batch main sumcheck

[hero78119]

Problem

Design Rationale

Change Highlights

Benchmark / Performance Impact

Operation

Operation	master (s)	this PR (s)	Improve (master -> this PR)

Layer

Layer	master (s)	this PR (s)	Improve (master -> this PR)

Benchmark command(s):

# paste exact command(s)

Environment (CPU/GPU, core count, rust toolchain, commit hash):

raw data:

• master:
• this PR:

Testing

# paste exact command(s), for example:
# cargo fmt --all --check
# cargo make clippy
# cargo make tests

Risks and Rollout

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Copilot Reviewer Directive (keep this section)

When Copilot reviews this PR, apply .github/copilot-instructions.md strictly.