fix(prover): align CPU sign bit constraints with SIGN template spec (#435)

[ColoCarletti]

Aligns the CPU table's sign/extension bit handling with the updated spec (PR #435),
which replaced raw MSB16/MSB8 interactions with the SIGN template.

Changes

Column renames (no index changes):

• rv1_sign_bit → rv1_ext_bit
• arg2_sign_bit → rv2_ext_bit (clarifies it derives from rv2, not arg2)
• res_sign_bit → res_ext_bit

res extension bit: MSB8 → MSB16

• Old: MSB8[res[3]] — extracted bit 7 of byte 3 (= bit 31 of res)
• New: MSB16[res[2] + 256*res[3]] — extracts MSB of half at bits 16-31 (= bit 31 of res)
• Matches spec: SIGN(res::DWordHL[1], word_instr)
• Both extract bit 31, but the new version uses MSB16 consistently for all three ext bits

Constraint split (CE57)

• Old: single constraint (rv1_sign_bit + arg2_sign_bit + res_sign_bit) * (1 - word_instr) = 0
• New: three separate constraints per the SIGN template:
  • (1 - word_instr) * rv1_ext_bit = 0
  • (1 - word_instr) * rv2_ext_bit = 0
  • (1 - word_instr) * res_ext_bit = 0
• Constraint count: 64 → 66

[github-actions]

Codex Code Review

No actionable issues found in this PR diff.

Residual risk/testing gap:

• I could not run the targeted tests in this environment because cargo/rustup failed with a read-only temp/toolchain path error (/home/runner/.rustup/tmp), so this review is static-only.

[claude]

Overall the changes look correct and the logic is sound.

Constraint equivalence: The old combined constraint (rv1 + rv2 + res) * (1 - word_instr) = 0 and the new three separate constraints are equivalent because all three columns are binary (they're in BIT_FLAG_COLUMNS, so IS_BIT constraints apply). The split is cleaner and easier to reason about.

MSB16 vs MSB8 for res_ext_bit: Both extract the same bit (bit 31 of res). The change to MSB16 on the halfword res[2] + 256*res[3] is consistent with the other two extension bits.

Minor nits (two inline, one here):

• test_trace_generation_sign_bits in cpu_tests.rs:289 was not renamed to test_trace_generation_ext_bits to match the rest of the rename.

[ColoCarletti]

/bench

[github-actions]

Benchmark — fib_iterative_2M (median of 3)

_{Table parallelism: 32 (auto = cores / 3)}

Metric	main	PR	Δ
Peak heap	113806 MB	114032 MB	+226 MB (+0.2%) ⚪
Prove time	27.970s	28.199s	+0.229s (+0.8%) ⚪

✅ No significant change.

✅ Low variance (time: 3.3%, heap: 1.1%)

Memory Growth

_{Measured with TABLE_PARALLELISM=1 (sequential) · best of 2 samples per point}

Program	Steps	main (MB)	PR (MB)	Δ
fib_iterative_250k	250k	7349	7765	+416 MB (+5.7%)
fib_iterative_500k	500k	10268	10169	-99 MB (-1.0%)
fib_iterative_1M	1M	16348	16600	+252 MB (+1.5%)
fib_iterative_2M	2M	26538	26522	-16 MB (-0.1%)

Growth rate: 10813 MB / 1M steps (main: 10949, Δ: -1.2%)
Fit: R² = 0.9970 (main: 0.9981)

✅ No significant change in memory scaling.

_{Commit: 5824479 · Baseline: built from main · Runner: self-hosted bench}

[ColoCarletti]

/bench

[MauroToscano]

/bench 10