[[9,1,3]] Shor · nested basketballs

your nest, realized — a phase-code inside each block, a bit-code across the blocks · TEST: PASS
Nine physical qubits in three blocks of three, drawn as three inner balls inside one outer ball.

the two nested layers TEST PASS

inner · cubit 1 — inside each block
3-qubit phase code · catches a Z (phase) flip · guard faces inward
outer · cubit 2 — across the blocks (the ball)
3-qubit bit code · catches an X (bit) flip · guard faces the whole

live state

logical qubit|0⟩_L intact
last errornone
caught by—
block hit—

toddler corner · a ball made of balls

this is your nest built for real. nine hands, but grouped: three little basketballs (blocks), each held by three hands, and all three little balls sit inside one big basketball. each little ball guards against one kind of slip — a phase wobble (Z). the big ball guards against the other kind — a bit flip (X). neither layer can see the other's error type, so you need both, nested. that's why nine: 3×3, an inner code inside an outer code. a single slip of either kind gets caught by whichever layer it belongs to, and the value survives. a ball made of balls, each watching a different way to fail.

The Shor [[9,1,3]] code as nested basketballs: three inner phase-code balls inside one outer bit-code ball.