> For the complete documentation index, see [llms.txt](https://maru-2.gitbook.io/maru/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://maru-2.gitbook.io/maru/zk-implementation/schema/arithmetic-proof.md).

# Arithmetic proof

Arithmetic proof via zk-STARKs enables efficient verification of addition operation of volume values combined with Sum proof through CTL.

## Circuit

**Private inputs** include data fields about each value:

* `operator` flag of arithmetic operator
* `input0` first operand of arithmetic operation
* `input1` second operand of arithmetic operation
* `input2` third operand if we have ternary arithmetic operation
* `result` of arithmetic operation

Please refer to the ArithmeticStark description to learn more about how this STARK was implemented and what fields and constraints were used:

{% file src="/files/57yRt0PsAmSRr6n26Jku" %}
