Gaussian Seams for Risk-Neutral Compression

This companion note verifies the Gaussian-Volterra source-family assumptions used by the option-surface branch of Risk-Neutral Compression and the Geometry of Latent Market Stress. The technical problem is to connect primitive Volterra kernels to the scalar seam through which a priced Perron loading appears in a local Gaussian/Bachelier option coefficient. The note derives the leading singular-value estimates, identifies the centered quadratic loading, repairs the scalar one-mode reduction through an anchored quadratic lift, and proves the resulting common-channel option-factor consequence. It also records temporal, visible-origin, lower-cell, and local-flatness routes as alternative sufficient conditions for the same seam. The ledger is technical by design: these routes are checks on one Gaussian reduction, not separate economic claims.