feat(threads): distinguish branched conversations

README.md

@@ -1038,7 +1038,7 @@ Interrupted first-turn runs still persist a fallback conversation title, so stop
 
 Streaming Markdown responses animate only newly arrived words; text that is already visible is not faded out and replayed when the next chunk extends the same block.
 
-In the Web UI, completed assistant turns can be branched into a new main conversation. The new thread starts from that turn's checkpoint and keeps the preceding replay checkpoint, so the branched response can be regenerated immediately. The latest response can also be regenerated after an interruption, even when its streamed partial text never reached a checkpoint. Regenerating the latest response preserves the thread's current title, including a title you renamed manually after the original response. Legacy or imported histories without checkpoint parent links use a bounded chronological fallback; if no earlier replay checkpoint exists, branching still succeeds with the legacy single-checkpoint shape, while regeneration remains unavailable for that inherited response. Existing single-checkpoint branches are left unchanged rather than attempting an unsafe checkpoint copy. Because workspace files are not checkpointed, the branch only receives a best-effort copy of the current workspace when you branch from the latest turn; branching from an older turn keeps just the restored message history so the branch never inherits files that were created in a later part of the conversation.
+In the Web UI, completed assistant turns can be branched into a new main conversation. Automatically inherited branch titles use the next free language-neutral numeric suffix (`Title (2)`, then `Title (3)` for another sibling or a branch of the numbered conversation) so generated sibling titles remain distinct without persisting a locale-specific label; matching explicit or renamed sibling titles also reserve their displayed suffix even though they carry no generated sequence metadata. An explicit API title is preserved. Renaming a branch clears its generated sequence, so its next automatic branch starts from the renamed title at `(2)`. Recent chats also groups loaded branches directly beneath a loaded parent with subtle tree connectors. Missing parents, malformed or cyclic lineage, and branches in a different pinned state stay visible at the top level instead of being hidden or moved across the pinned boundary. The new thread starts from that turn's checkpoint and keeps the preceding replay checkpoint, so the branched response can be regenerated immediately. The latest response can also be regenerated after an interruption, even when its streamed partial text never reached a checkpoint. Regenerating the latest response preserves the thread's current title, including a title you renamed manually after the original response. Legacy or imported histories without checkpoint parent links use a bounded chronological fallback; if no earlier replay checkpoint exists, branching still succeeds with the legacy single-checkpoint shape, while regeneration remains unavailable for that inherited response. Existing single-checkpoint branches are left unchanged rather than attempting an unsafe checkpoint copy. Because workspace files are not checkpointed, the branch only receives a best-effort copy of the current workspace when you branch from the latest turn; branching from an older turn keeps just the restored message history so the branch never inherits files that were created in a later part of the conversation.
 
 The Web UI reports completed task time once per run. This is total wall-clock time—including model reasoning, tool calls, and waiting—not a per-step or model-only thinking duration. Reasoning content remains available through its own separate disclosure.
 

README_zh.md

@@ -572,7 +572,7 @@ Tools 也是同样的思路。DeerFlow 自带一组核心工具：网页搜索
 
 Gateway 生成后续建议时，现在会先把普通字符串输出和 block/list 风格的富文本内容统一归一化，再去解析 JSON 数组响应，因此不同 provider 的内容包装方式不会再悄悄把建议吞掉。
 
-Web UI 支持从已完成的 assistant 回复分叉出一个新的主对话。新 thread 会保留该轮回复的 checkpoint 以及用户消息之前的重放 checkpoint，因此分叉后可以立即重新生成该回复。对于缺少 checkpoint 父链接的旧历史或导入历史，Gateway 会进行有界的时间顺序查找；如果不存在更早的重放 checkpoint，分叉仍会按旧版单-checkpoint 形态成功创建，但无法重新生成继承的回复。已有的单-checkpoint 分叉会保持不变，不会通过不安全的 checkpoint 复制尝试修复。只有从最新回合分叉时才会尽力复制当前 thread 的工作区文件；从历史回合分叉不会带入后续时间线创建的文件。
+Web UI 支持从已完成的 assistant 回复分叉出一个新的主对话。自动继承的分叉标题会使用下一个空闲的数字后缀（`标题 (2)`、`标题 (3)`……）；显式指定或手动重命名得到的同名后缀也会占号，即使它没有生成序号 metadata，后续自动分叉也不会与它重名。API 调用方显式提供的标题保持不变；重命名会清除旧的生成序号，因此从新标题继续自动分叉时会重新从 `(2)` 开始。最近对话列表还会把已加载的分叉直接排列在已加载的父对话下方，并显示低干扰的树形连接线。父对话尚未加载、谱系数据错误或成环、父子置顶状态不一致时，分叉会安全地保留在顶层，不会被隐藏或跨越置顶边界移动。新 thread 会保留该轮回复的 checkpoint 以及用户消息之前的重放 checkpoint，因此分叉后可以立即重新生成该回复。对于缺少 checkpoint 父链接的旧历史或导入历史，Gateway 会进行有界的时间顺序查找；如果不存在更早的重放 checkpoint，分叉仍会按旧版单-checkpoint 形态成功创建，但无法重新生成继承的回复。已有的单-checkpoint 分叉会保持不变，不会通过不安全的 checkpoint 复制尝试修复。只有从最新回合分叉时才会尽力复制当前 thread 的工作区文件；从历史回合分叉不会带入后续时间线创建的文件。
 
 ```text
 # sandbox 容器内的路径

backend/AGENTS.md

@@ -163,6 +163,10 @@ modules that only need lightweight types, config, or registries should import
 the concrete submodule instead of adding eager package-root imports that pull in
 the tool graph or subagent executor during state/schema imports.
 
+`ThreadMetaStore.search()` keeps JSON filter semantics identical across memory,
+SQLite, and PostgreSQL: missing differs from null, bool differs from int, and
+float filters accept integer or real JSON numbers through `json_value_matches`.
+
 ## Development Workflow
 
 ### Test-Driven Development (TDD) — MANDATORY