Chronos Time-First: Lean-Verified Einstein-Scalar Evolution and Local Calibration of a Geometric Change Readout

This technical report presents selected Lean-verified results from Matthew J. Hall’s Chronos Time-First mathematical reconstruction through version 410. The development constructs a short-time continuum solution of a 55-component nonlinear Fourier evolution system using Galerkin approximations. The archived proofs establish preservation of gravitational constraints, reconstruction of a Lorentzian coordinate spacetime satisfying the Einstein-scalar equations, scalar stress-energy conservation, and an independently derived geometric Bianchi identity. Genuine one-sided curvature satisfies the field equations at both endpoints of the constructed interval. The recent results introduce a geometric Change readout formed from the difference between two specified spatial expansion readouts. Its initial rate is calculated directly from the original nonlinear source. After normalization, the readout has zero initial value and unit right derivative. For every positive relative error tolerance, the proofs establish a sufficiently short initial window in which this readout approximates elapsed evolution time within that tolerance. Additional results establish scale-separated ordering, two-instant error bounds, and constraints on the separation of times producing equal readings. The report identifies the relevant formal theorem declarations, verification environment, assumptions, physical conventions, and remaining mathematical obligations. Global nonlinear continuation, unrestricted readout injectivity, invariant probe selection, and identification of the early temporal-response Gram metric with the reconstructed spacetime metric remain open. Supporting archives are provided for versions 176, 179, and 410. They contain source material, verification records, and nested development history. The verification records describe incremental checking with pinned Lean and Mathlib dependencies; the accompanying files are not a newly consolidated standalone build of the entire project.