Deterministic Integer Topologies: Bypassing the Matrix-Multiplication Bottleneck via Cache-Resident Graph Traversal

Q: What does this research mean for the field?

A cache-resident 6-regular integer lattice can perform state routing at up to 174 million hops per second, providing a highly efficient alternative to standard matrix-multiplication operations. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Matthew Scott Gibson

doi:10.5281/zenodo.22431979

September 6, 2026Open Access

Deterministic Integer Topologies: Bypassing the Matrix-Multiplication Bottleneck via Cache-Resident Graph Traversal

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Key Points

To evaluate whether a deterministic 6-regular integer lattice residing entirely within CPU L2 cache can circumvent the computational bottlenecks of matrix multiplication via rapid graph traversal.
Configured a 6-regular integer lattice topology of order N = 6,328 occupying 74.16 KiB to fit inside a 256 KiB L2 cache.
Measured per-hop traversal latency and fail-closed halt intervals across two hardware platforms: an Intel Core i7-7700 and an Intel Core i7-14700F.
Compared graph traversal throughput directly against the execution time of a standard 1024×1024 float32 general matrix multiply (GEMM) benchmark.
Achieved traversal latencies of 9.76 ns per hop (102 million hops/s) on the i7-7700 and 5.75 ns per hop (174 million hops/s) on the i7-14700F.
Recorded fail-closed halt latencies of 1.5 µs on the i7-7700 and 800 ns on the i7-14700F.
Demonstrated that a single 1024×1024 float32 GEMM operation required 7.48 ms on the i7-7700, an interval equivalent to executing 767,000 graph hops.

Implication

Experimental benchmark demonstrates nanosecond-scale cache-resident graph traversal on commodity processors, indicating an alternative to matrix-multiplication operations.

Abstract

A 6-regular integer lattice of order N = T112 = 6328 occupies 74.16 KiB and fits in a 256 KiB Kaby Lake L2. Two-socket telemetry: 9.76 ns/hop on an i7-7700 (102 M hops/s) and 5.75 ns/hop on an i7-14700F (174 M hops/s). Fail-closed halt 1.5 µs / 800 ns. One 1024×1024 float32 GEMM on the 7700 is 7.48 ms (767k hops). Not a language model. Hops versus FLOPs. This is a measured cache-resident state router, not a transformer. Software: https://github.com/ultranetcommand-neo/t112-l2-lattice Table (dataset, not a model): https://huggingface.co/datasets/UltranetCommand/t112-l2-lattice

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Cite This Study

Matthew Scott Gibson (2026) studied this question.

synapsesocial.com/papers/6a9fd78a58e84d0ff5b46479 https://doi.org/10.5281/zenodo.22431979

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Deterministic Integer Topologies: Bypassing the Matrix-Multiplication Bottleneck via Cache-Resident Graph Traversal

Key Points

Implication

Abstract

Discussion

Cite This Study

Deterministic Integer Topologies: Bypassing the Matrix-Multiplication Bottleneck via Cache-Resident Graph Traversal

Key Points

Implication

Abstract

Discussion

Cite This Study

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