[ZkcTracer] feat: simple zkc program that compiles to a binary file which is then…

[amkCha]

… go-corset check against a json input file

This PR implements issue(s) #

Checklist

• I wrote new tests for my new core changes.
• I have successfully ran tests, style checker and build against my new changes locally.
• If this change is deployed to any environment (including Devnet), E2E test coverage exists or is included in this
  PR.
• I have informed the team of any breaking changes if there are any.

---

Note

Low Risk
Low risk: adds a new CI workflow and Makefile targets for compiling/executing a small test ZKC program, without changing production logic.

Overview
Adds a new GitHub Actions workflow (arithmetization-simple-zkc-binary-run-and-go-corset-check.yml) that installs zkc, compiles a small ZKC program into a binary, and runs zkc exec --check against a JSON input on PRs/pushes affecting arithmetization.

Updates arithmetization/Makefile to make ZKC inputs configurable via env vars, and introduces zkc-check/zkc-compile-and-check targets.

Adds a minimal simple_add.zkc and matching simple_add.json fixture used by the CI check.

^{Reviewed by Cursor Bugbot for commit 4d4ec69. Bugbot is set up for automated code reviews on this repo. Configure here.}

[github-actions]

prover Changelog Preview (informational)

[Unreleased] diff (commits touching prover/** since latest releases/prover/v* tag)

[unreleased]

_{Generated by git-cliff-action using cliff.toml. This comment is informational and does not gate the PR.}

[github-actions]

linea-besu Changelog Preview (informational)

[Unreleased] diff (commits touching linea-besu/** since latest releases/linea-besu/v* tag)

[unreleased]

_{Generated by git-cliff-action using cliff.toml. This comment is informational and does not gate the PR.}

[github-actions]

postman Changelog Preview (informational)

[Unreleased] diff (commits touching postman/** since latest releases/postman/v* tag)

[unreleased]

_{Generated by git-cliff-action using cliff.toml. This comment is informational and does not gate the PR.}

[github-actions]

coordinator Changelog Preview (informational)

[Unreleased] diff (commits touching coordinator/** since latest releases/coordinator/v* tag)

[unreleased]

_{Generated by git-cliff-action using cliff.toml. This comment is informational and does not gate the PR.}

[github-actions]

tx-exclusion-api Changelog Preview (informational)

[Unreleased] diff (commits touching tx-exclusion-api/** since latest releases/tx-exclusion-api/v* tag)

[unreleased]

_{Generated by git-cliff-action using cliff.toml. This comment is informational and does not gate the PR.}

[cursor]

Cursor Bugbot has reviewed your changes and found 2 potential issues.

There are 4 total unresolved issues (including 2 from previous reviews).

^{❌ Bugbot Autofix is OFF. To automatically fix reported issues with cloud agents, have a team admin enable autofix in the Cursor dashboard.}

^{Reviewed by Cursor Bugbot for commit b50f8b7. Configure here.}

[lorenzogentile404]

LGTM