Holographic Vacuum Elasticity and the Pb-Pb Chronometer: Metric Stratigraphy as a Paleo-GPS for the Early Solar System

We apply the Holographic Vacuum Elasticity (HVE) framework and its governing Vacuum Suppression Law (VSL), Oobs = Oideal · exp(−χ · σ0G · W(x) · Ωn · fG), to the problem of gravitational modulation of alpha-decay constants in the early Solar System. Within the QED sector (G = U(1)EM, fG = 1, σ0G = α/2), the vacuum coupling coefficient is derived from first principles via the Atiyah–Singer index theorem applied to the Dirac functional determinant, yielding σv = α/2 ≈ 3.647 × 10−3 without free parameters. The field weight W(x) encodes the local gravitational potential difference ΔΦ/c2 between the crystallisation site of Calcium-Aluminium-rich Inclusions (CAIs) in the early solar accretion disk and the terrestrial calibration frame; for the inner disk (Rform ≈ 0.3 AU), |W| ≈ 2.3 × 10−8. The VSL predicts a fractional modulation of the alpha-decay tunnelling probability of order σv · |W| · Ω2 · fG ≈ 10−9, which with the topological amplification inherent in the Gamow barrier integral (GGamow ≈ 40–50 for 235,238U) scales to ∼ 10−7 — a structural prediction that is currently below the sensitivity of thermal ionisation mass spectrometry (TIMS) at the parts-per-million level. We introduce the concept of Metric Stratigraphy: the prediction that, under HVE, the apparent isotopic discordance of a primitive solar system solid encodes its heliocentric formation distance, providing a gravitational “paleo-GPS” for the protoplanetary disk. The framework is consistent with existing geochemical data, makes three specific falsifiable predictions independent of the nucleosynthetic-heterogeneity hypothesis, and identifies the minimum instrumental precision required for experimental discrimination.