Prove the axioms underlying the trace-based Certificate Transparency log model

Prove the axioms that define the semantics and security properties of Merkle-tree operations, inclusion proofs, append-only proofs, and log contents in the trace-based Certificate Transparency model.

Background

The paper models Certificate Transparency logs through trace actions and restrictions rather than explicitly representing Merkle trees. These restrictions axiomatically relate log computations to inclusion and append-only proofs and thereby encode the correctness of the underlying data structure.

Although this abstraction supports equivocation, multiple ledgers, maximum merge delay, and network-transmitted proofs, the paper explicitly states that the axioms themselves are not proved. Establishing their soundness would be necessary to connect the symbolic trace model more rigorously to the concrete Merkle-tree implementation.