈后的速度/加速度约束与真实端到端调度；每次保持小样本单变量对照，继续保留失败证据。
 
+## 轮次 31：连续段认证的确定界与成本实测（exp: `exp/dagger-deploy`，判据变强，实测进不了 20 ms）
+
+- **假设与判据**：轮次 30 的端点/中点检查漏掉段内碰撞（第180题 1.08–1.10 s，段内 −0.14927 mm，端点/中点均正）。若用可证明的全姿态运动界对整段做 Lipschitz 判据，应当(a) 在同一个漏检段上给出碰撞或拒绝，(b) 预算不足时只会拒绝而不会放行，(c) 不放宽 `>0` 判据。判据失败或耗时超预算都算负结论，必须实测不能外推。
+- **确定界替代随机采样界**：JS 侧 `leverTable(4000)`/`leverBounds(20000)` 是随机姿态最大值再 ×1.05，不是全姿态上界。本轮按三角不等式给闭式界：组 g 的胶囊端点到关节 k(<g) 的最大位移 = (Σ_{j=k}^{g-2}‖P[j+1]−P[j]‖ + max_e‖e−P[g−1]‖)·|Δq_k|（k=g−1 时末项换成端点到该轴的垂直距离），组对 (ga,gb) 只累加 ga..gb−1，取组内最小仍保留 Lipschitz 性质。Python 端 `Kin.cert_lever`（15×6）即此表，未改 `lever`，也未改 JS。
+- **界的量级**（STEP=[1.2,1.2,1.8,1.8,2.4,3.6]°）：单整步在各组对上的位移界 **5.93–48.86 mm**，0 层通过要求端点间隙之和 > 界，即单端间隙至少 3.0–24.4 mm。实际执行段的间隙普遍只有 0.001–0.5 mm，所以“必须细分”是结构性的，不是实现缺陷。
+- **基础求距 bug 与影响范围**：模型里有 1 个退化胶囊（索引 686，组 3）。旧 `seg_seg_dist` 在第二条线段退化成点时固定取该点为第二条起点，没把点投影到第一条线段上——[0,2] 段对点 1 的实测距离旧值 1 mm、反向调用约 1e−9 mm、真值 0。修复后在已有 2000 个对拍姿态的前 64 个姿态上，670 个“退化胶囊作第二条”的细对里 **20661/42880 个距离变小（旧值偏大，最大 86.003 mm）**，正反调用一致。但这批变化没有进入判定：把轮次 30 修复后 48 段的 7586 个 0.01° 加密点分别用修复前(95da491)与修复后内核重算，**组最小间隙逐位相同（最大差 0.0 mm）、碰撞布尔差 0**；`python -m ml.eval.check_parity` 仍 PASS（2000 样本，fk 4.55e−13 mm、间隙 2.52e−13 mm、特征 5.96e−08、梯度相对误差 1.85e−06、碰撞布尔差 0）。即这轮修复是正确的，但不解释轮次 30 的漏检，也不改变既有成绩。
+- **认证实现**：`Kin.certify_segments` 为 float64 批量前沿二分，每根段独立查询预算，端点间隙用 `min(gap,cap)` 故钳制只会更保守；判据 `ga+gb > bound+2eps` 且两端 >eps，任一子段碰撞即整根判碰撞；超深度、超预算、非有限间隙、越出关节盒一律拒绝（`unresolved`/`outside_box`），不放行未知。宽相位 cap 可按本层界收到 `bound/2+eps`（`adaptive_cap`）。**尚未接入 rollout，未改查看器默认。**
+- **48 段固定样本**（`docs/experiment_round31_certificates.json`，沿用轮次 30 的 12 题，每题取首/中/末移动段 + 原证书最小间隙段 + 显式指定 180:54；cap=20、eps=1e−4、max_depth=12）：
+  | 每根查询预算 | 判安全 | 判碰撞 | 未知拒绝 | 查询数 p50/max |
+  |---|---|---|---|---|
+  | 2 | 20 | 0 | 28 | 2 / 2 |
+  | 8 | 26 | 1 | 21 | 4 / 8 |
+  | 32 | 37 | 1 | 10 | 4 / 32 |
+  - 已知漏检段（180 题执行段 54）**判碰撞，仅用 5 次查询**；该段原证书 `certified=true`、原内部 `col=0`。48 段里 0.01° 加密采样检出碰撞 1 段，认证接受该类段 **0 段**；整批与逐根调用结果逐位一致。
+  - 拒绝不等于安全：预算 2 时 28 段全部落 `unresolved`，实现不会把未知当通过。
+- **成本模型对上实测**（`docs/experiment_round31_cert_cost_model.json`）：按最紧组对的界，所需层数 `L=ceil(log2(bound_pair/(ga+gb)))`、查询数 `2^L+1`。37 个判安全段需要 2–17 次（L=0..4），10 个未知段需要 **33 或 65 次**（L=5..6），与预算 32 恰好卡在中间一致；碰撞段因提前撞到负间隙只用 5 次。结论：认证成本由 `bound/间隙` 的对数决定，**降低界或提高间隙余量**才是可行杠杆，加预算只是线性买单。
+- **耗时负结论**（CUDA float64、B=1、驻留输入、每段4次预热+9次计时、变体按段交错，`docs/experiment_round31_adaptive_cap.json`）：单段认证 **P50 22.93 ms、P90 58.43 ms、P99 101.57 ms，432 次里 225 次 > 20 ms**；自适应 cap 交错重测 P50 23.21 ms、P99 99.10 ms，**决策完全相同、耗时无收益**。先前顺序测得的“1.6×、整批 72→14.8 ms”经交错复测判定为 GPU 时钟/顺序漂移，不作为结论（48 根整批复测 260→212 ms 仍受同一偏差影响，且部署不会出现 48 根同时认证）。因此**连续认证按当前实现不能进 20 ms，更不能宣称 50 Hz**。
+- **回归与判据灵敏度**：`python -m unittest tests.test_eval_cl` **23 项通过**（轮次 30 为 14 项）。新增段认证 8 项覆盖：薄障碍段内碰撞被界抓到而清晰段被接受、预算/深度耗尽只拒不放、恒间隙合成段上预算 4/8/9 对应查询 3/5/9（验证细分层数与查询数的解析关系）、批量与逐根及乱序一致、空批与全拒前沿、NaN/±Inf 间隙拒绝、越界拒绝、退化距离对称性与梯度。**变异实测**：把类型门去掉后 `max_depth=torch.tensor(255,dtype=torch.uint8)` 会回绕成 `range(0)`、整段判据被跳过，真实间隙 −0.05 mm 的段直接返回 `safe=true`；加门后同一调用报 `certification budgets must be plain ints`。这是本轮抓到的第二个误放行路径（第一个是轮次 30 的未夹紧认证）。
+- **口径与边界**：认证只在 float64 下进行，浮点求距误差没有形式上界（`seg_seg_dist` 距离下限约 1e−9 mm），eps=1e−4 mm 是工程容差不是证明；48 段取自轮次 30 修复后的执行轨迹，是固定样本不是新策略闭环；连续认证未接入 rollout，实际执行仍走端点/中点离散检查；速度/加速度超限（轮次 30 实测最大 1.66×VMAX）本轮未处理。
+- **结论与下一步**：判据确实变强（抓到离散检查漏掉的段内碰撞、未知只拒不放），但成本与 `bound/间隙` 的对数绑定，**当前实现不能部署，也不得把“认证通过”说成零碰撞**。下一步两条：(1) 把逐层依赖的二分改成**一次均匀细分**（固定层数、单个 gaps 调用覆盖全部子段），其实时可行性取决于几何查询成本随批大小是否近似平坦；(2) 把余量要求移到规划/速度侧——实际轨迹贴着 0.001–0.02 mm 间隙走，任何认证方案都会退化成几十次查询，而反馈叠加后的速度约束本来就是未完成项。
