refactor(prover): align byte range-checks with ARE_BYTES spec

[ColoCarletti]

Description:

Spec #532 splits the old IS_BYTE lookup into the IS_BYTE template and the ARE_BYTES[X, Y] paired interaction. Two changes:

1. Rename IS_BYTE → ARE_BYTES across the prover (BusId, multiplicity column, BitwiseOperationType, doc comments, tests).

2. Fix KECCAK and KECCAK_RND, which were sending single-element values on the (now 2-element) ARE_BYTES bus LogUp fingerprints couldn't balance. Pair the sends:

   • keccak: addr bytes → 4 (addr[2i], addr[2i+1]) pairs
   • keccak_rnd theta: cxz_left → 20 adjacent-byte pairs per round
   • keccak_rnd rho: (rot_left[b], rot_right[b]) → 200 pairs per round

Trace builder emits matching paired ops; bus/op count assertions updated.

[github-actions]

Codex Code Review

No issues found in the PR diff.

I checked the IsByte to AreBytes rename and the changed Keccak byte-pairing against the corresponding BITWISE receiver signatures and multiplicity collection. The updated sender signatures appear matched by collect_bitwise_from_* changes.

Verification note: I attempted cargo check -p prover, but the sandbox blocked rustup/cargo writes under /home/runner/.rustup / .cargo and network access for dependencies, so I could not complete a compile check locally.

[claude]

Review: refactor(prover): align byte range-checks with ARE_BYTES spec

Overall: Clean, well-scoped refactor. The rename is consistent across all files, the pairing logic is semantically correct, and the count assertions check out arithmetically (440→220 per round for keccak_rnd, 8→4 per call for keccak addr). No security or correctness issues found.

Low: Two stale counts in summary comments

In collect_bitwise_from_keccak (trace_builder.rs), two inline comments were updated from IS_BYTE to ARE_BYTES but their numeric counts were not halved to reflect the pairing:

• Line 1748: ARE_BYTES on Cxz_left (40) → should be (20) (5 x-cols × 4 pairs)
• Line 1827: ARE_BYTES (400) → should be (200) (5×5×8 pairs)

The section-header comments and test assertion comments in the same function already use the correct updated counts (20 and 200), so this is just a minor inconsistency.

Everything else looks correct

• LogUp fingerprint semantics: ARE_BYTES[X, Y] checks both X and Y are in [0, 256); pairing (rot_left[b], rot_right[b]) and (cxz_left[2i], cxz_left[2i+1]) is semantically equivalent to two separate single-byte checks. ✓
• Trace builder pairing matches bus interaction pairing in all three keccak sites (addr, theta cxz_left, rho rot_left+rot_right). ✓
• single_byte() / byte_op(..., 0) pattern for IS_BYTE-style single-byte checks preserved everywhere. ✓
• Bus interaction counts: 138→134 (keccak), 1371→1151 (keccak_rnd), math verified. ✓
• Test assertion for total bitwise ops updated correctly (109+24*1368 → 105+24*1148). ✓