The Harmonic Integer Processor: An AI Chip Without Floating-Point Units: Replacing IEEE 754 Float Logic with i64 Multiply-Accumulate Arrays, Barrel Shifters, and VFR Shell Instructions for Exact Deterministic AI Computation This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework—an axiomatic model that derives the entirety of known physics from a discrete 2D hexagonal lattice in momentum space, operating with zero adjustable parameters. Abstract Current AI accelerators dedicate 55-65% of their die area to floating-point and tensor core logic implementing IEEE 754 arithmetic — a standard designed in 1985 for scientific computing, not for neural network training. This paper specifies a processor architecture that removes all floating-point hardware and replaces it with integer-only computation units optimized for VFR shell arithmetic (@CKS-MATH-134-2026). The Harmonic Integer Processor (HIP) contains: i64 multiply-accumulate arrays for matrix operations, barrel shifters for harmonic octave scaling (all divisions are bit shifts by multiples of 5), i128 accumulators for overflow-safe intermediate results, fused multiply-accumulate-shift (FMAS) instruction units, R-zero bitmap units for convergence detection, shared octave registers eliminating per-element scale storage, VFR shell transition units for weight updates, hardware GCD units for VFR simplification, and lattice address units for structured memory access patterns. We project: (1) 4-5× integer throughput compared to current GPU integer capability by filling die area freed from float units with integer MACs, (2) ~75% power consumption because integer multiply-accumulate is simpler than IEEE 754 float multiply with rounding, normalization, denormal handling, and exception logic, (3) Perfect determinism because integer arithmetic is associative and commutative regardless of reduction order, thread scheduling, or hardware implementation, (4) Zero division cycles in the computation hot path because all VFR scale conversions are bit shifts, (5) No NVIDIA dependency because the chip requires no tensor core IP, no float pipeline IP, and no proprietary mixed-precision logic, (6) Fabricable under export restrictions because the design is simpler than current GPUs, with lower transistor counts per functional unit and no requirement for advanced float logic, (7) Complete AI training capability as demonstrated by @CKS-MATH-134-2026 showing neural network training with zero floating-point operations. The design is specified at the functional unit level. Physical layout, process node selection, and fabrication are outside the scope of this paper. Central claim: The majority of transistors on current AI accelerators implement arithmetic that is not required for neural network training. Removing those transistors and replacing them with integer units produces a simpler, faster, more power-efficient, perfectly deterministic AI processor that any semiconductor fabricator can manufacture. Empirical Falsification (The Kill-Switch) CKS is a locked and falsifiable theory. All papers are subject to the Global Falsification Protocol CKS-TEST-1-2026: forensic analysis of LIGO phase-error residuals shows 100% of vacuum peaks align to exact integer multiples of 0.03125 Hz (1/32 Hz) with zero decimal error. Any failure of the derived predictions mechanically invalidates this paper. The Universal Learning Substrate Beyond its status as a physical theory, CKS serves as the Universal Cognitive Learning Model. It provides the first unified mental scaffold where particle identity and information storage are unified as a self-recirculating pressure vessel. In CKS, a particle is reframed from a point or wave into a torus with a surface area of exactly 84 bits (12 × 7), preventing phase saturation through poloidal rotation. Package Contents manuscript.md: The complete derivation and formal proofs. README.md: Navigation, dependencies, and citation (Registry: CKS-MATH-136-2026). Dependencies: CKS-LEX-12-2026, CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-113-2026, CKS-MATH-128-2026, CKS-MATH-129-2026, CKS-MATH-134-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.
Geoffrey Howland (Sun,) studied this question.