Observation Without Optimization: Dual-Space Surplus and Self-Reading Convergence in Compositional Semantics

We present Habitat, a semantic infrastructure that observes intelligence in the divergence between compositional structure and semantic meaning — without optimization, training, or loss functions. Natural language is decomposed into a 17-dimensional compositional vector space derived from linguistic theory (Bach/Vendler eventuality classification, Levin verb classification, proto-role analysis) and simultaneously embedded in a 768-dimensional semantic space via SentenceTransformer. These two independently computed representations enter a session manifold whose covariance structure evolves through append-only composition. The gap between structural proximity (Mahalanobis distance through the session covariance) and semantic similarity (cosine in embedding space) constitutes what we term *surplus* — an observable gradient that is neither an error to minimize nor a loss to optimize.

We extend the surplus concept from session-level observation to per-phrase semantic centrality across multiple sessions. When multiple document collections (sessions) are coupled through their covariance matrices via a diagonal lens (L = Σ_A · Σ_B⁻¹), the eigenvalue spectrum reveals where sessions agree (resonance), where one foregrounds what the other backgrounds (expansion/compression), and where meaning is actively forming (the Bayberry zone). Cross-session phrases are classified as convergent (both spaces agree, meaning crystallized), peripheral (eigenstructure leads, meaning forming), or fuzzy (spaces diverge) — a constitutional classification derived from surplus magnitude, cross-session recognition, and the relation between the two spaces. Session abstracts report convergences, divergences, and bridges in the corpus's own vocabulary. The observation can be parameterized by any session's covariance, producing different stories from the same data depending on which geometric perspective frames the inquiry.

We demonstrate these properties on a litmus corpus (5 domain-specific texts, 128 compositions) and a four-session climate adaptation corpus (~30 documents, ~170 compositions), showing that the system produces interpretable cross-dimensional structure — including two emergent modes of predication recovered via SVD of the assertion cross-block — meaningful semantic centrality classifications, cross-session tensions with real discriminative power, and session abstracts grounded in the corpus's own vocabulary. We further demonstrate a self-reading capability: when the system's coupling articulation is re-ingested as a composition, the covariance differential reveals that the articulation stabilizes described dimensions while cross-influence channels propagate structural consequences into undescribed dimensions. A second self-reading pass converges (Δ²Σ/ΔΣ = 0.638), confirming that the gap between self-description and geometry closes under iteration. All without training, optimization, or generation.

Habitat represents a departure from optimization-based intelligence: the geometry is not learned, it is composed; the field is not trained, it is observed; and the structured gap between composition and meaning is not a loss — it is the primary signal.