Global state totals

sum_state() sums every element of every declared state buffer, including scalar compartments and stages generated by chain. Aliases, parameters, synthetic operator constants, and extra keys supplied to a structured evaluator are not additional states. The result is an unweighted sum; continuous-axis quadrature remains an explicit modeling choice through the integration helpers.

Optional state representations and physical measures describe extensive counts/mass and intensive densities without changing this helper. A density's physical integral requires its declared measure; an unweighted density sum generally has a different meaning.

The helper works in expressions, aliases, transition rates, and exported reaction propensities on qualified CPU backends. Flat and structured evaluation use native array reductions, so JAX tracing and Torch parameter gradients retain the same calculation. Totals are cached within an evaluation and refreshed on the next call with its new state.

A global total across groups is a coupling dependency. The compiler rejects a factorize_axes declaration that would turn such a model into independent blocks. When the intended equations are local, write an explicitly local total, for example N[group] = sum_over(S[group,age:a] + I[group,age:a], age=a). Changing a global denominator to a local denominator changes the equations.

For a staged chain named I, declaring state: [S, R] lets the helper generate I1, I2, and so on. Declaring I as well creates an additional, separate compartment, and its value contributes to sum_state() even if its derivative is zero. The chain prefix alone is not a compartment declaration.

Reaction export preserves numerical propensity evaluation. A population-normalized rate need not have a polynomial mass-action description or a certified elasticity bound. Follow the chosen engine's metadata requirements and the documented reactants: auto restrictions independently of whether export succeeds.