Finite-Resource Estimates of Riemann Zeros: Laboratory Diagnostics and a Conditional Cosmic-Time Hypothesis

Physical systems can encode functions whose zeros correspond to Riemann-zero ordinates, but estimation precision depends on encoding, calibration, noise and resources. We reassess whether experiments support a universal observable-height ceiling or its increase with cosmic age. Reanalysis of 269 published trapped-ion estimates finds setting-dependent uncertainties without a common endpoint breakdown. A July 2026 nuclear-spin experiment supplies processed data near the first five zeros; its higher-index demonstrations are simulations. Motivated by a published numerical correspondence involving a non-autonomous quadratic map, we formulate an inverse-log-squared dependence for an additional uncertainty scale. At an illustrative Planck-time reference scale, its present fractional drift is approximately $-1.03\times10^{-12}\,\mathrm{yr}^{-1}$. We extend an initial spectroscopic pilot with joint ESPRESSO Fe II fits, native-pixel diagnostics of 17 exposures, and screening of 36 catalogued absorbers in 32 UVES spectra. Relative-shift preferences depend on covariance, strong-core masks and gas structure. Same-transition differences between adjacent ESPRESSO orders motivate calibration, extraction and profile-model checks at tens of metres per second. Conventional gas models adequately describe two additional absorber pilots under the tested noise assumptions. These limitations inform a staged spectroscopy program. An independently specified physical response remains necessary to connect line shifts or shape changes to the proposed uncertainty component; no universal cutoff or preferred aging exponent is established.