Abstract

We formulate and prove a finite-dimensional interface package for testing proposals that identify an interior partner with an observable encoded in radiation. We first give a quantitative independent-factor AMPS benchmark, an entropy-growth bound under explicit near-pair hypotheses, and a sharp two-purifier projection inequality. We then construct one linear unitary finite model with a state-independent partner algebra, exact reference-preserving message recovery, a complete constant complement, and exact statistics for a declared pair-vacuum proxy instrument. The partner algebra is a subalgebra of the radiation algebra, not an additional commuting copy. A quantitative commutator obstruction proves why two commuting representations cannot both intertwine the same noncommutative logical algebra. An explicit purifier-distillation intervention changes the original pair test, while preserving the message channel.

All model-specific mathematical statements are proved locally. Standard entropy and Stinespring results are identified as external mathematical inputs. A separate stability theorem explains what additional physical bridges would turn the finite package into a certificate for named infalling measurements and recovery. No such gravitational bridge is constructed here. In particular, pair-proxy regularity is not Hadamard regularity, a message register is not a spacetime-localized infalling diary, and the construction is not a Page curve, an evaporation endpoint, or a resolution of the physical firewall problem.