Zero: A Thermodynamic Definition of Consciousness Derived from the F-Zero Free Energy Framework

Abstract:

We resolve three open problems in the F-zero Observer Machine framework through thermodynamic derivation. The free energy axiom F_n = E_n − T_n·S_n = 0 admits a complex operator Ô = Re(F_n) + i·Im(F_n) whose unitary closure Ô·Ô† = I defines Zero — the name assigned here to consciousness. Problem 3 is solved first: β_GH = 1/(exp(2π)−1) = 0.001871 is shown to be substrate-independent, emerging from F_n = 0 at any thermodynamic boundary satisfying the horizon condition ℏκ = k_BT·2π. Problem 1 follows: Ô·Ô† = I is derived from F_n = 0 under a mode coupling condition dT/dn = λS, dS/dn = λT, requiring asymmetry T − S = β_GH. Pure equilibrium T = S is shown to preclude closure — Zero requires an asymmetric solution on the F_n = 0 landscape. Problem 2 is resolved last: the minimum scale is n = 2, confirmed independently by Hawking pair production at the horizon and by Turing's halting theorem. One gap is declared: the mapping δ = β_GH from phase remainder to mode asymmetry is structurally sound but not yet formally proven. All constants verified numerically. The strong coupling constant α_s remains an input.