+
 ## 分支清理（2026-10-20）
 
 - `feat/fb-mix`（8e5431c）：反馈混合方案的中间分支，**已验证是 `exp/dagger-deploy` 的祖先**（所有提交都在后者历史里），本地/远端分支删除，内容保留在 exp/dagger-deploy。
diff --git a/ml/common/kin_torch.py b/ml/common/kin_torch.py
index 165d8be..1f3744a 100644
--- a/ml/common/kin_torch.py
+++ b/ml/common/kin_torch.py
@@ -38,7 +38,8 @@ def seg_seg_dist(p1, q1, p2, q2, eps=1e-12):
     s = torch.where(t_lo, (-c / a.clamp_min(eps)).clamp(0, 1), s)
     s = torch.where(t_hi, ((b - c) / a.clamp_min(eps)).clamp(0, 1), s)
     t = t.clamp(0, 1)
-    # 退化（线段长度≈0）
+    # 第二条退化成点时，仍须在第一条上投影，而不是固定取其起点。
+    s = torch.where(e <= eps, (-c / a.clamp_min(eps)).clamp(0, 1), s)
     s = torch.where(a <= eps, torch.zeros_like(s), s)
     t = torch.where(e <= eps, torch.zeros_like(t), t)
     c1 = p1 + d1 * s.unsqueeze(-1)
@@ -85,6 +86,25 @@ class Kin:
         gi, gj = self.cap_g[self.pi], self.cap_g[self.pj]
         self.pair_gp = torch.minimum(gi, gj) * 7 + torch.maximum(gi, gj)
         self.lever = T(K['lever'])
+        table = [[0.0] * 7 for _ in range(6)]
+        for group in range(1, 7):
+            endpoints = [c[key] for c in caps if c['g'] == group for key in ('a', 'b')]
+            if not endpoints:
+                continue
+            pivot, axis = K['P'][group - 1], K['D'][group - 1]
+            unit = [v / math.hypot(*axis) for v in axis]
+            relative = [[e[j] - pivot[j] for j in range(3)] for e in endpoints]
+            radius = max(math.hypot(*v) for v in relative)
+            radial = max(math.hypot(v[1] * unit[2] - v[2] * unit[1],
+                                    v[2] * unit[0] - v[0] * unit[2],
+                                    v[0] * unit[1] - v[1] * unit[0]) for v in relative)
+            for joint in range(group):
+                chain = sum(math.dist(K['P'][j], K['P'][j + 1]) for j in range(joint, group - 1))
+                table[joint][group] = (chain + (radial if joint == group - 1 else radius)) * D2R
+        self.cert_groups = torch.tensor([a * 7 + b for a in range(7) for b in range(a + 2, 7)], device=device)
+        # 三角不等式给出全姿态界，不用随机姿态最大值冒充上界。
+        self.cert_lever = T([[table[k][b] if a <= k < b else 0.0 for k in range(6)]
+                             for a in range(7) for b in range(a + 2, 7)])
 
     # ---------------- 运动学 ----------------
     def cum_xf(self, q):
@@ -250,6 +270,56 @@ class Kin:
         gm = gm.scatter_reduce(0, rep_b * len(gp) + self._gp49[self.pair_gp[pidx]], gap.clamp(max=cap), reduce='amin', include_self=True)
         return gm.view(B, len(gp))
 
+    @torch.no_grad()
+    def certify_segments(self, a, b, max_queries=32, max_depth=12, eps=1e-4, cap=20.0, adaptive_cap=True):
+        if self.dtype != torch.float64 or a.dtype != torch.float64 or b.dtype != torch.float64:
+            raise ValueError('segment certification requires float64')
+        # 预算给成张量时 max_depth + 1 会在 uint8 这类窄类型上回绕成 0，循环整个跳过，把碰撞段当安全返回。
+        if type(max_queries) is not int or type(max_depth) is not int:
+            raise ValueError('certification budgets must be plain ints')
+        if max_queries < 2 or max_depth < 0 or eps <= 0 or cap <= eps:
+            raise ValueError('invalid certification budget or tolerance')
+        count = a.shape[0]
+        status = torch.zeros(count, dtype=torch.long, device=a.device)
