  Recently two pairs of authors have aimed to vindicate the longstanding
conventional claim that a first-class constraint generates a gauge
transformation in typical gauge theories such as electromagnetism, Yang-Mills
and General Relativity, in response to the Lagrangian-equivalent reforming
tradition, in particular Pitts, _Annals of Physics_ 2014. Both pairs emphasize
the coherence of the extended Hamiltonian formalism against what they take to
be core ideas in Pitts 2014, but both overlook Pitts 2014's sensitivity to ways
that one might rescue the claim in question, including an additive redefinition
of the electrostatic potential. Hence the bulk of the paper is best interpreted
as arguing that the longstanding claim about separate first-class constraints
is _either false or trivial_ -- de-Ockhamization (using more when less suffices
by splitting one quantity into the sum of two) being trivial. Unfortunately
section 9 of Pitts 2014, a primarily verbal argument that plays no role in
other works, is refuted.
  Pooley and Wallace's inverse Legendre transformation to de-Ockhamized
electromagnetism with an additively redefined electrostatic potential, however,
opens the door to a precisely analogous calculation introducing a photon mass,
which shows that a _second-class primary_ constraint generates a gauge
transformation in the exactly same sense -- a reductio ad absurdum of the claim
that a first-class constraint generates a gauge transformation and a
second-class constraint does not. Gauge freedom by de-Ockhamization does not
require any constraints at all, first-class or second-class, because any
dynamical variable in any Lagrangian can be de-Ockhamized into exhibiting
trivial additive artificial gauge freedom by splitting one quantity into the
sum of two. Physically interesting gauge freedom, however, is typically
generated by a tuned sum of first-class constraints.
