In Watching Habitat Load, we showed the extraction pipeline: 768D embeddings decomposed into 17D compositional vectors through Bach/Vendler aspectual classification and Dowty proto-role properties. In Metabolic Rate, we showed the tonic — a self-calibrating reference frame that tracks the manifold's own tempo.

Now we instrument both spaces simultaneously and watch what happens.

The Two Spaces

Habitat operates across two independently constructed semantic spaces.

Construction space (17D) is built from linguistic theory. Every text passes through an extraction pipeline grounded in Bach/Vendler aspectual classification (1960s–1980s) and Dowty proto-role properties (1991). Five dimensions for the actor. Twelve for the predicate. These dimensions are not learned, not optimized — they are the structure language already has.

Observation space (768D) is built from neural embeddings. SentenceTransformer encodes the same text into a dense vector trained on a billion-word corpus of internet text. Statistical co-occurrence patterns, compressed into geometry.

These two spaces were constructed from completely different theoretical foundations. One from formal linguistics. The other from distributional statistics. They share no parameters, no training signal, no optimization objective.

The question: do they agree?

What We Measured

We instrumented two scores per composition in the system's vocabulary:

Zone overlap (from 17D) — Each composition is projected onto the eigenvectors of the user's covariance matrix Σ, producing a continuous weight distribution across Fresnel zones. The dot product of two such spectral profiles measures how similarly two compositions sit in the eigenstructure. This score knows nothing about 768D.

Emergence (from 768D) — Cosine similarity between the composition's neural embedding and the current observation point. This score knows nothing about eigenvectors.

We classified each composition into one of four quadrants:

This diagnostic runs per composition, per vocabulary lookup, in real time. It is not a post-hoc analysis. It is the system observing its own fidelity.

What We Observed

Five compositions. A vocabulary growing from 3 to 12 items. Each item scored in both spaces independently.

The 17D space built from Bach/Vendler/Dowty linguistic theory and the 768D space built from neural co-occurrence statistics are observing the same semantic structure.

Nobody trained the 17D projections to match the 768D embeddings. They were constructed independently from different theoretical foundations. They agree because they are both observing something real about language.

The Tonic Converges

Alongside the fidelity diagnostic, we observed the manifold's metabolic rate — the tonic — tracking eigenvalue shift magnitudes as compositions accumulated.

The tonic dropped 77% in five compositions. The shift magnitudes across the session: 0.01229, 0.01229, 0.01228, 0.01228 — essentially identical. The manifold found a consistent metabolic rate without being told what consistency looks like.

Dissonance (distance from the running average) fell from 0.833 to 0.456. Stability reached 0.9997. The manifold is in rhythm with itself.

Relationships Emerge From Geometry

The system computes a lens between each composition pair — L = Σ⁻¹target · Σsource — and classifies the relationship from its eigenvalue spectrum.

The first three compositions produced "echo" — the covariance matrices saw each other symmetrically. At the fourth composition, the relationship shifted to "asymmetric" and five dimensions expanded. Comfrey's compositional signature stretched the eigenstructure in a direction the prior compositions hadn't explored.

No classification model detected this. No labeled data defined what "asymmetric" means. The eigenvalue spectrum of the lens matrix revealed it from the geometry alone.

The Space Doesn't Collapse

Many systems under accumulation collapse into low-rank approximations — eigenvalues concentrate, most dimensions become noise, the space effectively shrinks. We tracked the effective rank of Σ:

The covariance matrix uses nearly all 17 dimensions. The space develops directional preferences (eigenvalues differ) while retaining full geometric capacity. It does not degenerate.

What This Means

Linguistic theory tracks neural statistics. The 17D compositional space (Bach, Vendler, Dowty — 1960s–1990s) and the 768D embedding space (2019 transformer architecture) agree on what is semantically relevant. Not because one was trained to match the other. Because both are measuring structure that exists in language.

Self-calibration without optimization. The tonic converges, stability reaches near-unity, dissonance drops — all without a loss function, convergence target, or gradient descent. The manifold's reference frame adapts to its own observed behavior.

Relationships from eigenstructure. The transition from "echo" to "asymmetric" at the fourth composition emerged from the eigenvalue spectrum of the lens matrix. The geometry detected when a new composition introduced genuinely novel directional information. No one told it what to look for.

Vocabulary from observation. The vocabulary pool grew from 3 to 12 compositions during the session. Some entries are recursed — the system's own articulations re-entered the vocabulary as new compositions, positioned by the field's own eigenstructure. The vocabulary evolves from its observations, not from an external corpus.

Full dimensionality preserved. Effective rank stays near 17. The space maintains its full geometric capacity under accumulation. It specializes without collapsing.