  Under natural conditions (such as split property and geometric modular action
of wedge algebras) it is shown that the unitary equivalence class of the net of
local (von Neumann) algebras in the vacuum sector associated to double cones
with bases on a fixed space-like hyperplane completely determines an algebraic
QFT model. More precisely, if for two models there is unitary connecting all of
these algebras, then --- without assuming that this unitary also connects their
respective vacuum states or spacetime symmetry representations --- it follows
that the two models are equivalent. This result might be viewed as an algebraic
version of the celebrated theorem of Rudolf Haag about problems regarding the
so-called "interaction-picture" in QFT.
  Original motivation of the author for finding such an algebraic version came
from conformal chiral QFT. Both the chiral case as well as a related conjecture
about standard half-sided modular inclusions will be also discussed.
