Abstract This paper identifies a specific hardware condition on the Apple M4 unified memory architecture where the sequential carry assumption of standard multi-precision libraries (GMP/MPFR) no longer holds. By utilizing Julia's stack-allocated NTuple primitives and a speculative carry-select (parallel-prefix) implementation, we achieve a median latency of 2.250 ns for 256-bit addition with zero heap allocations. This represents a 7.7x performance increase over native MPFR BigFloat(256) operations. Citation: Askamp, N. (2026). Beyond the Carry-Chain: Constant-Time Parallel-Prefix Bignum Arithmetic on ARM Unified Memory Architectures. Key Results: Verification of sub-3ns bignum arithmetic on consumer ARM64 hardware. Elimination of Garbage Collector (GC) jitter through zero-allocation stack primitives. Deterministic result validation via SHA-256 limb hashing. Supplementary Material: The complete step-by-step derivation, failed attempts, and raw REPL logs are documented in the companion Reproduction Log: 10.5281/zenodo.20063061 Verification Hashes: Canonical Result Hash (pi + e, 256-bit): 03c68ec2283606656347ad28a8abf044cc29a837f9adb91ba18d390417ff5349 Stack Integrity Hash (manifest, 37 files): dd76dc54c1c23c46b5aebf9582237ab5acb672eaa59da67cb8dbe274c7866bd5
Nick Askamp (2026) studied this question.