perf(stark): hoist query-invariant deep-composition sums out of the FRI query loop

[Oppen]

Summary

• Hoist sums that depend only on challenges and proof-level OOD/gamma data (ood_row_sum, number_of_parts, z_pow, h_sum_zpow) out of the per-query reconstruct_deep_composition_poly_evaluation_pair into a new once-per-proof compute_query_invariant_deep_terms, eliminating the O(num_queries × height × width) coeff * ood multiplies down to O(height × width).
• Derive number_of_parts from proof.composition_poly_parts_ood_evaluation.len() (already validated against the AIR's degree bound in multi_verify_archived) instead of each query's own opening length, and check both regular/symmetric per-query openings against that fixed value — strictly stronger than the previous regular-vs-symmetric-only guard, since it also rejects a proof whose per-query opening length varies query to query.

Numbers

Metric	Before	After	Change
Single-query total cycles	86,368,803	85,810,707	−0.65%
Single-query step3:fri	≈7.97M	7,807,225	≈−2%
Multi-query total cycles	1,951,764,531	1,818,365,778	−6.84%
Multi-query step3:fri	≈652.1M	529,415,199	≈−18.8%

Test plan

• cargo check -p stark
• cargo test -p stark (137 tests pass)
• make test-ethrex
• cargo test -p lambda-vm-prover --lib test_recursion_execute_1query -- --ignored --nocapture (in-VM verify accepted)
• make test-profile-recursion-single / make test-profile-recursion-multi (cycle counts above)
• Adversarial soundness review (independent Opus pass): confirmed no reject-path was weakened, the number_of_parts guard change is a genuine strengthening, and hoisted sums are algebraically identical to the per-query-recomputed values for honest proofs
• Independent correctness, simplicity, and performance reviews: no issues found