F-positivity for posets with interval feet

For all-weak posets generated by a common chain and arbitrary interval feet, we give a complete criterion for fundamental positivity of the difference of their P-partition generating functions. The criterion compares the numbers of attachment intervals contained in every window. It is equivalent both to containment of fundamental supports and to support containment in the maximum-descent layer. A product of interval sums gives necessity. A self-contained integer-matrix switch construction reduces sufficiency to interval widenings and exchanges, and an explicit ordinarily labeled poset certifies positivity of every exchange in arbitrary unchanged context. Repeated intervals and feet comparable through the spine are allowed. The result resolves the window-count conjecture in its stated all-weak domain with common chain length and foot count. The principal results are provisional candidates supported by complete written proofs and exact finite diagnostics; no human mathematical examination or formal verification is recorded.