Quantum linearity is usually postulated rather than derived. We ask: under what microscopic conditions on a quantum-gravity regulator does linearity follow from the erasure structure of gravitational records? Two results are established. A no-go theorem shows that gravitational records and primitive erasure do not by themselves enforce linearity: a stationary nonlinear anomaly can always be constructed unless a microscopic Ward, modular, or constraint identity removes it. A conditional closure theorem then shows that, if a finite regulator satisfies five conditions---a projective record system, a uniform erasure resolvent, stationary anomaly cancellation, transport-exactness, and a bounded contracting homotopy for a two-term Koszul causal complex---the record-erased operational dynamics converges to an affine quantum channel with an explicit error bound. All five conditions are instantiated in four quantum-gravity regulators: JT gravity (via the SL (2, R) Schwarzian Ward identity on the non-identity primary sector), an AdS--Rindler entanglement wedge (via the JLMS first law), a finite-cutoff holographic operator-algebra code (via the gauge--logical dichotomy), and a spin-network corner (via Peter--Weyl averaging, subject to an explicit singlet-exclusion assumption). This is not a derivation of linearity for the real universe; it is a finite-regulator conditional theorem that reduces quantum linearity to a checkable list of microscopic identities.