`multiPCS`: make Oink-phase `BATCH_SIZE`-agnostic

[iakovenkos]

Context

The OinkProver handles interleaved (BS > 1) and non-interleaved (BS = 1) commitment paths via if constexpr (BATCH_SIZE > 1) branches in every commit_to_* method.

The BS > 1 path currently hardcodes entity-to-group mappings by name.

This approach does not scale — adding BS = 2 or changing the group structure requires editing every method.

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Proposed solution

Have the Flavor define round-to-group mappings and let OinkProver iterate generically:

// Flavor defines which groups are committed in each round:
static constexpr std::array WIRE_GROUP_INDICES = {8, 9, 10, 11, 12, 13};
static constexpr std::array W4_GROUP_INDICES = {16, 14};

// OinkProver iterates:
if constexpr (BATCH_SIZE > 1) {
    for (auto g : Flavor::WIRE_GROUP_INDICES) {
        commit_group_by_index(g);
    }
}

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Benefits

• Eliminates per-entity naming in the BS > 1 path
• Makes adding new batch sizes (e.g. BS = 2) trivial — just define GroupAccessors
• Removes commit_group’s O(n) linear scan for group buffer lookup (use index directly)
• Consolidates ZK tail logic, which currently also performs a linear scan to find the group index

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Current state

The explicit approach works correctly for BS = 1 and BS = 4.

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Related

• allocate_interleaved_groups in prover_polynomials.hpp is already generic over BS
• GroupAccessors_<BS> already defines group structure per batch size
• Gemini / Shplemini PCS infrastructure already supports arbitrary shift_exponent