We develop a spacetime-free reconstruction from a faithful state on a structured family of observable algebras. Compatible half-sided modular inclusions generate positive translations and, after finite homogeneous assembly, a pointed Lorentz cone. Each faithful standard split inclusion determines a canonical Petz--Gram transfer, and we isolate a faithful modular boundary-code condition with three clauses: compact discarded response, a uniquely dominant displacement sector, and complete-order recovery of product defects. Under this condition, overlap transport, and the assembly hypotheses, we prove strict tail contraction, completely bounded two-boundary factorization, exact coherently aligned M2 (C) embeddings, selection of three response dimensions, and complex multiplication up to the opposite algebra. Exact finite-dimensional and type-III counterexamples show that none of the three local code clauses follows from faithfulness, split or modular nuclearity, positivity, KMS symmetry, or covariance alone. A genuinely interacting spin-1 AKLT/Haldane chain realizes the logical edge algebra without microscopic qubits, with closed-form transfer bands and completely bounded encoding distortion 1+O (3^-N). Relative modular two-jets define the response fields (C, u, Q) ; their Gaussian covariance dynamics are Lie--Poisson with modular-spectrum Casimirs, and pseudodifferential commutators yield the mass-independent Q^ij deformation anchor. Spatial locality, branch smoothness, and two-derivative closure remain explicit conditional inputs.
Tom S. Weber (Mon,) studied this question.