Continuation

zkMIPS implements an advanced continuation framework within its zkVM architecture, combining recursive proof composition with ​multi-shard execution capabilities. This design enables unbounded computational scalability with cryptographically verifiable state transitions while minimizing resource overhead. It has the following advantages:

• Scalability ​ Shards avoid single proof size explosion for long computations.

• Parallelism

  Independent shard proving enables distributed proof generation.

• ​State Continuity

  Overall memory consistency checking and consecutive program counter verifying ensures protocol-level execution integrity beyond individual shards.

Session-Shard Structure

A program execution forms a ​Session, which is dynamically partitioned into atomic ​shards based on cycle consumption. Each shard operates as an independent local execution with its own proof/receipt, while maintaining global consistency through cryptographic state binding.

Key Constraints

• Shard Validity

  Each shard's proof must be independently verifiable.

• Initial State Consistency

  First shard's start state must match verifier-specific program constraints (i.e., code integrity and entry conditions).

• Inter-Shard Transition

  Subsequent shards must begin at the previous shard's terminal state.

Proof Overflow

• Shard Execution Environment

  Shards operate with isolated execution contexts defined by:

  • ​Initial Memory Image: Compressed memory snapshots with Merkle root verification.
  • Register File State: Including starting PC value and memory image.

• Shard Proof

  Prove all instructions' execution in this shard, collecting all reading memory and writing memory records.

• Session Proof Aggregation

  Global session validity requires ​sequential consistency proof chaining:

  • Overall memory consistency checking.
  • Program counters consistency checking.
  • Combine shard proofs via folding scheme.