Implement Real Groth16 State Circuit Constraints

[Steake]

Part of Epic: #72 - RC2: Zero-Knowledge Proof Production

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Goal: Implement full Groth16 constraints for state transition verification and proof flow.

Requirements:

• Enforce state root updates, nullifier double-spend protection, merkle proof validation
• Inputs/outputs based on protocol specification
• Optimize for <20s proof time
• Add all relevant tests

Acceptance Criteria:

• Circuit verifies valid state transitions and nullifier logic
• Proofs and verification keys are published
• All protocol invariants tested

See RELEASE_REQUIREMENTS.md

[Steake]

[autopilot] @copilot please start work on this issue and open a PR that references #45 in the PR description.