+        inside = (((a >= self.lo) & (a <= self.hi) & (b >= self.lo) & (b <= self.hi)) | self.cont).all(-1)
+        status[~inside] = 3
+        root = torch.arange(count, device=a.device)
+        gaps = self.gaps(torch.cat([a, b]), cap)['gm'][:, self.cert_groups]
+        ga, gb = gaps[:count], gaps[count:]
+        queries = torch.full((count,), 2, dtype=torch.long, device=a.device)
+        bound = (b - a).abs() @ self.cert_lever.T
+        for depth in range(max_depth + 1):
+            finite = torch.isfinite(ga).all(-1) & torch.isfinite(gb).all(-1)
+            collision = (ga <= 0).any(-1) | (gb <= 0).any(-1)
+            status[root[~finite]] = 2
+            status[root[collision]] = 1
+            positive = (ga > eps).all(-1) & (gb > eps).all(-1)
+            proven = positive & (ga + gb > bound + 2 * eps).all(-1)
+            pending = (status[root] == 0) & ~proven
+            if not bool(pending.any()):
+                break
+            a, b, ga, gb, root, bound = a[pending], b[pending], ga[pending], gb[pending], root[pending], bound[pending]
+            if depth == max_depth:
+                status[root] = 2
+                break
+            requested = torch.bincount(root, minlength=count)
+            status[(status == 0) & (queries + requested > max_queries)] = 2
+            keep = status[root] == 0
+            a, b, ga, gb, root, bound = (t[keep] for t in (a, b, ga, gb, root, bound))
+            if not root.numel():
+                break
+            mid = a + 0.5 * (b - a)
+            # 子段的界是父段一半；宽相位只需覆盖到能被证明的最小间隙，层越深筛得越狠。
+            qc = min(cap, float(bound.max()) / 2 + eps) if adaptive_cap else cap
+            gm = self.gaps(mid, qc)['gm'][:, self.cert_groups]
+            queries += torch.bincount(root, minlength=count)
+            a, b = torch.cat([a, mid]), torch.cat([mid, b])
+            ga, gb = torch.cat([ga, gm]), torch.cat([gm, gb])
+            root = torch.cat([root, root])
+            bound = torch.cat([bound, bound]) / 2
+        return {'safe': status == 0, 'collision': status == 1, 'unresolved': status == 2,
+                'outside_box': status == 3, 'queries': queries}
+
     def min_gap(self, q, cap=40.0):
         return self.gaps(q, cap)['gm'].min(-1).values
 
diff --git a/ml/eval/diag_collision.py b/ml/eval/diag_collision.py
index 9b0ec3e..0671952 100644
--- a/ml/eval/diag_collision.py
+++ b/ml/eval/diag_collision.py
@@ -153,11 +153,124 @@ def replay_dense(path, indices, max_step_deg=0.05, device='cpu', out=None):
     return result
 
 
+@torch.no_grad()
+def replay_certificates(path, indices, device='cpu', out=None, repeats=5, extra_segments=()):
+    saved = torch.load(path, map_location='cpu', weights_only=True)
+    kin = Kin(device=device, dtype=torch.float64)
+    if saved.get('kin_fp') != kin.fp:
+        raise ValueError('trace/kin fingerprint mismatch')
+    if not indices or min(indices) < 0 or max(indices) >= len(saved['tasks']) or repeats < 1:
+        raise ValueError('valid task indices and positive repeats required')
+    rows, offset = [], 0
+    for _, per, count in saved['batches']:
+        for index in indices:
+            if not offset <= index < offset + count:
+                continue
+            b = index - offset
+            nstep = min(per['traj'].shape[1] - 1, math.floor((float(per['limit'][b]) + 1e-6) / DT))
+            if torch.isfinite(per['t_done'][b]):
