Uses an adaptive search over the entire closed shape interval, exact fixed-shape quadratic slices, necessary box bounds, and feasible witnesses. The refined enclosure is intersected with the original finite-budget enclosure, using at most 256 reference splits. Tolerance and split-budget defaults match the completed research implementation.
Value
An `emax_projection` list with the outer `interval`, endpoint brackets, `width_bounds`, `endpoint_gaps`, `status`, `converged`, `termination`, `witnesses`, and a diagnostic `trace`. Empty-set width is zero and interval endpoints are missing, matching the research convention. An empty set counts as noncoverage in coverage studies.
Details
Bounds hold by the exact-arithmetic argument and are evaluated in ordinary double precision with roundoff cushions. They are not formal machine certificates: `outward_rounding_certified` is always `FALSE`.
An empty model intersection has no confidence interval. A finite search without a feasible witness returns `unresolved_feasibility`, not an empty set. Inspect both `status` and `converged`, and report unresolved results.
Examples
region <- emax_region_from_summary(c(0, 0.5, 1), rep(20, 3),
c(0.2, 0.6, 0.8), pooled_variance = 1)
result <- emax_project(region)
result
#> Integrated Emax response | contrast calibration
#> Status: nonempty; termination: endpoint_tolerance
#> Outer interval: [0, 1.16684]
#> Endpoint gaps: 0.000000000, 0.000637259; converged: TRUE
#> Ordinary double precision; no directed-rounding certificate.