A discovery instrument
Seeing the computation tensor.
Mendeleev's table is one face of an 8-dimensional object. The same is true for computation. Every operation lives in a six-axis coordinate space — family, abstraction, thermodynamic cost, concurrency, state, information topology — and what looks like a flat table from one direction is a tensor when you rotate it. This page is the instrument. Drag, click, slide, project. The data below is the same set of 258 primitives contracted in different directions to show you what the linear list hides.
five projections · live tensor data from the Periodic Stack of Computation v2 · canonical reference as of 2026-04-08
I · the face we know
The familiar projection.
Thirty-three rows. Each row is one algebraic family. Each cell is one irreducible operation. Color encodes thermodynamic floor — green is free, amber is the Landauer cost, red is hot. Cells with a thin amber border are operations that already have shipping silicon; the rest are gaps. Click any cell to read out everything the table hides.
II · the discovery map
The 528-cell tensor face.
Project the stack onto the three purely-mathematical axes — family, state topology, information topology — and you get a 528-cell coordinate space (33 × 4 × 4). Only about a quarter of the cells are occupied. The empty cells with occupied neighbors are predictions: positions where the structure of the stack says an operation should exist, the way Mendeleev's empty cells predicted gallium and germanium. This is the highest-leverage face of the instrument — every empty neighbor is a research target.
scripts/ef_overrides.py. Empty cells with occupied neighbors are predictions — Mendeleev gaps where the structure says an operation should exist but none has been named.
III · the rotating landscape
The thermodynamic surface.
Rotate this. Two horizontal axes: family (33) and thermodynamic class (L₀ … L₂max). The vertical axis is the count of primitives at that coordinate. Tall amber peaks are the workhorse families that have absorbed most of the stack — TR, FF, OPT, CALC. The green peaks are the L₀ free operations; the orange ones are the maximally-reductive Landauer hot zones. The flat plain is where the next generation of silicon will be built.
IV · contract any axis
Project the tensor.
Pick which axes to keep and which to integrate out. Every contraction reveals different structure. "Family × thermo cost" tells you which families have the most free ops. "Family × hardware status" tells you which families the silicon industry has ignored. "Concurrency × thermo cost" tells you the systolic vs sequential trade-off. Pick a projection, see live counts.
V · where to build first
The leverage leaderboard.
Not all 229 hardware gaps are equal. Some sub-operations sit at the base of the dependency tree — build them and you unlock many downstream operations at once. Others concentrate the most algorithmic work into a single datapath. The leaderboard below ranks both views and highlights the L₀ free ops with the highest energy-savings multiplier.
The three most depended-on operations (#18 matmul, #21 reduction, #4 FMA) already have shipping silicon. That's why the entire industry converges on them. But the next four — #76 matrix decomposition (11 downstream, GAP), #94 differentiation (11 downstream, GAP), #59 symbolic rewriting (10 downstream, SW only), and #95 integration (9 downstream, GAP) — have no dedicated hardware anywhere on Earth. These are the highest-leverage silicon targets in the stack. Build them and the entire upper stack gets faster.