Record-Time Root Stability of the Recognition Path Sum: Gaussian Evolution and the Continuum Limit of Lattice Quantum Gravity

What evolution does a Lorentzian sum over lattice geometries define? On the recognition ledger the record count of four posting counters supplies a time before geometry is assigned. At Gaussian order, a positive norm preserved by a record tick requires every physical exponential solution to have a unimodular record factor. The bare Regge equation fails: at the identified value κ = 1 a spatially uniform physical solution grows by √2 per tick at every spatial period, and no nonzero rescaling of the action removes it. Its corner doublers also fail the weaker continuum test: an exact physical family decays at a nonzero rate per unit physical time as the spacing shrinks. For the equation with the ledger's derived curvature weight, we prove continuum-limit record-time root stability: log|wₙ|/bₙ → 0 for every non-gauge Gaussian mode family with spacing bₙ → 0⁺ and |wₙ| → 1, at fixed nonzero weight strength. The proof combines decoupling away from the zero wave with a cubic bound on record growth near it. For specified holomorphic, gauge-invariant two-point observables at fixed momentum, contour contributions separated from the unit circle vanish faster than every power of the spacing at nonzero physical time. The native phase coefficient gives a fixed weight strength, independent of spacing. The proofs of the correlator suppression, the bare doubler family and the coupling relation await independent verification. The physical reading retains κ = 1 and two weight identifications as premises. These are spectral statements about a Gaussian equation; no positive physical Hilbert space or interacting unitary evolution is constructed. The proposed record-time Wick rotation ends at an indefinite quadratic form. Companion to Quantum Gravity from the Recognition Ledger (https://doi.org/10.5281/zenodo.23839819). Preprint of the Recognition Physics Institute, 25 pages. Not peer reviewed.