Bootstrapping 2d ϕ4 theory with Hamiltonian truncation data

We combine the methods of Hamiltonian Truncation and recently proposed generalisation S-matrix bootstrap that includes local operators to determine two-particle scattering amplitude form factor stress tensor at $s>0$ in 2d $\phi^4$ theory. use $s\le 0$ its spectral density computed using Lightcone Conformal (LCT), inject them into generalized set-up. The obtained results for are fully reliable only elastic regime. independently construct "pure" bounds (bootstrap without including matrix elements operators), find sinh-Gordon model analytic continuation "staircase model" saturate these bounds. Surprisingly, also very nearly saturates bounds, moreover is extremely close sinh-Gordon/staircase model.