From the Infinite Cosmological Thermal Gradient Conjecture to the Asymptotic Cosmic Thermal Decline Framework: A Critical Reformulation, Formal Mathematical Model, and Falsifiability Program

A recently circulated conceptual proposal — the Infinite Cosmological Thermal Gradient (ICTG) conjecture — suggests that an unbounded universe may possess a thermal degree of freedom that continues to decline beyond the conventional absolute-zero limit of the Kelvin scale, acting as an unrecognised cosmological cooling channel. This manuscript subjects that proposal to a first-principles audit against four established bodies of physics: (i) the thermodynamics of horizons in expanding Friedmann–Robertson–Walker (FRW) spacetimes, (ii) the statistical-mechanical literature on negative absolute temperature, (iii) the covariant holographic entropy bound, and (iv) the Nernst unattainability statement of the third law of thermodynamics. We show that the literal reading of the ICTG conjecture — a monotonic decline of a temperature-like quantity through and below T = 0 K — is not supported by, and is in tension with, this literature, because states conventionally labelled "negative temperature" in statistical mechanics are population-inverted, higher-energy, and thermodynamically hotter than any positive-temperature state, not colder. We then construct a distinct, internally consistent, falsifiable reformulation, which we term the Asymptotic Cosmic Thermal Decline (ACTD) framework: a scalar relaxation variable Θ that tracks the local Gibbons–Hawking horizon temperature of an FRW spacetime with a dynamical dark-energy equation of state in the Chevallier–Polarski–Linder (CPL) parametrisation. We prove analytically that Θ is positivity-preserving (it can approach but never cross zero), consistent with the third law, and we integrate the governing ordinary differential equation numerically for parameter ranges motivated by the DESI Data Release 2 baryon acoustic oscillation results, which report a 2.8–4.2σ preference for a dynamical dark-energy equation of state over ΛCDM. A global Sobol' sensitivity analysis (n = 10,000 base samples with bootstrap confidence intervals, implemented from first principles via Saltelli and Jansen estimators) shows the long-run behaviour of Θ is dominated jointly by the two dark-energy equation-of-state parameters, with wa the larger contributor (total-order index ST ≈ 0.61) and w0 second (ST ≈ 0.33), and with a first-order-versus-total-order gap for both parameters indicating strong interaction between them. We outline a Bayesian statistical protocol and a four-stage empirical roadmap by which the ACTD framework could, in principle, be distinguished from ΛCDM and from static-w dark energy using forthcoming survey data, and we state explicit falsification conditions. We emphasise throughout that ACTD is a speculative, exploratory theoretical construction, not an established or empirically confirmed theory, and that no simulated result in this manuscript should be interpreted as a fit to real observational data.