A Clock Held Up by Its Own Error Bars: The Oldest Stars Against the Age of the Universe

The oldest stars set a floor under the age of the Universe: nothing can be older than the time since it began, plus nothing — a star's age plus the delay before the first stars could form cannot exceed the expansion age. This paper defines the defect statistic D = (t_star + Δ_form − t_U)/√(σ_star² + σ_U²) and evaluates it for the stellar clocks listed in §2 against the Planck expansion age t_U = 13.787 ± 0.020 Gyr, at three formation delays (0.2, 0.5, 0.9 Gyr, spanning first-star formation redshifts z ≈ 20 down to z ≈ 6). No clock breaches at the 2σ standard at Δ = 0.2 Gyr (the first-stars floor of the bracket, below the ≈ 0.5 Gyr globular-cluster formation scale stated in §2), on full published errors; at Δ = 0.5 Gyr the HD 140283 2025 reading stands at +2.28σ. (At Δ = 0.9 Gyr that reading reaches +3.28σ, and the 2013 reading breaches on the parallax-only error discussed below.) The binding clock is the globular cluster M92 at 13.80 ± 0.75 Gyr: its defect runs D = +0.28σ (Δ = 0.2) to +1.22σ (Δ = 0.9), and the breakeven delay at central values is negative — M92's central age alone already equals the age of the Universe, so its consistency with cosmology is purchased entirely by its error bar, four-fifths of which is distance uncertainty. The one historical breach (HD 140283 at 14.46 ± 0.31 Gyr (2013)) breached only on a parallax-only error bar; at its authors' own total error (±0.8) it never breached, and Gaia-era work reads the same star at 12.0 ± 0.5 Gyr. The white-dwarf clock sits more than 3σ inside the ceiling at the smallest delay; the radioactive-decay clocks are uninformative at their large errors (defects −0.36σ to +0.10σ). The verdict is printed at the size it earns: The clock holds, on credit. The credit has a stated price: if M92's error shrinks to ≲ 0.46 Gyr with its central value unmoved — a factor of 1.6, inside the reach of the distance improvements already in progress — the conservative-delay reading of the same clock breaches at 2σ, and the oldest-star problem returns as a measurement, not a memory.