4 problems

Parent-number threshold conjecture. For general CKPs with preferential attachment, the true error-elimination threshold depends on $M$.

Parent-number monotonicity conjecture. If the CKP with $M=m_1$ eliminates all errors, then the CKP with $M=m_2$ also eliminates all errors.

Checking-parameter monotonicity conjecture. If a CKP with checking parameters $(p_1,k_1)$ eliminates all errors, then a CKP with parameters $(p_2,k_2)$ also eliminates all errors.

Multi-parent monotonicity conjecture. Monotonicity of error elimination with respect to the checking parameters $p$ and $k$ should hold when nodes can connect to more than one pare…