feat(eigen-client-m1): Improve Merkle Proof #1072

Job	Run time
Get changed files	2m 6s
CI for Core lint Components	0s
CI for Prover Components	0s
CI for Docs	0s
Build prover images	0s
Build prover images with avx512 instructions	0s
CI for Core Components / integration-tests	1s
CI for Core Components / loadtest (OLD)	1s
CI for Core Components / unit-tests	1s
CI for Core Components / loadtest (NEW)	1s
CI for Common Components (prover or core) / build	1s
Build contract verifier / Prepare contracts	1s
Build core images / Prepare contracts	1s
Build TEE Prover images / Build and Push Docker Images	1s
CI for Core Components / lint / code_lint	1s
Build core images / Build and Push Docker Images	1s
Build contract verifier / Build and Push Docker Images	1s
Build core images / Create release manifest	1s
Build contract verifier / Create release manifest	1s
Github Status Check	1s
	2m 20s

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