Zook: return the final evaluation point from prove

[BornPsych]

Stacked on #270 — review that first; this PR's diff is only the last commit.

What

ProtocolConfig::prove currently returns () and discards everything the transcript derived, so a caller that wants to continue reasoning about the proof (e.g. wiring Zook into an outer protocol, or checking prover/verifier agreement in tests) has no way to get at the final evaluation point. This PR returns it.

prove now returns a ProverClaim<F>:

pub struct ProverClaim<F: ark_ff::Field> {
    /// Sumcheck challenges followed by the basecase evaluation points.
    pub evaluation_point: Vec<F>,
    /// Fiat-Shamir RLC coefficients for the input forms.
    pub rlc_coefficients: Vec<F>,
}

These are the prover-side mirror of the FinalClaim fields the verifier already returns.

How

• ProverRoundState gains all_round_challenges: Vec<M::Target>, accumulating each round's sumcheck challenges in transcript order.
• After the rounds, the basecase opening's evaluation_points are appended, giving the full point in the same order the verifier reconstructs it.
• A debug_assert pins evaluation_point.len() == log2(vector_size).
• The basecase opening was previously bound to let _ =; it is now used.

Tests

• build_and_prove returns a Proven struct instead of a 4-tuple — the tuple was already 4 fields wide and this adds a 5th.
• Roundtrip tests assert the prover's evaluation_point and rlc_coefficients match the verifier's FinalClaim, so a divergence between the two sides fails loudly rather than silently.

cargo test zook → 21 passed. cargo fmt --check and cargo clippy --all-targets clean.

[codspeed-hq]

Merging this PR will not alter performance

✅ 10 untouched benchmarks
⏩ 22 skipped benchmarks¹

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_{Comparing ys/zook-prover-final-eval-point (007c560) with main (c274cd5)}

Footnotes

1. 22 benchmarks were skipped, so the baseline results were used instead. If they were deleted from the codebase, click here and archive them to remove them from the performance reports. ↩

[zkfriendly]

Looks great! thanks. Only thing is CI is failing due to a Clippy error; it's coming from an unchanged file, but it would be nice to fix it here and then merge with a green CI.