Add field element comparison script

[nicole-graus]

Adds a script to compare the amount of field elements in Lambda VM against SP1 v5 and SP1 v6.

It runs a Fibonacci program of size 100k, 200k, and 400k and counts main-trace field elements (base field, rows × columns across all AIR tables) and auxiliary field elements (extension field, committed interaction columns × rows).

How to run it:

./bench_vs/run_elements.sh                        # default: n = 100k, 200k, 400k
./bench_vs/run_elements.sh -n 100000 1000000      # custom sizes

[github-actions]

Codex Code Review

1. High (Security): Remote script execution via curl | bash on a self-hosted runner.
   • File: .github/workflows/bench-vs-nightly.yml:37
   • Why it matters: This executes mutable remote code without pinning or integrity verification. If the endpoint or transit is compromised, attacker code runs on your self-hosted machine.
   • Action: Replace with a pinned, verified install path (versioned artifact + checksum/signature verification) or preinstall SP1 on the runner image.

No other concrete security/bug/perf issues stood out in the PR diff.

[claude]

Review Summary

Overall: Clean, well-structured addition. No security vulnerabilities or logic bugs in the core prover changes. Two issues worth addressing, both flagged inline.

Issues

Medium – CI supply chain risk (.github/workflows/bench-vs-nightly.yml:36)
SP1 is installed via curl | bash without a version pin or hash check. This means the nightly CI silently runs against a moving target, and any compromise of sp1up.succinct.xyz executes arbitrary code on the self-hosted bench runner. Pin to a specific SP1 release.

Low – Silent element under-count if tables grow (prover/src/tables/trace_builder.rs)
total_field_elements and total_auxiliary_field_elements manually list every table type with no exhaustiveness guard. A new table added to Traces would silently not be counted, making benchmark numbers quietly wrong.

No Issues

• Core API changes (prover/src/lib.rs): prove_with_inputs, prove_with_options_and_inputs, and count_elements are clean wrappers. Refactoring preserves the existing public API.
• CLI (bin/cli/src/main.rs): --private-input, --cycles, --elements, and the count-elements subcommand are straightforward. Error handling is consistent throughout.
• Guest program (bench_vs/lambda/fibonacci/src/main.rs): read_n() correctly skips the 4-byte length prefix prepended by load_private_inputs — the 12-byte buffer and input[4..12] slice are intentional and correct.
• Benchmark scripts: Shell quoting and arithmetic are safe; set -euo pipefail is set; numeric values are extracted via sed before being passed to awk/python3.