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diff --git a/docs/index.md b/docs/index.md
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--- a/docs/index.md
+++ b/docs/index.md
@@ -83,8 +83,8 @@ Pendulum and trains a policy through it, as well as the Python env client does
 ## Other trainers train through it
 
 The protocol is not tied to PlugRL's own server. Small adapters present it as
-the environment interface a trainer already has (`plugrl-bridges`, not public
-yet). Through them, three trainers that were not written for PlugRL train
+the environment interface a trainer already has
+([`plugrl-bridges`](https://github.com/PlugRL/plugrl-bridges)). Through them, three trainers that were not written for PlugRL train
 PlugRL env clients, and every seed of every pairing learns:
 - RLinf's PPO, on the C++ Pendulum client;
 - Stable-Baselines3's PPO, on the C++ Pendulum client and on HalfCheetah;
@@ -114,6 +114,50 @@ Only the time changes: 0.4-0.6 ms per step of 16 environments on one machine,
 2.6-3.0 ms when each step carries 16 frames, and about two one-way delays per
 step behind a slow link.
 
+## When the boundary is wrong, nothing says so
+
+<video src="/media/boundary-faults.mp4" controls muted playsinline preload="metadata"
+       style="width:100%;max-width:720px"></video>
+
+*70 seconds, no sound: one value changed on its way to the trainer, a learning
+curve that rises anyway, and the step ledger that finds the change.*
+
+The same bridge let us ask how a broken boundary shows itself. While SB3's
+PPO trained Pendulum, HalfCheetah, Hopper and Pusher, a 7-joint arm, the env
+client changed one field of what crossed, in one way: an observation, action,
+reward or final observation zeroed, stale, swapped with the next
+environment's or rounded to float16, an episode end invented or sent as the
+wrong kind, a step skipped. Nothing raised an error. Unless every value was
+wrong, the learning-curve threshold we had relied on caught at most one run
+in ten, and a comparison with ten fault-free seeds at most 21%
+([E54](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e54-boundary-faults),
+[E56](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e56-hopper-faults),
+[E58](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e58-pusher-faults)).
+A clean evaluation of every final policy agreed with the curves: of the 728
+boundary-fault runs that passed both curve checks, 723 scored like fault-free
+seeds ([E57](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e57-clean-eval)).
+The runs were not the same runs, though. Nearly all ended on other weights,
+and reward faults changed the returns the trainer logged.
+
+What saw every fault was a check of the run itself. A step ledger keeps a
+record on each side of the boundary, what each environment took and gave and
+what the trainer sent and received, and compares the two step by step. On
+one machine it caught and located all 585 boundary-fault runs on Pendulum,
+Hopper and Pusher, and across two machines all 21 on Pendulum, with no
+fault-free run to compare against, for a median 3% of training time on
+Pendulum ([E55](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e55-step-ledger);
+Hopper and Pusher in E56 and E58).
+An episode record kept at the environment caught the faults planted in the
+trainer's own log. Such faults happen outside experiments too: under
+`SAME_STEP` autoreset, Gymnasium 1.3's vector episode statistics dropped the
+first reward of every episode after an environment's first, until 1.4
+([E51](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e51-episode-accounting)).
+
+This is the paper *Detecting Silent Faults at the Environment-Trainer
+Boundary in Reinforcement Learning*, accepted to the CoRL 2026 Workshop on
+Everything Beneath the Policy ([PDF](/assets/silent-faults-webp2026.pdf);
+[citing it](#citing)).
+
 ## What the split costs
 
 On one machine, almost nothing: an exchange takes 0.1 ms with states only and
@@ -208,3 +252,16 @@ side that uses them.
 - [Environments](env/index.md)
 - [Policies](policy/index.md)
 - [Contributing](contributing/index.md)
+
+## Citing
+
+If the boundary checks are useful to you, cite the paper:
+
+```bibtex
+@inproceedings{gou2026silent,
+  title     = {Detecting Silent Faults at the Environment-Trainer Boundary in Reinforcement Learning},
+  author    = {Gou, Zuo and Lu, Chenhao},
+  booktitle = {CoRL 2026 Workshop on Everything Beneath the Policy},
+  year      = {2026}
+}
+```
diff --git a/docs/index.zh.md b/docs/index.zh.md
index 491ee15..a1d0338 100644
--- a/docs/index.zh.md
+++ b/docs/index.zh.md
@@ -62,7 +62,7 @@ Pendulum，通过 PlugRL 训练出了策略，学得和 Python 环境端一样
 ## 别的训练框架也能通过它训练
 