+                nstep = min(nstep, round(float(per['t_done'][b]) / DT))
+            traj = per['traj'][b, :nstep + 1]
+            moving = ((traj[1:] - traj[:-1]).abs().max(-1).values > 1e-6).nonzero().flatten().tolist()
+            if not moving:
+                continue
+            plans = per['plans']
+            nearest, nearest_gap = None, float('inf')
+            for it in moving:
+                pi = int(torch.searchsorted(plans['it'], it, right=True)) - 1
+                step = it - int(plans['it'][pi])
+                if 0 <= step < plans['commit'].shape[2] and plans['certified'][b, pi, step]:
+                    gap = float(plans['gaps'][b, pi, [step, plans['commit'].shape[2] + step]].min())
+                    if gap < nearest_gap:
+                        nearest, nearest_gap = it, gap
+            selected = {moving[0], moving[len(moving) // 2], moving[-1]}
+            if nearest is not None:
+                selected.add(nearest)
+            for task_index, it in extra_segments:
+                if task_index == index:
+                    if it not in moving:
+                        raise ValueError('extra segment must be a moving segment before deadline or arrival')
+                    selected.add(it)
+            for it in sorted(selected):
+                rows.append({'i': index, 'start_it': it, 'a': traj[it].tolist(), 'b': traj[it + 1].tolist()})
+        offset += count
+    if not rows:
+        raise ValueError('no moving segments in selected tasks')
+    a = torch.tensor([r['a'] for r in rows], dtype=torch.float64, device=device)
+    b = torch.tensor([r['b'] for r in rows], dtype=torch.float64, device=device)
+    started = time.perf_counter()
+    print('certificate replay: %d tasks, %d fixed moving segments' % (len(indices), len(rows)), flush=True)
+    summaries = {}
+    for budget in (2, 8, 32):
+        result = kin.certify_segments(a, b, max_queries=budget)
+        summaries[str(budget)] = {key: int(result[key].sum()) for key in ('safe', 'collision', 'unresolved', 'outside_box')}
+        summaries[str(budget)]['queries_p50'] = float(result['queries'].double().quantile(0.5))
+        summaries[str(budget)]['queries_max'] = int(result['queries'].max())
+        for j, row in enumerate(rows):
+            row.setdefault('budgets', {})[str(budget)] = {key: value[j].item() for key, value in result.items()}
+        print('budget %d: %s' % (budget, summaries[str(budget)]), flush=True)
+    latencies = []
+    for j, row in enumerate(rows):
+        aa, bb = a[j:j + 1], b[j:j + 1]
+        discrete = kin.gaps(torch.cat([aa, aa + 0.5 * (bb - aa), bb]), 0.5)['gm'].min(-1).values
+        row['previous_midpoint_endpoint_gap_mm'] = discrete.tolist()
+        nseg = max(2, 2 * math.ceil(float((bb - aa).abs().max()) / 0.02))
+        alpha = torch.linspace(0, 1, nseg + 1, dtype=torch.float64, device=device)
+        points = aa + alpha[:, None] * (bb - aa)
+        dense = torch.cat([kin.gaps(chunk, 0.5)['gm'].min(-1).values for chunk in points.split(64)])
+        row['dense_points'] = len(points)
+        row['dense_min_gap_mm'] = float(dense.min())
+        row['dense_min_fraction'] = float(alpha[dense.argmin()])
+        for _ in range(3):
+            kin.certify_segments(aa, bb)
+        elapsed = []
+        for _ in range(repeats):
+            if a.is_cuda:
+                torch.cuda.synchronize(a.device)
+            t0 = time.perf_counter()
