Maximal specieslike clusters with a fixed real founding window

Yes. Every organism belongs to an inclusion-maximal member of the fixed-window class. The proof constructs an actual seed, proves reflection under appropriate intersections, proves IAP and the real window survive the required directed unions, and applies constrained maximal extension. Relabelling preserves original real birthdates, including ties, and the duration shared by every candidate and competitor. No finite-root premise is needed. This supplies a checked replacement-constraint theorem responding to the source direction, not merely a conditional result assuming the needed seed. The eight-module proof chain has 50 selected endpoints. It does not yield uniqueness, a partition, an effective classifier or empirical species validation. Maximality keeps connectivity, convexity, IAP, reflection and the same founding window. Biological plausibility, priority and whether the constraint matches the author's intended qualitative distinction remain for review.

Yes. Every organism belongs to an inclusion-maximal member of the fixed-window class. The proof constructs an actual seed, proves reflection under appropriate intersections, proves IAP and the real window survive the required directed unions, and applies constrained maximal extension. Relabelling preserves original real birthdates, including ties, and the duration shared by every candidate and competitor. No finite-root premise is needed. This supplies a checked replacement-constraint theorem responding to the source direction, not merely a conditional result assuming the needed seed. The eight-module proof chain has 50 selected endpoints. It does not yield uniqueness, a partition, an effective classifier or empirical species validation. Maximality keeps connectivity, convexity, IAP, reflection and the same founding window. Biological plausibility, priority and whether the constraint matches the author's intended qualitative distinction remain for review.