Fix: Constrain table multiplicities

[nicole-graus]

Motivation

Several AIR tables leave their multiplicity column μ unconstrained. Since μ lives in the field, it can be set to −1, which flips a row's role on the bus: it starts receiving its range checks instead of sending them. This is exploitable: each bug below is proven end-to-end by a test where the verifier accepts a false statement against an unmodified ELF:

Description

Two fix shapes, by whether the table deduplicates repeated rows:

• MUL, DVRM, LT, BRANCH: keep dedup and bound μ by sending IS_HALF[μ] with multiplicity μ, forcing μ ∈ [0, 2^16). Rows whose count exceeds 2^16−1 are split (dedup_*_rows), and the BITWISE collector counts the new lookup over the same rows.
• SHIFT, LOAD: add a boolean constraint μ·(1−μ)=0 (plus zbs·(1−zbs)=0 for SHIFT).

Note: the first bound soundness relies on no other table emitting an out-of-range halfword with +1, the same assumption every range check already makes. mul_mu_carrier_poc.rs documents this explicitly.

[nicole-graus]

/bench

[github-actions]

Benchmark — real block (ethrex_mainnet_25368371.bin) (median of 3)

_{continuations · epoch 2^22 · 8 epochs}

Metric	main	PR	Δ
Peak heap	48142 MB	46624 MB	-1518 MB (-3.2%) ⚪
Prove time	109.853s	102.464s	-7.389s (-6.7%) 🟢

❓ -6.7% — beyond what 3 runs resolve. Use /bench-abba for a paired test of the same block (default 12 pairs, ~72 min, resolves ~1%).

_{Prove-time spread 1.1% (102.464s / 101.989s / 103.125s)}

_{Commit: 4dd1ee5 · Baseline: cached · Runner: self-hosted bench}