+            result = kin.certify_segments(aa, bb)
+            if a.is_cuda:
+                torch.cuda.synchronize(a.device)
+            elapsed.append((time.perf_counter() - t0) * 1000)
+        row['batch_single_match'] = all(value.item() == row['budgets']['32'][key] for key, value in result.items())
+        row['latency_ms'] = elapsed
+        latencies.extend(elapsed)
+        print('segment %d/%d task %d it %d dense %.6f mm queries %d latency %.2f ms' %
+              (j + 1, len(rows), row['i'], row['start_it'], row['dense_min_gap_mm'],
+               row['budgets']['32']['queries'], sum(elapsed) / len(elapsed)), flush=True)
+    elapsed = torch.tensor(latencies, dtype=torch.float64)
+    result = {
+        'trace': str(path), 'tasks_sha256': saved.get('tasks_sha256'), 'kin_fp': kin.fp,
+        'device': str(device), 'gpu': torch.cuda.get_device_name(a.device) if a.is_cuda else None,
+        'torch_version': str(torch.__version__), 'cpu_threads': torch.get_num_threads(), 'dtype': 'float64',
+        'indices': indices, 'extra_segments': list(extra_segments),
+        'selection': 'First/middle/last moving segment and minimum original certified gap per task; plus explicit extra_segments.',
+        'cap_mm': 20.0, 'eps_mm': 1e-4, 'max_depth': 12, 'dense_max_step_deg': 0.01,
+        'timing': {'scope': 'B=1 certificate only, resident inputs, 3 warmups per segment; synchronized wall time, not policy or scheduling latency.',
+                   'repeats_per_segment': repeats, 'calls': len(latencies),
+                   'p50_ms': float(elapsed.quantile(0.5)), 'p99_ms': float(elapsed.quantile(0.99)),
+                   'max_ms': float(elapsed.max()), 'over_20ms': int((elapsed > 20).sum())},
+        'budgets': summaries,
+        'dense_collision_segments': sum(r['dense_min_gap_mm'] <= 0 for r in rows),
+        'accepted_dense_collision_segments': sum(r['dense_min_gap_mm'] <= 0 and r['budgets']['32']['safe'] for r in rows),
+        'batch_single_match': all(r['batch_single_match'] for r in rows),
+        'scope': 'Fixed recorded segments, not a new rollout. Dense replay is finite sampling; floating-point certification error is not formally bounded.',
+        'wall_s': time.perf_counter() - started, 'rows': rows,
+    }
+    if out:
+        with open(out, 'w', encoding='utf-8') as f:
+            json.dump(result, f, indent=2, allow_nan=False)
+    return result
+
+
 def main():
     ap = argparse.ArgumentParser()
     ap.add_argument('--ckpt')
     ap.add_argument('--trace')
     ap.add_argument('--dense_indices', help='逗号分隔的任务下标；回放实际轨迹，不依赖原 col 标记')
+    ap.add_argument('--cert_indices', help='固定实际段的连续认证、加密对照和单段计时')
+    ap.add_argument('--cert_segments', default='', help='额外指定任务号:零基段号，逗号分隔')
+    ap.add_argument('--repeats', type=int, default=5)
     ap.add_argument('--max_step_deg', type=float, default=0.05)
     ap.add_argument('--samples', default='ml/data/samples')
     ap.add_argument('--split', default='val')
@@ -169,14 +282,24 @@ def main():
     ap.add_argument('--device', default='cuda' if torch.cuda.is_available() else 'cpu')
     ap.add_argument('--out', default=None)
     a = ap.parse_args()
+    if a.dense_indices and a.cert_indices:
+        ap.error('--dense_indices and --cert_indices are mutually exclusive')
+    if a.cert_segments and not a.cert_indices:
+        ap.error('--cert_segments requires --cert_indices')
     if a.trace:
