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EonState asks whether a dense state-update loop can be transformed into a sparse program that advances across inactive intervals, jumps at events and returns to dense execution when events become frequent.

The central requirement is not that events are always faster. It is that both executors refine the same observable semantics and switch only at a certified quiescent boundary.

The first system targets declared kernel families such as affine recurrences, leaky integration, rate limiters, supported threshold/reset forms and selected observation structures. Unsupported effects or source shapes should be rejected rather than optimised unsafely.

That makes the compiler easier to reason about because the transformation starts from a known semantic envelope instead of pretending to understand arbitrary Python or arbitrary hybrid dynamics.

The compiler emits a structured representation, guard analysis and certificate material that an independent checker can inspect. Depending on the arithmetic domain, the result may be exact abstract semantics, bit-exact execution or a declared finite-precision error bound.

Those categories must remain separate. A mathematically exact formula does not automatically make a floating-point execution bit-exact.

A measured cost model is allowed to choose the dense executor when event density makes sparse execution unattractive. The system therefore treats crossover, controller overhead and fallback behaviour as things to measure, not as benefits to assume.

This keeps the project focused on a trustworthy transformation and a truthful operating envelope rather than a universal optimisation slogan.