This rare kanji has no clear standalone meaning. Treat its meaning as uncertain.
綷 combines 糸 (thread) with 卒, which likely contributes sound. The exact historical development is uncertain.
The left side 糸 suggests thread or fabric, and the right side 卒 looks like a soldier. Imagine a soldier's uniform made of special thread, but the exact meaning is uncertain.
For サイ, imagine a sigh of relief when the soldier's uniform is finally sewn: sigh -> サイ.
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