fix(rectification): stop unwritten-evidence claims and same-cluster dasha false conflicts (BUG-635–640)

Host only says 记下了 after a real write; Mastra schema rejections fail closed. Ledger year keys no longer drop quality probes, dual-dasha agreement is per cluster, width uses cluster span, and public house tables follow the inference minute.

Co-authored-by: Cursor <cursoragent@cursor.com>

frontend/DESIGN.md

@@ -227,7 +227,7 @@ The birth-time rectification session is the consultation transcript plus a house
 | `opening` | live row “正在读取你的出生资料，准备第一个问题…”, then tool labels | enabled (typing queues), stop visible |
 | `empty` | “这段校正还没有开始。” and one primary action “开始提问” | enabled |
 | `question-live` | the asking message carries the embedded card or the spoken stem | enabled, placeholder points at the card |
-| `question-gap`, persisted question | snapshot already has the next prompt; a host question row (`data-testid="persisted-question"`) | enabled, placeholder “请回答上面的问题…” |
+| `question-gap`, persisted question | snapshot already has the next prompt, including a completed turn that claimed to record evidence but left the same focus unanswered; a host question row (`data-testid="persisted-question"`) | enabled, placeholder “请回答上面的问题…” |
 | `question-gap`, retries left | one timeline live row “正在准备下一个问题…”, refetching on a 2s timer up to two retries | enabled |
 | `question-gap`, retries spent | “没有拿到下一个问题。” and a 44px “接着问” | enabled |
 | `verified_idle` | one closing line `postAdoptVerifyDone` under the still-visible range card (same assistant column); no spinner, no reload | enabled |