On the Hofer–Zehnder conjecture on ?Pd via generating functions

We use generating function techniques developed by Givental, Th\'eret and ourselves to deduce a proof in $\mathbb{C}\text{P}^d$ of the homological generalization Franks theorem due Shelukhin. This result proves particular Hofer-Zehnder conjecture non-degenerated case: every Hamiltonian diffeomorphism that has at least $d+2$ periodic points infinitely many points. Our does not appeal Floer homology or theory $J$-holomorphic curves. An appendix written Shelukhin contains new Smith-type inequality for barcodes diffeomorphisms arise from theory, which lends itself adaptation setting functions.