The Notebook Light Finds Belongs to Sidoh, Not Ryuk
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Stolen by Ryuk · Dropped for a Human to Find
The first Death Note Light picks up is not Ryuk's personal notebook. Ryuk stole it from another Shinigami, Sidoh, then dropped it into the human world because he was bored. Ryuk remains beside Light because he is the Shinigami attached to the notebook in human hands, but the physical book itself began as Sidoh's.
Why it matters
The story's first notebook already has a history Light does not know. Years later, its original owner comes looking for it, turning an object Light treats as his weapon into someone else's missing property.
Light Rearranges the Notebooks Before He Gives Up His Memories
SPOILER!
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Ownership Is Part of the Plan, Not Bookkeeping
Before surrendering his Kira memories, Light does not simply abandon a notebook and hope for the best. He rearranges which Shinigami is attached to which notebook and prepares the chain of possession that will keep Kira active after he no longer remembers being Kira.
Why it matters
Ownership Relinquishment & Memory Erasure only works as strategy because Light plans the notebook's future before removing his own knowledge of the plan. The object keeps moving even after the planner disappears from his own mind.