aiur: ground the FFT cost model in the prover's actual transforms

[arthurpaulino]

The per-circuit FFT cost statistic (Ix/Aiur/Statistics.lean) was (stage1 + stage2 width) * h * log2(h) over function and memory circuits only. Compared against the pinned prover (multi-stark be1755e, Plonky3 e9d7561), that misses:

• the quotient chunk columns: q*D committed base columns per circuit, q = next_pow2(max(d, 2) - 1) — constraint-degree changes were invisible to the statistic;
• the commit transform structure: Radix2DitParallel::coset_lde_batch runs one size-h inverse DFT plus B size-h coset DFTs per column, not one size-B*h DFT;
• the two quotient-rebasing transforms: the iDFT of the (q*h) x D flattened quotient and the size-h DFT of the q*D coefficient slices;
• the Bytes1/Bytes2 gadget circuits, whose witness builders always emit full tables (256 / 65536 rows with zero multiplicities on unqueried rows), so they are active in every proof as a fixed cost.

The new per-circuit cost, with F(0) = 0, F(x) = x*log2(max(x, 2)), and the raw (unpadded) height h so one-row changes stay visible while structural powers of two (B, q) stay exact:

(B+1)*(m + s2 + q*D)*F(h) + D*F(q*h) + q*D*F(h)

summed over constrained functions, memories, Bytes1, and Bytes2.

Circuit shapes (main/stage-2 width, quotient degree, preprocessed dimensions) are read off the compiled Rust System through a new AiurSystem::circuit_shapes API and FFI — never re-derived in Lean, since max_constraint_degree requires the compiled constraint graph. ix check statistics use a one-shot build-extract-drop variant (that flow never builds a system otherwise, and pays the build only when stats are requested). The prove/verify/stats parameter triple is deduplicated into Aiur.defaultCommitmentParameters / defaultFriParameters.

The report now prints per-circuit costs in scientific notation (two-decimal mantissa); the total stays in full digits with the scientific form in parentheses.

A new aiur-cost primary suite covers the pure formula: exact values at power-of-two heights, one-row monotonicity across power-of-two boundaries (where the padded prover plateaus), per-input monotonicity in width, lookups, quotient degree, and blowup, and the scientific formatter (including the mantissa-carry edge). A Rust test pins circuit_shapes against System.circuits field-for-field, including canonical order and the fixed gadget table dimensions.

FFT pins regenerated from one lake test -- --ignored ixvm run (only the FFT pin assertions moved; all execution/parity tests passed). Small constants now sit on a ~174M fixed floor that is almost entirely the always-active Bytes2 commit: 5 * 32 * F(65536) ≈ 168M.

[arthurpaulino]

!bencher-thresholds-reset aiur-check-prove aiur-check-execute aiur-recursive

[github-actions]

♻️ Baseline reset queued for: aiur-check-execute aiur-check-prove aiur-recursive — will anchor to the merge commit when this PR merges.