Deterministic Inference Engine with Pre-Applied Structural Tension for Normative Corpora

This working paper presents an inference architecture for normative and legal corpora that does not use neural embeddings, transformer models, attention mechanisms, or any component of the GPT family. The system does not predict the next token from co-occurrence statistics. It solves a different problem entirely: given a structured normative corpus, compute the exact semantic position of a query by solving a linear system Ax = b. The mathematical foundation — Cauchy (1815), Toeplitz (1911), Levinson–Durbin (1947), Kailath (1979) — is over 200 years old The dominant paradigm in computational semantics descends from the distributional hypothesis (Harris, 1954): meaning is approximated by co-occurrence statistics. This line — Shannon → Rumelhart → Bengio → Vaswani → GPT — rests on a statistical foundation roughly 70 years old. The present work takes a different mathematical fork: meaning is determined by position in a directed normative graph, and inference reduces to solving a well-posed linear system. The architecture extends the dual-layer SPO model presented in: Chudinov, Y. (2026). Dual-Layer SPO Architecture for Embedding-Based Index Ranking. DOI: 10. 5281/zenodo. 19261510 Contributions Pre-applied tension principle. All probabilistic complexity is absorbed at index construction time — not at query time. The key analogy is pre-stressed concrete: structural constraints (SPO links, tier weights, coupling rules) are calibrated in advance, so a query hits an already tensioned structure. Closed World Assumption as axiom. The vocabulary of any normative domain is finite at time X. Unknown input triggers deterministic structural refusal, not hallucination. Derivational matrix in log-space. Morphological derivation is multiplicative (root × affix) ; the logarithmic transformation B = log (D) makes derivational distances additive, enabling direct linear solution. VAR (p) on root space → Yule-Walker → Ax = b. The autoregressive model on domain roots yields multivariate Yule-Walker equations — a block-Toeplitz linear system solvable in O (p²n²) via block Levinson–Durbin. No gradient descent. No iterative optimization. Structural refusal via rank deficit. When the constraint matrix A loses rank, the system refuses formally — a designed, explainable failure mode rooted in linear algebra. Ontological loop decomposition. The divergence between human and machine interpretation is modeled explicitly as a distortion vector zdistortion, tied to rank pressure in the constraint system. Tension tensor as corpus maturity indicator. The departure from block-Toeplitz stationarity (ΔΓ) measures corpus maturity — large values signal early-phase corpora, convergence toward zero signals structural completeness. Index-Q: 8 → 5 signal compression. The 8-role ontological model is compressed to a 5-signal query profile for the linear solver, reducing block matrix dimensionality. Endogeneity as configuration. Mutual dependence of roots is not a statistical complication but a designed property — the normative structure itself. Causation direction is an input (from the SPO graph), not an inference. ARIMA drift governor. Vocabulary evolution in normative domains follows temporal autocorrelation with seasonal components. ARIMA monitors collective spectral drift post-admission as a control layer. Paradigm: different mathematical lineage. The distributional path (Harris → GPT) asks "predict the next token. " The Cauchy path asks "compute the exact semantic position. " Two hundred years of theorem vs. seventy years of unproved hypothesis. Relationship to Prior Work The base navigation system (DOI: 10. 5281/zenodo. 18944351) achieves 99. 95% accuracy on 246 specification queries using 14 pre-compiled indices and deterministic chain resolution. The dual-layer SPO architecture (DOI: 10. 5281/zenodo. 19261510) extends it with embedding-based ranking. The present work replaces the embedding layer with a fully deterministic linear-algebraic engine — the system no longer requires any neural component for its core inference path. Access This deposit is restricted. The document is available for review upon request. Contact the author for access. Patent Status Patent pending. This architecture is covered by a provisional patent application filed 29 March 2026.