[Tabaie]

Depending on Consensys-Incorporated/gnark#1913, this PR implements a GKR verifier in Prover-Ray.

route	module	rows used	height	width (committed)	cells	constraints (max degree)	lookups per row
AIR	P2 core	$2^{20}$	$2^{20}$	$158$ ($134$ witness)	165.7M	$117$ ($3$)	1 write
GKR	table $T$, $E$, sum	$2^{20}$	$2^{20}$	$49 = 25 + 6 + 18$	51.4M	$n + 1 = 21$ ($2$), plus sum	target of the lookups
GKR	proof	$104n + 836 = 2916$	$2^{12}$	$19$	0.08M	$0$	1 write
GKR	transcript	$84n + 617 = 2297$	$2^{12}$	$73$	0.30M	$36$ ($2$)	2 reads, 1 table lookup, 1 write
GKR	gates	$1528$	$2^{11}$	$61$	0.12M	$6$ ($3$)	3 reads, 1 write
GKR	folds	$695$	$2^{10}$	$92$	0.09M	$24$ ($3$)	4 reads, 2 writes
GKR	eqs	$\lceil n/3 \rceil \cdot 256 = 1792$	$2^{11}$	$109$	0.22M	$54$ ($4$)	6 reads, 1 write
GKR	rounds	$28n = 560$	$2^{10}$	$114$	0.12M	$66$ ($2$)	8 reads
GKR	inputs	$n + 25 = 45$	$2^{6}$	$31$	0.002M	$6$ ($2$)	1 read, 1 write
GKR	verifier's own compressions	$2297$	rows in next layer's $T$	$49$	0.11M	—	—
AIR	total				165.7M
GKR	total				52.4M

$n = 20$: $2^{20}$ compressions per layer, the realistic size for 2-to-1. Width: committed base columns per row, an extension column counting $6$, including the compiler's running sums and quotient shares. Constraints: base-field constraints declared in the code, each holding on every row, not counting the compiler's lookup constraints. The $49$ cells per row of $T$, $E$ and the sum are from the R5 measurement; the rest from this PR. The GKR total is $51.4\mathrm{M} + 0.94\mathrm{M}$ (verifier) $+ 0.11\mathrm{M}$ (its own compressions) $= 52.4\mathrm{M}$. The hashing-chain logic (md chip), needed by both routes alike, is left out of both.

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Note

High Risk
Touches core proof verification: a flaw in the new GKR constraints or dependency mismatch could break soundness of recursive proofs.

Overview
Introduces gkrverifier, which turns a gnark KoalaBear E₆ GKR circuit plus schedule into wiop modules (proof, transcript with Poseidon2 lookups, gate lowering, fold/eq/round sumcheck rows, and claim inputs) wired through a shared value bus, including Define, Assign, and Compressions helpers.

Adds layout/evaluation logic mirroring gnark’s verifier (transcript replay, gate bytecode lowering, sumcheck folding) and heavy regression tests (Poseidon2 proofs, synthetic circuits, corrupted-witness cases, input validation).

Bumps gnark/gnark-crypto (and related golang.org/x/*) in prover-ray and arithmetization to the commits required by the new APIs.

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