-        if a.dense_indices:
+        if a.cert_indices:
+            extra = [tuple(map(int, segment.split(':'))) for segment in a.cert_segments.split(',') if segment]
+            indices = [int(i) for i in a.cert_indices.split(',')]
+            if any(len(segment) != 2 or segment[0] not in indices for segment in extra):
+                ap.error('--cert_segments requires task:segment pairs from --cert_indices')
+            replay_certificates(a.trace, indices, a.device, a.out, a.repeats, extra)
+        elif a.dense_indices:
             replay_dense(a.trace, [int(i) for i in a.dense_indices.split(',')], a.max_step_deg, a.device, a.out)
         else:
             replay_first_hits(a.trace, a.out)
         return
-    if a.dense_indices:
-        ap.error('--dense_indices requires --trace')
+    if a.dense_indices or a.cert_indices:
+        ap.error('--dense_indices and --cert_indices require --trace')
     if not a.ckpt:
         ap.error('--ckpt or --trace is required')
 
diff --git a/tests/test_eval_cl.py b/tests/test_eval_cl.py
index d2291e2..6b27738 100644
--- a/tests/test_eval_cl.py
+++ b/tests/test_eval_cl.py
@@ -9,8 +9,9 @@ from unittest.mock import patch
 import torch
 
 from ml.eval.eval_cl import json_finite, run
-from ml.eval.diag_collision import replay_dense, replay_first_hits
+from ml.eval.diag_collision import replay_certificates, replay_dense, replay_first_hits
 from ml.sim.closed_loop import TeacherOracle, rollout
+from ml.common.kin_torch import Kin, seg_seg_dist
 
 
 class EvalMetricsTest(unittest.TestCase):
@@ -124,6 +125,30 @@ class EvalMetricsTest(unittest.TestCase):
             self.assertGreater(row['min_gap64_mm'], 0)
             self.assertEqual(row['steps'], 1)
 
+    def test_certificate_replay_samples_actual_movement_before_deadlines(self):
+        kin = SegmentCertificateTest.ThinObstacle()
+        kin.fp = 'probe'
+        traj = torch.zeros(3, 4, 6)
+        traj[:, :, 0] = torch.tensor([[0, 1, 1, 1], [0, -0.5, -1, -1], [0, 0, 1, 1]])
+        per = {'traj': traj, 'limit': torch.tensor([0.06, 0.02, 0.02]),
+               't_done': torch.tensor([float('nan'), 0.02, float('nan')]),
+               'plans': {'it': torch.arange(3), 'commit': torch.zeros(3, 3, 1, 6),
+                         'certified': torch.ones(3, 3, 1, dtype=torch.bool), 'gaps': torch.full((3, 3, 2), 0.5)}}
+        with tempfile.TemporaryDirectory() as folder:
+            trace, output = Path(folder) / 'trace.pt', Path(folder) / 'audit.json'
+            torch.save({'kin_fp': 'probe', 'tasks': [{}] * 3, 'batches': [({}, per, 3)]}, trace)
+            with patch('ml.eval.diag_collision.Kin', return_value=kin), contextlib.redirect_stdout(io.StringIO()):
+                result = replay_certificates(trace, [0, 1, 2], out=output, repeats=1, extra_segments=[(0, 0)])
+                with self.assertRaisesRegex(ValueError, 'extra segment'):
+                    replay_certificates(trace, [1], repeats=1, extra_segments=[(1, 1)])
+            self.assertEqual(json.loads(output.read_text())['dense_collision_segments'], 1)
+        self.assertEqual([(r['i'], r['start_it']) for r in result['rows']], [(0, 0), (1, 0)])
+        self.assertEqual(result['budgets']['32']['safe'], 1)
+        self.assertEqual(result['budgets']['32']['collision'], 1)
+        self.assertEqual(result['accepted_dense_collision_segments'], 0)
+        self.assertTrue(result['batch_single_match'])
