Forecasting Event Propagation in Environmental Governance: What a Fitted Excitation Kernel Estimates

The event layer developed earlier in this series produces a stream of timed, typed, source-assessed reports across the parties of an interdependent field. Such a stream invites a familiar statistical treatment, since point processes in which past events raise the intensity of future ones are well understood and their multivariate form supplies exactly a matrix of cross-excitations among sources. This paper takes up that treatment and argues that its most natural interpretation is wrong in a way that matters. The method is analytical, with one verified simulation. The paper's central claim is that an excitation kernel fitted to a governance event stream is not an estimate of the field's physical coupling structure. An observed excitation from party $i$ to party $j$ is generated by a chain of four things: a coupling that obtains, a threshold at which the second party's instruments register a consequence, a carriage arrangement that delivered the first party's report, and the second party's own emission decision. Two of the four are institutional settings, and both are revisable, so a fitted kernel measures the composition and cannot be decomposed into its factors without information the stream does not contain. The consequence is a division of uses. The fit is invalid for structural inference, so a coupling may not be asserted from an excitation, nor denied from its absence; and it is valid and useful for operational purposes, since what an arrangement needs in order to route reports, allocate attention, and anticipate load is precisely the reporting-conditional propagation the fit does estimate. The paper develops three further results. The branching ratio of the stream is a relational quantity computable from the stream alone and is a candidate network-level indicator of the kind the criticality paper of this series calls for, with the caveat that it measures the reporting cascade and not the physical one. As that ratio rises, the share of activity attributable to the stream's own history rises with it, so what a forecast is forecasting changes, and near unity the forecast concerns the arrangement more than the field. And valid estimation presupposes that thresholds and carriage were stable over the fitting window or that their changes are retrievable, which makes the versioned registers required elsewhere in this series a precondition of the method and not an administrative convenience. The paper surveys the point-process, seismological, network-cascade and infrastructure-modelling literatures, states what each owns, and identifies the residue.