Technical White Paper
Delta-State Algebra: Mathematical Foundations, Hardware Implementation, and Production Results
Abelian group properties (commutativity, associativity, self-inverse, identity) with 92 formally verified Lean4 theorems.
From PicoRV32 on a $13.50 FPGA to custom RV64I with ATOMiK ISA extensions to Zynq scaling at 69.7 Gops/s with 512 parallel banks.
7,670x to 916,000x memory traffic reduction. Deterministic latency with zero timing side channels.
Copy-on-write detection via kretprobe, TCP send deduplication with CRC32C, per-cgroup waste tracking, 27 real-time sysfs metrics.
ATOMiK vs CRDTs, event sourcing, and consensus protocols. Where delta-state algebra converges and where it diverges.
The path from FPGA validation to custom silicon. Scaling projections, target process nodes, and production timeline.
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Formally verified in Lean4 proof assistant. Every algebraic property machine-checked.
Peak throughput on Xilinx Zynq XC7Z020 with 512 parallel banks at 135.6 MHz.
Across atomik-core (218), SDK pipeline (353), hardware (80), CDC (37). All passing.
Peak memory traffic reduction. 7,670x at minimum across all validated workloads.
LOAD, ACCUM, READ, SWAP. The complete algebra. Nothing else needed.
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Read the architecture docs →Start free with the Python SDK. Scale to kernel-level optimization and hardware acceleration when you need it.