The following smart contract implements a Fact Registry design pattern for verifying cryptographic claims. The MemoryPageFactRegistry contract extends the FactRegistry contract and provides methods for registering facts based on memory (address, value) pairs. It supports two types of memory pages: regular pages and continuous pages. The contract computes a hash of the memory pairs and a cumulative product of a linear combination of the pairs. The fact consists of (pageType, prime, n, z, alpha, prod, memoryHash, address). The contract emits events for registering facts and implements an interface for querying the fact registry.