MERA-NALP: Zero-Allocation Tensor Contraction on Apple M4 with Canonical Audit Verification

We demonstrate that the Non-Allocating Limb-Parallelized (NALP) principle, originally developed for 256-bit bignum arithmetic on Apple M4, generalises to tensor network contraction.
Applying Julia's in-place BLAS mul! with pre-allocated buffers to Multi-scale Entanglement Renormalisation Ansatz (MERA) coarse-graining achieves 12.8x speedup over equivalent JAX-JIT matrix-vector contraction and ~300x over the full JAX MERA pipeline, with 0 heap allocations at all bond dimensions chi in [4, 128].
We subject the implementation to a 13-checkpoint canonical audit following the Boundary Proof Principle, identifying one formally documented boundary gap in Julia's underlying BLAS layer.
The implementation is certified via a Verifiable Edge Artifact (VEA) canonical hash, making results tamper-evident and hardware-fingerprinted.

The implementation is certified as a Verifiable Edge Artifact.
The canonical hash is generated from the benchmark results and audit manifest,
sealed with SHA-256: Field Value Canonical Hash c6a0009d665b2bb846596e7a1ffdb116fed876f0bef6bbb81a26f4b3e673eb51
Timestamp 2026-05-17 Hardware Apple M4 (24GB unified memory)
Julia version 1.12.6
Audit result 12/13 PASS Boundary gap L0-1 (chi=0, documented)
The hash certifies that this artifact was generated on specific hardware at a specific moment.
A different machine or a different run will produce a different hash — this is not a limitation but the intended behaviour
. The hash is the physical anchor.