 协议不绑定 PlugRL 自己的训练端。几个小适配器把它包装成训练框架本来就认的环境接口
-（`plugrl-bridges`，暂未公开）。通过它们，三个不是为 PlugRL 写的训练框架训练 PlugRL
+（[`plugrl-bridges`](https://github.com/PlugRL/plugrl-bridges)）。通过它们，三个不是为 PlugRL 写的训练框架训练 PlugRL
 的环境端，每种组合的每个种子都学会了：
 - RLinf 的 PPO，训练 C++ Pendulum 客户端；
 - Stable-Baselines3 的 PPO，训练 C++ Pendulum 客户端和 HalfCheetah；
@@ -89,6 +89,42 @@ RLinf 还训练了跑在一台笔记本上的 16 个 HalfCheetah 环境端，那
 变的只有时间：同一台机器上 16 个环境每步多 0.4 到 0.6 毫秒，每步带 16 帧画面时多 2.6 到
 3.0 毫秒，链路慢时每步大约多两个单程延迟。
 
+## 边界出错时，什么都不会报错
+
+<video src="/media/boundary-faults.mp4" controls muted playsinline preload="metadata"
+       style="width:100%;max-width:720px"></video>
+
+*70 秒，无声：一个值在送往训练端的路上被改掉，学习曲线照样上升，步账本找到了这处改动。*
+
+借同一个 bridge，我们还能看边界出错时会有什么表现。Stable-Baselines3 的 PPO 训练
+Pendulum、HalfCheetah、Hopper 和 7 关节机械臂 Pusher 时，环境端把发出去的某一个字段按
+某一种方式改掉：观测、动作、奖励或回合最后一帧观测被置零、换成上一步的、换成下一个环境的，
+或者经过 float16 舍入；凭空多出一个回合结束，或者把回合结束的类型发错；跳过一步。没有任何
+报错。除非每个值都错了，我们原来依赖的学习曲线阈值最多只抓到十分之一的运行，和十个无错
+种子比较的检查最多抓到 21%
+（[E54](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e54-boundary-faults)、
+[E56](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e56-hopper-faults)、
+[E58](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e58-pusher-faults)）。
+在干净的环境里评估每个最终策略，结论和曲线一样：两项曲线检查都通过的 728 个边界出错运行中，
+723 个和无错种子表现相当
+（[E57](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e57-clean-eval)）。
+但这些运行已经不是原来那次运行了：几乎全都停在了不同的权重上，奖励出错时训练端记下的回报
+也变了。
+
+能看到每一处错误的，是检查运行本身。步账本在边界两侧各记一份：每个环境收到了什么、给出了
+什么，训练端发出了什么、收到了什么，然后逐步比对。单机上，它在 Pendulum、Hopper 和 Pusher
+上抓到并定位了全部 585 个边界出错的运行；跨两台机器时，抓到了 Pendulum 上全部 21 个。全程
+不需要无错运行做参照，在 Pendulum 上训练时间的中位数只多 3%
+（[E55](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e55-step-ledger)；
+Hopper 和 Pusher 见 E56、E58）。在环境端记的回合记录，抓到了故意埋进训练端日志里的错误。
+这类错误在实验之外也会发生：Gymnasium 1.3 的向量回合统计在 `SAME_STEP` 自动重置下，每个
+环境从第二个回合起都会丢掉回合的第一个奖励，直到 1.4 才修好
+（[E51](https://github.com/PlugRL/plugrl-server/tree/main/experiments/e51-episode-accounting)）。
+
+这部分内容是论文 *Detecting Silent Faults at the Environment-Trainer Boundary in
+Reinforcement Learning*，已被 CoRL 2026 Workshop on Everything Beneath the Policy 录用
+（[PDF](/assets/silent-faults-webp2026.pdf)；[引用方式](#citing)）。
+
 ## 拆开的代价
 
 同一台机器上几乎没有代价：只传状态时一次交换 0.1 毫秒，观测有 588 KiB 也不到 1 毫秒。
@@ -171,3 +207,16 @@ episode 回报从 -300 附近起步，三个随机种子到 50 万步达到 **19
 - [环境](env/index.zh.md)
 - [策略](policy/index.zh.md)
 - [贡献指南](contributing/index.zh.md)
+
+## 引用 {#citing}
+
+如果边界检查对你有用，请引用这篇论文：
+
+```bibtex
+@inproceedings{gou2026silent,
+  title     = {Detecting Silent Faults at the Environment-Trainer Boundary in Reinforcement Learning},
+  author    = {Gou, Zuo and Lu, Chenhao},
+  booktitle = {CoRL 2026 Workshop on Everything Beneath the Policy},
+  year      = {2026}
+}
+```
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