Add weak-subjectivity execution proof sync

[frisitano]

Summary

This draft adds an EIP-8025 proof-sync sketch for weak-subjectivity checkpoint execution proof sync.

The core idea is to keep the base EIP-8025 execution proof interface unchanged, with execution proofs still proving Engine API validation for new_payload_request_root, and add a recursive BeaconChainProof layer above it.

Each extend_chain step verifies:

• one parent BeaconChainProof;
• one inner ExecutionProof;
• one BeaconBlockExecutionBinding for the beacon block being extended.

The recursive proof outputs BeaconChainProofPublicInput:

class BeaconChainProofPublicInput(Container):
    ws_checkpoint_root: Root
    ws_checkpoint_slot: Slot
    head_root: Root
    head_slot: Slot

Related writeup

Design writeup:

• Weak-Subjectivity Checkpoint Execution Proof Sync: https://frisitano.github.io/slides/writeups/weak-subjectivity-checkpoint-proof-sync.html