WHOLE CHARACTER
刻kè
to carve; to engrave; a quarter hour (15 minutes); moment; instant; deep; cutting (of words or treatment)
刻 pairs a knife with 亥: to carve (刻字), a quarter hour (一刻钟), and moments like 立刻 'right away'.
ZDIC: 形声,从刂、亥声 — the knife side with 亥 as the sound side.
LEFT: THE OLD SOUND SIDE 亥 (HÀI)
亥hài
twelfth earthly branch
The serial dictionary meaning is kept separate from its sound role.
In 刻: left: the old sound side 亥 (hài) A historical sound side, not a modern hint: kè shares tone 4 only with hài; the initials (k-/h-) and finals (-e/-ai) differ.
RIGHT: THE KNIFE SIDE — CARVING IS DONE WITH A BLADE
刂dāo
the vertical knife radical (from 刀)
A bound radical form on the right of many characters; not a standalone word.
In 刻: right: the knife side — carving is done with a blade Shown with its documented or clearly limited role.