Sharp scalar positivity in two-coupling postquantum classical gravity: de Sitter classification, FLRW stability, and a calibration-free covariance test

Abstract

A covariant postquantum classical-gravity path integral uses a two-coupling generalized DeWitt kernel to suppress departures from Einstein's equation. Retaining the cosmological term already present in the covariant action, this preprint classifies the complete Newtonian-gauge scalar metric-image sector about vacuum de Sitter. At every fixed nonzero comoving wave number, the quadratic precision is nonnegative on all smooth compact scalar metric histories if and only if beta/alpha <= 1/4. Sufficiency follows from an exact compact-boundary sum of squares; sharp necessity follows from an explicit smooth compact staircase sequence. Negativity above the boundary persists on sufficiently small accelerating FLRW deformations generated by a fixed positive-energy Einstein-scalar theory. The same frozen coupling pair yields a calibration-free finite-window covariance criterion r = 1/[18(1-3 beta/alpha)], so the de Sitter positivity condition is equivalent to 0 < r <= 2/9. The result is model-specific: it is not a universal classical-quantum no-go theorem and does not claim present detector feasibility. The record includes the manuscript and an autonomous source/reproducibility archive with 94 standard-library regression tests and a SHA-256 manifest.