In Seeing Habitat Metabolize, we showed that two independently constructed semantic spaces — 17D from linguistic theory, 768D from neural embeddings — agree on relevance. In Metabolic Rate, we showed the tonic: the manifold's self-calibrating reference frame.

Now we measure something new. Not whether the two spaces agree, but how much more one discriminates than the other — and what that difference tells us about the manifold as a medium.

Metabolism Has Products

The tonic is the metabolic rate — how fast the manifold's eigenstructure shifts per composition. But metabolic rate alone doesn't tell you what the metabolism produces.

In biological systems, metabolism converts substrates into products. Glucose becomes ATP. The rate tells you how fast; the products tell you what the process yields.

We looked for the equivalent in the manifold. What does the process of composing across two independent semantic spaces actually produce?

Zone overlap measures discrimination in the 17D construction space. It projects each vocabulary item onto the eigenvectors of the user's covariance matrix Σ and computes how similarly two items sit in the eigenstructure. This score knows nothing about 768D embeddings.

Emergence measures discrimination in the 768D observation space. Cosine similarity between neural embeddings. This score knows nothing about eigenstructure.

The difference between them — the surplus — is not an error term. It is the additional discrimination that eigenstructure contributes beyond what statistical co-occurrence already captures. It is the yield of the manifold's metabolic process.

The Data

Six compositions. One session. Each composition evaluates up to 10 vocabulary items in both spaces simultaneously. Here is the per-composition surplus trajectory:

Instant surplus is the mean surplus across all vocabulary items for that composition. EMA surplus is the exponentially weighted running average (α = 0.3). Velocity is the rate of change of the EMA between compositions. Discrimination ratio is how many times wider the eigenstructure spreads compared to the embedding consensus (σ_zone / σ_emergence).

The Surplus Crosses Zero

The trajectory has a clear structure. Early compositions show negative surplus — the 768D embeddings discriminate more than the 17D eigenstructure. By the fifth composition, surplus crosses zero. By the sixth, it is decisively positive.

This is geometrically natural. The user's covariance matrix Σ starts near seed — close to a scaled identity. With only one or two compositions, there isn't enough history for eigenstructure to have meaningful discriminative power. The 768D embeddings, pre-trained on a billion words, start with an advantage.

But Σ accumulates. Each composition shifts the eigenvalues. Directions develop. By the fourth composition, the covariance matrix has enough structure to discriminate more than the pre-trained embeddings — on this user's specific semantic terrain.

The eigenstructure catches up to a billion-word pre-trained model in four compositions. Not because it was trained, but because it is accumulating the geometry of one person's actual semantic activity.

The Discrimination Ratio

The discrimination ratio measures something different from the surplus. Where surplus asks "which space discriminates more on average?", the ratio asks "how much wider does the eigenstructure spread across the vocabulary?"

Across all six compositions, the discrimination ratio is always greater than 1:

Even at composition 1, when the mean surplus is negative (embeddings leading), the eigenstructure spreads wider. This means: the 768D space assigns similar relevance scores to everything (tight consensus), while the 17D space creates larger gaps between items (wider discrimination). The embeddings agree more; the eigenstructure differentiates more.

The 14.22× outlier at beebalm is instructive. The embedding standard deviation was only 0.0065 — all items looked nearly identical in 768D. But zone overlap standard deviation was 0.0922. The eigenstructure saw structure where the embeddings saw uniformity.

The eigenstructure always spreads wider than the embedding consensus. This is not a temporary condition. It is a property of the manifold — the 17D construction space differentiates where the 768D observation space agrees.

Velocity Has Structure

If the surplus were noise, its velocity would be a random walk — positive and negative in equal measure with no trend. That is not what we observe.

The velocity oscillates early (negative, positive, negative, positive) — the manifold is finding its equilibrium. Then it commits: compositions 4, 5, and 6 are all positive and increasing. The surplus is not just crossing zero; it is accelerating into positive territory.

