Glossary

A compression format that represents dense multidimensional data as a product of smaller matrices.

Quantized Tensor-Train decomposition is a mathematical technique that finds the structural form underlying high-dimensional data and encodes it as a chain of small tensor cores. Compression ratio scales with the smoothness and separability of the data. QTT is the storage and execution basis for the entire HolonomiX platform.

The maximum internal dimension in a TT-core. Controls compression vs. precision trade-off.

The rank budget constrains the internal dimension of each tensor-train core. Higher rank budgets preserve more detail and produce more accurate results at the cost of larger memory footprint and slower computation. Lower budgets prioritize speed and compression. The Rank Governor manages this trade-off dynamically.

How data is arranged in memory before TT decomposition. Different orderings exploit different patterns.

Before QTT decomposition, multidimensional data must be reshaped into a tensor. The sequence in which dimensions are ordered affects which structural patterns the decomposition can exploit. Lexicographic ordering is simplest; Hilbert ordering follows space-filling curves; bit-reversed ordering is optimal for certain frequency-domain data. The Atlas classifies which orderings work for which workload types.

A workload where QTT rank stays bounded and compression is predictable. Verdict class A.

A workload is governable when the Oracle Governor can predict, with high confidence, that QTT compression will achieve stable compression ratios at production scale. Rank stays bounded, memory usage is predictable, and query latency meets service-level targets. This is verdict class A in the Atlas classification system.

Classifies the structural form of data on arrival and assigns verdict classes.

The Oracle Governor is the classification engine at the entry point of the HolonomiX platform. It examines the smoothness, separability, and dimensional structure of incoming data to determine how it should be decomposed, what compression ratio to expect, and which verdict class applies. It is informed by the Canonical Data Atlas.

Constrains precision budgets to keep execution bounded and predictable.

The Rank Governor enforces precision constraints across all QTT operations. It monitors memory pressure, adapts rank budgets dynamically based on workload characteristics, and ensures that no operation exceeds its allocated VRAM or latency budget. It works in concert with the Oracle Governor to maintain system-wide execution guarantees.

894 workloads classified across 4 axes. The empirical foundation for governance decisions.

The Canonical Data Atlas is a systematic classification framework containing 894 entries and 92 predictive rules. It classifies computational workloads across four axes (data structure, task type, tensorization ordering, algorithm choice) and assigns verdict classes (A through D) predicting QTT compression effectiveness. It serves as the evidence base for Oracle Governor decisions.

2.2M SLOC GPU runtime executing QTT operations directly on NVIDIA hardware.

The HyperTensor-VM is a custom GPU runtime built for executing operations directly on quantized tensor-train cores in VRAM. It includes custom Triton kernels, cuBLAS GEMM for tensor contractions, cuSOLVER for decomposition, and specialized memory management. All 109 audited operations execute on compressed structural form without decompression.

Data stored as its mathematical structure rather than raw bytes. The basis of QTT compression.

Instead of storing data as raw bytes and copying it into format-specific indexes, structural representation stores the mathematical form that generates the data. This form can answer any query pattern directly: key-value lookups, similarity search, full-text search, aggregations, and streaming updates all operate on the same compressed structure.

A/B/C/D rating from the Atlas indicating QTT compression effectiveness for a workload.

Every workload classified in the Atlas receives a verdict class. A (Governable): compression is effective and predictable. B (Compressible): works with tuning. C (Conditional): saturates at some scales. D (Weak): QTT is the wrong tool for this workload. Verdict classes inform Oracle Governor routing decisions.

The growing gap between processor speed and memory bandwidth, widening since 1995.

The memory wall describes the divergence between processor clock speeds and memory bandwidth that has accelerated since 1995. Processors can compute far faster than memory can deliver data. The entire modern data infrastructure stack exists as compensation: caching, indexing, and format duplication are all strategies for moving data closer to compute. HolonomiX addresses the root cause by eliminating the need for copies entirely.