feat: add test sweeps for internal prover & root prover

[Aalanli]

Resolves: INT-8260

The workflow I have is:

1. generate parameter sets using this branch: https://github.com/openvm-org/stark-backend/tree/sweep_params
2. save parameter sets as json, check into the tests
3. the test will deserialize the json, loop over all the params and run fibonacci.

Another approach is to modify stark-backend to export some kind of get_sweeps function. Anyways if we don't want to deserialize we need to modify stark backend as making a SystemParam needs some non-public constants and functions from soundness.rs.

sweep parameters

Sweeping over internal config:

log_blowups: 1..=7
k_whirs: (1..=7).step_by(2)
l_skips: (1..=18).steup_by(4)
n_stack = 19 - l_skips
w_stack = 512

Sweeping over root config:

log_blowups: [2, 3, 4, 5, 6]
k_whirs: (1..=7).step_by(2)
l_skips: vec![2, 4, 8, 14, 18]
n_stack = 20 - l_skips
w_stack = 18

[Aalanli]

Currently the root sweep fails with this config:

SystemParams { l_skip: 14, n_stack: 6, w_stack: 18, log_blowup: 2, whir: WhirConfig { k: 1, rounds: [WhirRoundConfig { num_queries: 193 }, WhirRoundConfig { num_queries: 193 }, WhirRoundConfig { num_queries: 193 }, WhirRoundConfig { num_queries: 193 }, WhirRoundConfig { num_queries: 193 }, WhirRoundConfig { num_queries: 193 }, WhirRoundConfig { num_queries: 193 }, WhirRoundConfig { num_queries: 193 }, WhirRoundConfig { num_queries: 193 }, WhirRoundConfig { num_queries: 193 }], mu_pow_bits: 20, query_phase_pow_bits: 20, folding_pow_bits: 20, proximity: ListDecoding { m: 1 } }, logup: LogUpSecurityParameters { max_interaction_count: 2013265921, log_max_message_length: 7, pow_bits: 18 }, max_constraint_degree: 4 }

with error message

Error: Proof shape verification failed: Invalid StackingProof shape: Total stacked width across commits (38) exceeds w_stack (18)

Caused by:
    Invalid StackingProof shape: Total stacked width across commits (38) exceeds w_stack (18)

[Aalanli]

And internal sweep fails with this config:

SystemParams { l_skip: 1, n_stack: 18, w_stack: 512, log_blowup: 1, whir: WhirConfig { k: 1, rounds: [WhirRoundConfig { num_queries: 450 }, WhirRoundConfig { num_queries: 450 }, WhirRoundConfig { num_queries: 450 }, WhirRoundConfig { num_queries: 450 }, WhirRoundConfig { num_queries: 450 }, WhirRoundConfig { num_queries: 450 }, WhirRoundConfig { num_queries: 450 }, WhirRoundConfig { num_queries: 450 }, WhirRoundConfig { num_queries: 450 }], mu_pow_bits: 20, query_phase_pow_bits: 20, folding_pow_bits: 18, proximity: ListDecoding { m: 2 } }, logup: LogUpSecurityParameters { max_interaction_count: 2013265921, log_max_message_length: 7, pow_bits: 18 }, max_constraint_degree: 4 }

with this error:

thread 'tests::test_sdk_fibonacci_internal_sweep' (2885861) panicked at crates/sdk/src/lib.rs:543:18:
Trace heights did not generate properly: Stacked PCS: StackedLayout::new: column height 22 exceeds stacked height 19

Caused by:
    StackedLayout::new: column height 22 exceeds stacked height 19

Location:
    /home/allanl/Programs/openvm-worktree/param_tuning/crates/continuations/src/prover/inner/mod.rs:91:21
note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace
test tests::test_sdk_fibonacci_internal_sweep ... FAILED

[stephenh-axiom-xyz]

We need all the SDK tests, especially deferrals. It probably is better to not do everything from a single run, and instead have a script that runs the full SDK suite for a given parameter config.

[Aalanli]

Hi @stephenh-axiom-xyz , can you take a look?

[github-actions]

Code review

No issues found. Checked for bugs and CLAUDE.md compliance.

[stephenh-axiom-xyz]

Rn params are only modified in fib_sdk, every instance of *_params_with_100_bits_security should be replaced. Probably best to make a helper for this

[github-actions]

group	app.proof_time_ms	app.cycles	leaf.proof_time_ms
fibonacci	3,049	12,000,265	670
keccak	16,545	18,655,329	3,065
sha2_bench	9,226	14,793,960	1,127
regex	1,157	4,137,067	354
ecrecover	611	123,583	292
pairing	937	1,745,757	306
kitchen_sink	4,088	2,579,903	873

Note: cells_used metrics omitted because CUDA tracegen does not expose unpadded trace heights.

Commit: 0bdc24f

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