The Gaian Mutualism Selection Theorem: Partner Fidelity as the Continuum Between Darwinian and Survivorship Selection for Planetary Self-Regulation

Paper supported by machine-verified Lean 4. The Gaia hypothesis has long been challenged by a levels-of-selection objection: natural selection acts on reproducing individuals, not on planets, so environment-regulating biospheres seem to demand an implausible planetary-level selection. The modern reply invokes non-Darwinian mechanisms—selection by survival and sequential selection—in which destabilising configurations are simply short-lived. We show that this systemic, survivorship mechanism and the individual-level partner-fidelity feedback (PFF) of mutualism theory are not rivals but the two limits of a single control parameter: the fidelity coefficient rho_fin[0,1], the fraction of the environmental benefit a lineage generates that returns privately to that same lineage. We prove a transcritical Fidelity–Survival Bifurcation at rho_f^ast=c/b separating a fast, deterministic Darwinian Gaia (rho_f>rho_f^ast) from a slow, stochastic dice-playing Gaia (rho_f). We derive a Landauer Fidelity Ceiling rho_fle 1-e^-I_mathrmsus, set by the thermodynamic cost of the environmental memory that carries fidelity against a mixing rate kappa_mathrmmix, which forbids Darwinian Gaia in fast-mixing reservoirs while permitting it on slow, structured substrates. A Gaian externality Delta_G=r_mathrmsoc-r_mathrmpriv>0 quantifies the regulation individual selection under-provides. A reciprocity reading of the Watson–Lovelock Daisyworld, driven by individual selection alone, reproduces temperature regulation iff fidelity is positive, with regulation bandwidth monotone in fidelity. All results are numerically verified (35/35) and cast as an Intelligence-Bound self-application, the Symbiont. The framework partitions Earth's regulatory feedbacks by mechanism and grounds conservation-finance instruments in the physics of what a biosphere cannot regulate on its own.