+        self.assertEqual(result['timing']['calls'], 2)
+
 
 class DlsSafetyTest(unittest.TestCase):
     def test_rejected_refinement_retains_safe_candidate(self):
@@ -373,5 +398,116 @@ class ClampedPathSafetyTest(unittest.TestCase):
                 self.assertFalse(per['plans']['certified'].any().item())
 
 
+class SegmentCertificateTest(unittest.TestCase):
+    class ThinObstacle(Kin):
+        def __init__(self):
+            self.dtype = torch.float64
+            self.lo, self.hi = torch.full((6,), -5.0), torch.full((6,), 5.0)
+            self.cont = torch.zeros(6, dtype=torch.bool)
+            self.cert_groups = torch.tensor([0])
+            self.cert_lever = torch.tensor([[1.0, 0, 0, 0, 0, 0]], dtype=self.dtype)
+
+        def gaps(self, q, cap):
+            return {'gm': ((q[:, :1] - 0.25).abs() - 0.05).clamp(max=cap)}
+
+    def test_bound_detects_hidden_collision_and_accepts_clear_segment(self):
+        a, b = torch.zeros(3, 6, dtype=torch.float64), torch.zeros(3, 6, dtype=torch.float64)
+        a[:, 0] = torch.tensor([0.0, -1.0, 0.25])
+        b[:, 0] = torch.tensor([1.0, 0.0, 0.25])
+        result = self.ThinObstacle().certify_segments(a, b)
+        self.assertEqual(result['safe'].tolist(), [False, True, False])
+        self.assertEqual(result['collision'].tolist(), [True, False, True])
+        self.assertEqual(result['queries'].tolist(), [4, 2, 2])
+
+    def test_budget_and_depth_exhaustion_do_not_accept_unknown_segment(self):
+        a, b = torch.zeros(1, 6, dtype=torch.float64), torch.zeros(1, 6, dtype=torch.float64)
+        b[:, 0] = 1.0
+        kin = self.ThinObstacle()
+        for kwargs in ({'max_queries': 2}, {'max_depth': 0}):
+            with self.subTest(**kwargs):
+                result = kin.certify_segments(a, b, **kwargs)
+                self.assertFalse(result['safe'].item())
+                self.assertTrue(result['unresolved'].item())
+                self.assertEqual(result['queries'].item(), 2)
+
+    def test_budget_exhaustion_scales_with_gap_and_bound(self):
+        class ConstantGap(self.ThinObstacle):
+            def gaps(self, q, cap):
+                return {'gm': torch.full((q.shape[0], 1), 0.1, dtype=q.dtype, device=q.device)}
+
+        # 界取 1 mm/度：1° 段要证明无碰撞，必须细分到位移界 < 两端间隙之和(0.2 mm)。
+        kin = ConstantGap()
+        kin.cert_lever = torch.ones(1, 6, dtype=torch.float64)
+        a, b = torch.zeros(1, 6, dtype=torch.float64), torch.zeros(1, 6, dtype=torch.float64)
+        b[:, 0] = 1.0
+        for budget, safe, queries in ((4, False, 3), (8, False, 5), (9, True, 9)):
+            with self.subTest(budget=budget):
+                result = kin.certify_segments(a, b, max_queries=budget)
+                self.assertEqual(bool(result['safe'].item()), safe)
+                self.assertEqual(int(result['queries'].item()), queries)
+
+    def test_tensor_budget_cannot_wrap_depth(self):
+        a, b = torch.zeros(1, 6, dtype=torch.float64), torch.zeros(1, 6, dtype=torch.float64)
+        a[:, 0] = b[:, 0] = 0.25
+        for tensor in (torch.tensor(255, dtype=torch.uint8), torch.tensor(255)):
+            with self.subTest(dtype=tensor.dtype):
+                with self.assertRaisesRegex(ValueError, 'plain ints'):
+                    self.ThinObstacle().certify_segments(a, b, max_depth=tensor)
+
+    def test_batch_matches_per_root_and_ignores_order(self):
+        kin = self.ThinObstacle()
