ELYSIA: Proving What a Spiking Network Computed — A GPU-native architecture for compound SNN computation

We present **ELYSIA** (**E**xplicit**ly** Parallel **S**cheduling for **I**nference **A**rchitectures), a GPU-native architecture for compound spiking computation, and its prototype **ELYSIA-P**. An optional certified backend publishes a class only once it has proved that class equals the full computation's, and abstains otherwise. That proof covers the whole temporal computation. It is the only method we tested that releases classes early while returning the full trace's answer exactly: it releases 83.75–86.31% of test classes with no class changed, and no baseline reaches it. It costs 6–15% inside the exact-dyadic conditions and 2.23× per request; outside them an interval enclosure carries the same guarantee. Against our re-implementation of the strongest published early-exit method it costs 10.5–15× more per request and 173–226× batched; that method never exits at this accuracy. A truncated trace changes 150 classes; our calibrated control releases 1.46% early. On a 512-neuron model the enclosure releases all 2,264 classes at median round 11 of 100, none wrong; an exact-hull rule releases all 2,264 at round 12, with the same zero wrong releases, and improves coverage across four models, three passing the fp64 check. A fused LIF kernel runs a whole window in one dispatch, beating `snnTorch` and SpikingJelly by 1.14–1.82× at matched accuracy and 1.201× on the whole compound task. Numerical meaning survives suspension and revision. Over 18 independent streams it retains a median 0.479 [0.432,0.535] of ELYSIA-P's throughput; no dependent stream can use it.