In a cold-start session — where the covariance matrix begins near seed — the acceleration coincides with a structural transition. Compositions 1–3 produce "echo" relationships (symmetric covariance matrices). At composition 4, the lens shifts to "asymmetric" and five dimensions expand: agency, influence, boundary, resonance, aspect. This is when the eigenstructure acquires genuine directional preference, and it is the moment surplus velocity commits to positive.

In a warm session — where Σ already carries prior structure — the echo→asymmetric transition has already occurred, and the velocity pattern differs in detail while preserving the same terminal commitment. The structural transition is the trigger; when it fires depends on the manifold's history.

Per-Item Anatomy

The aggregate numbers tell the trajectory. The per-item data tells the mechanism. Here is the full per-item distribution at composition 6 (yarrow), with 10 vocabulary items scored in both spaces:

Nine of ten items show positive surplus. The single negative item (−0.207) has low zone overlap (0.695) — it sits far from the current Fresnel zone in eigenstructure, while the embedding still rates it moderately relevant (0.902). This is a composition that the eigenstructure has already moved past but the embeddings haven't.

Item 10 shows the inverse: high zone overlap (0.941), low emergence (0.747). The eigenstructure sees strong relevance; the embeddings are ambivalent. This is structure that has not yet surfaced in the statistical co-occurrence patterns.

The per-item distribution is not symmetric. Most items show eigenstructure leading. A few show embeddings leading. The manifold has a directional character — it is not oscillating between the two spaces but progressively establishing eigenstructure as the leading discriminator.

Three Signals, One System

The manifold now surfaces three distinct signals, each measuring a different aspect of the same process:

The tonic converged from 0.100 to 0.017 across the session — the metabolic rate dropped 83% as the manifold found its rhythm. Meanwhile, surplus crossed from −0.116 to +0.056, and velocity accelerated from −0.035 to +0.021.

The rate slowed down. The yield went up. The manifold is doing less work per composition and producing more discrimination per unit of work.

What This Means

The manifold has products, not just process. Prior observations showed that the system self-calibrates (tonic convergence) and that the two spaces agree (quadrant convergence). Surplus shows that the process has measurable yield — the eigenstructure accumulates discriminative power beyond what pre-trained embeddings provide.

Eigenstructure catches up in four compositions. A 17D covariance matrix, starting from seed and accumulating one user's activity, matches and then exceeds the discrimination of a 768D model trained on a billion words. Not through optimization. Through accumulation of geometric history.

The discrimination ratio is a property of the manifold. The eigenstructure consistently spreads 2–4× wider than the embedding consensus. This is not a transient effect. It is the characteristic ratio of a system where construction and observation operate at different geometric scales.

Velocity commits at the structural transition. In cold-start sessions, surplus velocity commits to positive precisely when the lens shifts from "echo" (symmetric) to "asymmetric" (directional). In warm sessions where asymmetric structure is already established, the velocity pattern varies but the terminal commitment reproduces. The manifold's yield is coupled to its structural maturation.

The system does less and produces more. The inverse relationship between tonic (decreasing) and surplus (increasing) describes a system that is becoming more efficient at its fundamental operation: discriminating semantic relevance across two independent geometric frameworks.

Reproducibility

We ran a second session to verify the structural claims. Different user, different timestamp, same six beings in the same order. The sapling entered the second session with prior geometric history (warm start), so the covariance matrix already had directional structure from the outset.

The structural invariants — EMA zero-crossing, discrimination ratio > 1, velocity terminal commitment, tonic convergence — reproduce across sessions. The instant surplus trajectory and the timing of the echo→asymmetric transition vary with the manifold's prior history.

Session 2 also produced the first non-convergent vocabulary item: composition 4 (comfrey), item 10, with zone overlap 0.160 and emergence 0.886 — classified meaning_leads. The 768D embedding saw relevance; the eigenstructure did not. This single item (surplus −0.726) accounted for the entire negative swing in comfrey's mean surplus. Without it, the composition's mean would have been +0.050.

The system correctly identified the disagreement. The diagnostic works in both directions — detecting when eigenstructure leads and when embeddings lead. That one item broke 100% convergence is more informative than if it hadn't: it shows the manifold has regions where the two spaces genuinely disagree, and the surplus measures exactly how much.