N-2 binds to the active-site metal cluster in the nitrogenase MoFe protein, the FeMo-cofactor ([7Fe-9S-Mo-homocitrate-X]; FeMo-co) only after the MoFe protein has accumulated three or four electrons/protons (E-3 or E-4 states), with the E-4 state being optimally activated. Here we study the FeMo-co Fe-57 atoms of E-4 trapped with the alpha-70(Val-Ile) MoFe protein variant through use of advanced ENDOR methods: 'random-hop' Davies pulsed 35 GHz ENDOR; difference triple resonance; the recently developed Pulse-Endor-SaTuration and REcovery (PESTRE) protocol for determining hyperfine-coupling signs; and Raw-DATA (RD)-PESTRE, a PESTRE variant that gives a continuous sign readout over a selected radiofrequency range. These methods have allowed experimental determination of the signed isotropic Fe-57 hyperfine couplings for five of the seven iron sites of the reductively activated E-4 FeMo-co, and given the magnitude of the coupling for a sixth. When supplemented by the use of sum-rules developed to describe electron-spin coupling in FeS proteins, these Fe-57 measurements yield both the magnitude and signs of the isotropic couplings for the complete set of seven Fe sites of FeMo-co in E-4. In light of the previous findings that FeMo-co of E-4 binds two hydrides in the form of (Fe-(mu-H-)-Fe) fragments, and that molybdenum has not become reduced, an 'electron inventory' analysis assigns the formal redox level of FeMo-co metal ions in E-4 to that of the resting state (M-N), with the four accumulated electrons residing on the two Fe-bound hydrides. Comparisons with earlier Fe-57 ENDOR studies and electron inventory analyses of the bio-organometallic intermediate formed during the reduction of alkynes and the CO-inhibited forms of nitrogenase (hi-CO and lo-CO) inspire the conjecture that throughout the eight-electron reduction of N-2 plus 2H(+) to two NH3 plus H-2, the inorganic core of FeMo-co cycles through only a single redox couple connecting two formal redox levels: those associated with the resting state, M-N, and with the one-electron reduced state, M-R. We further note that this conjecture might apply to other complex FeS enzymes.