How are page splits determined internally in MySQL?
The author is talking about PAGE_N_DIRECTION. This has nothing to do with triggering splitting, which is performed by page_dir_split_slot. Splitting/merging is determined by a MIN and MAX on the directory slot

/* The maximum and minimum number of records owned by a directory slot. The
number may drop below the minimum in the first and the last slot in the
directory. */
#define PAGE_DIR_SLOT_MAX_N_OWNED 8
#define PAGE_DIR_SLOT_MIN_N_OWNED 4


You don't split when you fall under MIN, you merge (via page_dir_balance_slot).

PAGE_N_DIRECTION is for an optimization,


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