Gaussian Seams for Risk-Neutral Compression

This companion note verifies the Gaussian-Volterra source-family assumptions used by the main risk-neutral compression paper. It starts from primitive Volterra kernel conditions under the pricing measure, isolates leading singular-value profiles, repairs the scalar one-mode reduction through an anchored quadratic lift, and proves that the resulting centered quadratic loading generates the scalar seam required by the main compression theorem. The note then connects this seam to the Gaussian/Bachelier option-transfer formula through an explicit second-chaos projection argument, showing when the public option coefficient inherits the same Perron-aligned common channel as the imported latent market-stress state. Several temporal, visible-origin, lower-cell, and local-flatness routes are retained as an auditable source-family ledger, but their role is technical: they provide alternative sufficient conditions for the same Gaussian seam rather than separate economic claims. The result is a ledger-preserving technical companion that supplies the Volterra verification layer behind the main paper’s option-surface branch.