Hitting a counter example in homomorphic encryption over the integers
The problem is that you're getting an "overflow" of the errors relative to the secret key.

We have $10 \bmod 9 = 1$, and $114100 \bmod 9 = 7$, so the "errors" in your ciphertexts are $1$, $1$, and $7$, which are all odd, hence the plaintext bits are $1$ (as desired).  When you add the ciphertexts, the errors add correspondingly, so you get a ciphertext with error $9$, which normally would decrypt to $1$.  However, in this case your secret key is also $9$, so in fact decryption "sees" an error of $0$, i.e., the "intended" error overflows back to zero.  This is why your final ciphertext decrypts to $0$ instead of $1$.

As the paper explains, the accumulated errors must stay smaller than the secret key in order for decryption to work.  (For simplicity, throughout this answer I'm assuming only non-negative errors, and that the modular reduction returns a non-negative representative.)