Nonminimally coupled exponential quintessence without the CMB: identifiability, Newton-constant normalisation and local-gravity consistency with DESI DR2 and Pantheon+

The study presents a background-level confrontation of the Jordan-frame scalar-tensor action $F(\\phi) = M_*^2 + \\xi\\phi^2$ with an exponential potential $V(\\phi) = V_0 e^{-\\lambda\\phi/M_*}$ against the DESI DR2 baryon acoustic oscillation (BAO) measurements and the Pantheon+ Type Ia supernova compilation (with validation on DES-SN5YR Dovekie), without incorporating cosmic microwave background (CMB) data. Key Features and Findings Cavendish Normalisation: Demonstrates that the bare scale $M_*$ cannot be identified with the measured Planck mass; sampling the Cavendish-normalised matter fraction $\\Omega_m^{(N)} = \\Gamma_0 \\Omega_m^*$ eliminates the sampler pathology and shows that the high-$\\Omega_m$ ridge found in bare parameterisations is a normalisation artefact. Shooting & Prior Attribution: Solves the $V_0$ shooting problem across eight decades using a multi-root scan. It classifies the uniform prior volume into histories without a self-consistent Hubble rate (36.7%), data exclusions (63.2%), and allowed histories (0.1%), with ghost and real-expansion walls never binding. Parameter Identifiability: Background distances constrain essentially a single combination of $(\\xi, \\lambda, x_{\\mathrm{ini}})$. The profile likelihood in $\\lambda$ is flat down to $\\lambda = 0$, and the full fit improvement over $\\Lambda\\mathrm{CDM}$ ($\\Delta\\chi^2_{\\mathrm{min}} = -5.18$, mock-calibrated $p = 0.013$ / $2.2\\sigma$, Bayes factor $\\ln B = +0.12 \\pm 0.22$) is already accessible at $\\xi = 0$. Local-Gravity Consistency: Tracks the light-scalar Brans–Dicke Cavendish coupling, PPN $\\gamma$, and $\\dot{G}/G$ per posterior sample. Only 1.9% of the cosmology-only posterior satisfies the Cassini bound ($\\vert{}\\gamma - 1\\vert{} < 2.3 \\times 10^{-5}$); when Cassini is enforced as a prior, the posterior collapses to minimally coupled exponential quintessence ($\\xi = 0.000 \\pm 0.002$). Included Materials Full MCMC chains (unflattened emcee ensembles and dynesty nested-sampling runs) including derived quantities ($\\Gamma_0$, PPN $\\gamma$, $\\dot{G}/G$, $G(z_i)/G_0$). Complete reproduction scripts, likelihood wrappers, and test suites for DESI DR2 BAO and Pantheon+/Dovekie. Pipeline manifests, run logs, and figure/table generation code.