feat(stark): shared FRI across all tables in batched mode

Replace per-table FRI with ONE shared FRI when all tables have the same
LDE domain size (batched mode). Each table still computes its own DEEP
composition polynomial (different z per table), then all DEEP polys are
alpha-batched into a single evaluation vector for one FRI commit phase,
one grinding step, and one query set.

Prover changes:
- Add compute_per_table_deep_evaluations: does Rounds 3-3.5 (OOD eval +
  DEEP poly computation) without running FRI
- Batched Step 3 now: (a) per-table DEEP computation in parallel,
  (b) build shared FRI transcript with all OOD data, sample alpha,
  (c) alpha-batch DEEP polys with iFFT+FFT extension to LDE domain,
  (d) one FRI commit + grind + query, (e) shared openings from batched trees
- Per-table StarkProofs get empty FRI fields in batched mode

Verifier changes:
- Add verify_composition_only: steps 1-2 without FRI (for shared FRI mode)
- multi_verify detects shared FRI via MultiProof fields
- Shared FRI path: per-table composition check, then reconstruct shared
  FRI transcript, sample alpha, alpha-batch per-table DEEP reconstructions
  at query points, verify one FRI fold chain + openings

Proof format:
- MultiProof gains optional shared FRI fields (fri_layers_merkle_roots,
  fri_last_value, query_list, deep_poly_openings, nonce)
- Non-batched path unchanged (shared fields are None)

Author: diegokingston

crypto/stark/src/proof/stark.rs

@@ -96,4 +96,22 @@ pub struct StarkProof<F: IsSubFieldOf<E>, E: IsField, PI> {
 #[serde(bound = "PI: serde::Serialize + serde::de::DeserializeOwned")]
 pub struct MultiProof<F: IsSubFieldOf<E>, E: IsField, PI> {
     pub proofs: Vec<StarkProof<F, E, PI>>,
+    // --- Shared FRI data (batched mode only) ---
+    // When present, per-table proofs have empty FRI fields;
+    // the verifier uses these shared fields instead.
+    /// FRI layer Merkle roots from the shared FRI commit phase.
+    #[serde(default)]
+    pub fri_layers_merkle_roots: Option<Vec<Commitment>>,
+    /// Final FRI folding value from the shared FRI.
+    #[serde(default)]
+    pub fri_last_value: Option<FieldElement<E>>,
+    /// FRI query decommitments from the shared FRI.
+    #[serde(default)]
+    pub query_list: Option<Vec<FriDecommitment<E>>>,
+    /// Deep polynomial openings from the shared FRI (one per query).
+    #[serde(default)]
+    pub deep_poly_openings: Option<DeepPolynomialOpenings<F, E>>,
+    /// Proof-of-work nonce from the shared FRI.
+    #[serde(default)]
+    pub nonce: Option<u64>,
 }