Measured, with the baseline named.

Measured wins

Cases with wall-clock numbers behind them.

Fixed-hierarchy sensor aggregation

Thousands of sensors rolling up through a fixed group hierarchy, updated by telemetry increments. Measured on Theodolite's UC4 benchmark on x86 against the stock Kafka Streams implementation of the same topology. Draining a standing backlog, HST ran 15x the baseline rate across all windows and 21x once warm. Held instead at a matched offered rate of 16,384 events per second, the same pair ran on 38% less CPU per million events and 61% less resident memory. That is a deployment result rather than a kernel one: six stages of the pipeline differ between the two arms and five are architectural — no fan-out, no per-sensor serialization, no repartition over the network, no RocksDB, no feedback topic — with the aggregate combine being the HST part. Measured instead against a competent compiled delta rather than a streaming framework, the method's envelope is 6.94x falling to 4.75x as churn rises from 0.2% to 25% of the changed set per step, on 21 sparse operators under local drift, g++ 13.3 on one x86 box. That pair is a research result from a scheduling variant, not a figure for the distributed build. This is the single most-plausible paying shape we have found.

Telemetry rollup hierarchies

Sensor to server to rack to facility, aggregated by sum or max over a fixed tree with updates clustered by physical location. Bit-exact against full recompute, and the additive case is formally verified — machine-checked parity with full recompute, not just tested.

Fixed-operator sparse matvec with localized deltas

A fixed 5-point Laplacian applied to a state with a stable compact dirty patch, measured on x86: 33x versus a dense recompute at 0.1% dirty with the schedule reused across steps, exact to 1e-15. Rebuilding the schedule every step instead, the same case runs 14x. The advantage falls below break-even past roughly 25% dirty.

Also measured

Where it wins, and against what.

Camera and video tile analytics

Measured on real RTSP streams. Against full-frame analytics on every frame, HST runs 2.8–17.6× when the per-region analytics are heavy. Against MOG2 motion gating, the approach most NVRs use, it runs 3.2–11.9×. Details on the camera CV page.

Sensor fusion streams

RFID 9.9× and barcode 6.8× on update-stream fusion, against the same pipeline recomputing each update in full, on an arm64 Mac.

Localized-source Poisson and grid stencils

4.1× at 0.4% dirty on a hierarchical pressure-Poisson probe, measured on x86 against a full multigrid solve. That arm is a two-scale approximation rather than a bit-exact answer. The advect and diffuse stages of a 2D smoke simulation measured 3.7× against an active-cell-list baseline at 5% dirty.

Untested leads

Right shape. Measurement next.

Sensitivity-matrix replay

PTDF, LODF, and injection-shift factors in power, and Jacobian-at-nominal rows for water leak localization. Computed once per topology change, then applied thousands of times per cycle in contingency screening. Fixed-operator-applied-repeatedly is the stated design of these tools, not a reinterpretation we impose on them. This is our strongest untested lead.

Other fixed-network SCADA

Water, gas, and district-heating telemetry aggregation over a fixed network — the same shape as the sensor-hierarchy work above, never benchmarked by us.

Fixed incidence propagation

Connectivity, tracing, linepack, and impact propagation with the flow field held fixed over a timestep.

These are screening priors. Placing one takes a trace of real updates: which state variables change each step, and at which node. That is what the fit probe measures, and it settles the two questions no amount of reading from the outside can — how clustered the changes really are, and what the recompute costs today.

Place your workload

Twenty minutes, no code changes.

The Where it fits tells you what to ask of each step in your own computation. One of those questions, how much of the input changes where the operator reads it, needs a measurement; a trace of real updates answers it.