  Three Fermion sumrules for interacting systems are derived at T=0, involving
the number expectation $\bar{N}(\mu)$, canonical chemical potentials $\mu(m)$,
a logarithmic time derivative of the Greens function $\gamma_{\vec{k} \sigma}$
and the static Greens function. In essence we establish at zero temperature the
sumrules linking: $$ \bar{N}(\mu) \leftrightarrow \sum_{m} \Theta(\mu- \mu(m))
\leftrightarrow \sum_{\vec{k},\sigma} \Theta\left(\gamma_{\vec{k}
\sigma}\right) \leftrightarrow \sum_{\vec{k},\sigma}
\Theta\left(G_\sigma(\vec{k},0)\right). $$ Connecting them across leads to the
Luttinger and Ward sumrule, originally proved perturbatively for Fermi liquids.
Our sumrules are nonperturbative in character and valid in a considerably
broader setting that additionally includes non-canonical Fermions and
Tomonaga-Luttinger models. Generalizations are given for singlet-paired
superconductors, where one of the sumrules requires a testable assumption of
particle-hole symmetry at all couplings. The sumrules are found by requiring a
continuous evolution from the Fermi gas, and by assuming a monotonic increase
of $\mu(m)$ with particle number m. At finite T a pseudo-Fermi surface,
accessible to angle resolved photoemission, is defined using the zero crossings
of the first frequency moment of a weighted spectral function.
