The S-Positioning Typology - Where bearers sit in the consciousness band, and why the apex is generically empty

This technical note derives a positioning law for where an individuated bearer locates within the consciousness band, working from the operational definition of identity strength S as one minus the recursion-inflated maintenance cost over the available budget. The partial derivatives set two selective economies in opposition: economizing on per-instant recursive work carries the bearer toward the upper, over-rigid edge, while economizing on standing budget carries it toward the lower, diffuse edge at the substrate-conditioned floor S_min(M). Since no term in the maintenance accounting references consciousness intensity, neither economy carries a gradient toward the band's interior maximum, which is therefore generically empty; the familiar near-S_min claim is recovered as one row of a typology indexed by which resource is scarce, not as a general law. The empty apex is conditional on a cost-only objective and so functions as a distributional prediction that departs from accounts on which consciousness is graded functional capacity, while which foot a given bearer occupies remains empirical and substrate-conditioned.