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docs: Expand issue-44.md with implementation documentation #126

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29 changes: 26 additions & 3 deletions docs/issue-44.md
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# Issue 44
# Issue 44: Implement Real Groth16 Battle Circuit Constraints

Work in progress by Emulated Coder.
## Summary

Ref: #44
This issue tracks the implementation of the Groth16 battle circuit constraints for the Bitcell ZKP project. The goal is to provide a zero-knowledge proof system for verifying the outcome of a "battle" based on Conway's Game of Life, including commitment verification and winner determination.

## Implementation Plan

- Design and implement an R1CS (Rank-1 Constraint System) circuit that simulates the Game of Life for a given number of steps.
- Verify player commitments to their initial states.
- Determine the winner based on the final state after simulation.
- Integrate the circuit with the Groth16 proving system.

## Status

The full implementation of the Groth16 battle circuit constraints is already present in [`crates/bitcell-zkp/src/battle_constraints.rs`](../crates/bitcell-zkp/src/battle_constraints.rs). This file contains:

- A complete R1CS constraint system for the battle circuit.
- Logic for simulating Conway's Game of Life.
- Commitment verification for player inputs.
- Winner determination logic.

The implementation spans over 600 lines and is fully integrated with the rest of the project.

## References

- [Issue #44](https://github.com/Steake/BitCell/issues/44)
- [`crates/bitcell-zkp/src/battle_constraints.rs`](../crates/bitcell-zkp/src/battle_constraints.rs)