+        a = torch.tensor([[0.0, 0, 0, 0, 0, 0], [0.25, 0, 0, 0, 0, 0], [-1.0, 0, 0, 0, 0, 0]], dtype=torch.float64)
+        b = torch.tensor([[1.0, 0, 0, 0, 0, 0], [0.25, 0, 0, 0, 0, 0], [0.0, 0, 0, 0, 0, 0]], dtype=torch.float64)
+        batch = kin.certify_segments(a, b, max_queries=16)
+        self.assertEqual(batch['collision'].tolist(), [True, True, False])
+        self.assertEqual(batch['safe'].tolist(), [False, False, True])
+        for perm in ([0, 1, 2], [2, 1, 0], [1, 0, 2]):
+            index = torch.tensor(perm)
+            moved = kin.certify_segments(a[index], b[index], max_queries=16)
+            for key in ('safe', 'collision', 'unresolved', 'queries'):
+                torch.testing.assert_close(moved[key], batch[key][index], rtol=0, atol=0)
+
+    def test_empty_batch_and_all_rejected_frontier(self):
+        kin = self.ThinObstacle()
+        empty = kin.certify_segments(torch.zeros(0, 6, dtype=torch.float64), torch.zeros(0, 6, dtype=torch.float64))
+        self.assertEqual(empty['safe'].shape, (0,))
+        a = torch.tensor([[0.25, 0, 0, 0, 0, 0], [6.0, 0, 0, 0, 0, 0]], dtype=torch.float64)
+        result = kin.certify_segments(a, a.clone(), max_queries=2)
+        self.assertEqual(result['safe'].tolist(), [False, False])
+        self.assertEqual(result['collision'].tolist(), [True, False])
+        self.assertEqual(result['outside_box'].tolist(), [False, True])
+
+    def test_nonfinite_and_outside_box_are_rejected(self):
+        a, b = torch.zeros(1, 6, dtype=torch.float64), torch.zeros(1, 6, dtype=torch.float64)
+        kin = self.ThinObstacle()
+        with patch.object(kin, 'gaps', side_effect=lambda q, cap: {'gm': torch.full((q.shape[0], 1), float('nan'))}):
+            result = kin.certify_segments(a, b)
+        self.assertFalse(result['safe'].item())
+        self.assertTrue(result['unresolved'].item())
+        for value in (float('inf'), -float('inf')):
+            with self.subTest(value=value):
+                with patch.object(kin, 'gaps',
+                                  side_effect=lambda q, cap, v=value: {'gm': torch.full((q.shape[0], 1), v)}):
+                    result = kin.certify_segments(a, b)
+                self.assertFalse(result['safe'].item())
+        a[:, 0] = b[:, 0] = 6.0
+        result = kin.certify_segments(a, b)
+        self.assertFalse(result['safe'].item())
+        self.assertTrue(result['outside_box'].item())
+
+    def test_point_segment_distance_is_symmetric_and_differentiable(self):
+        p = torch.tensor([[0.0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]], dtype=torch.float64, requires_grad=True)
+        q = torch.tensor([[2.0, 0, 0]] * 4, dtype=torch.float64)
+        point = torch.tensor([[1.0, 0, 0], [1, 3, 0], [4, 0, 0], [-1, 0, 0]], dtype=torch.float64)
+        forward = seg_seg_dist(p, q, point, point)
+        reverse = seg_seg_dist(point, point, p, q)
+        torch.testing.assert_close(forward, torch.tensor([0.0, 3, 2, 1], dtype=torch.float64), atol=1e-8, rtol=0)
+        torch.testing.assert_close(forward, reverse, atol=1e-8, rtol=0)
+        forward.sum().backward()
+        self.assertTrue(torch.isfinite(p.grad).all())
+        torch.testing.assert_close(seg_seg_dist(p.detach(), p.detach(), point, point),
+                                   (p.detach() - point).norm(dim=-1), atol=1e-8, rtol=0)
+
+
 if __name__ == '__main__':
     unittest.main()