11 · FA Case Study: the 2026-08-29 Snapshot

This chapter works through the first FA snapshot as a worked example of the measurement machinery — what it shows, what it does not show, and which of the paper's claims it evidences. It is FA-only by design: the live signal is not reproduced here, and no RI-related number appears. The snapshot is dated (2026-08-29 settlement).

11.1 · Snapshot and rank structure

The snapshot table is reproduced in Appendix G (Table 24): twelve Originators ordered by FA, with the two shadow units marked. The table reports the raw anchor FA; at this settlement the sustained-leadership adjustment $D$ is small and $R = 0$, so $\mathrm{FA}^{\mathrm{adj}}$ differs from $\mathrm{FA}$ only marginally and the base-pool conservation holds to within that margin. Three structural features are worth reading off the table. The leaderboard is close at the top. The top four Originators lie within a band of about eight points, and the top two within one point. The near-tie is reported transparently rather than broken by an arbitrary tiebreaker, per the paper's boundary disclosure (Section 8.9). A reader should interpret ranks inside this band as “statistically indistinguishable given the current window,” not as a decisive ordering. The range is compressed at the bottom. The bottom two Originators are the shadow units, and the shadow/included boundary is visible in the data: both shadow units are evaluated with the same parameters but do not define normalization extremes (Section 3.3), so their FA values are computed against the included set's extremes. The two component columns are the story. The capability and ecosystem composites ($\mathrm{cap}_{\mathrm{pts}}$, $\mathrm{eco}_{\mathrm{pts}}$) are deliberately shown alongside the aggregate, because the aggregate alone hides the structure that justifies the composition.

11.2 · Capability $\ne$ influence, in data

The strongest single observation in the snapshot is the inversion between capability and ecosystem stock. Two Originators illustrate it sharply. Anthropic has the highest capability composite in the set yet ranks second-lowest on ecosystem stock among the included units, and its overall FA rank (6) is far below its capability rank (1). DeepSeek, by contrast, leads the ecosystem composite while its capability composite is mid-pack, and its overall FA rank (2) is well above its capability rank. These are not measurement artifacts; they are the concrete content of the paper's premise that capability is necessary but not sufficient for influence (Section 1.2). If the system had measured only capability, it would place Anthropic first and DeepSeek ninth; the ecosystem channel — the “use $\times$ iteration” stock side — moves the ordering substantially. The inversion is also the discriminant-validity evidence of Section 4.5: the capability and ecosystem channel scores are visibly not a single latent factor (the Spearman correlation across the twelve rows is $\rho \approx 0.007$ — essentially orthogonal, far below any collinearity threshold), which is the precondition for the composition's weights to mean anything. A composition whose channels are near-collinear would be a disguised single factor; this snapshot shows they are not.

11.3 · Missing-value and coverage in practice

The snapshot exercises the missing-value taxonomy in real data. The capability coverage table (Appendix B describes the protocol; the production registry records each classification) shows that no Originator is covered by all seven capability sources; each is covered by a subset, and the composition is computed under two-level renormalization (Proposition 6.4). Three examples illustrate the taxonomy at work:

• True zero in the edge block. Several Originators have no model in the parameter bands the edge block measures; their edge-band contribution is zero and always present in the mean (Section 6.4). A missing edge band is a fact about participation — the unit does not field small models — and it is counted as such rather than renormalized away.
• Numerical absence in commerce factors. An Originator with no commercial routing has no price/value observations; those factors are non-punitively renormalized over its present commerce factors rather than zeroed. Absence of a routing is not evidence of zero commercial accessibility in the way that absence of official free API access is.
• Leaderboard floor in adoption. An Originator below the printed cutoff of the adoption board is valued at the last readable rank, taken dynamically from the current board — never hardcoded — so that “not photographed onto the board” is not converted into an absence discount.

The point of the chapter is not that these classifications are the only defensible ones; it is that they are registered and auditable. A reader who disagrees with a classification can in principle see which classification was made, why, and trace its effect on the aggregate. That is the difference between a data pipeline and a measurement.

11.4 · Conservation in practice

At this settlement $R = 0$ and $D$ is small, so the exact and approximate conservation propositions nearly coincide: the sum of the flagship over the included set equals the sum of the adjusted anchors exactly, and equals the sum of the base anchors up to the size of the $D$ adjustment (Propositions 6.9–6.11). The snapshot therefore doubles as a numeric instance of the conservation law: the published column can be summed and the identity checked to within that margin. This is the partial-reproducibility claim of the paper made concrete — the FA methodology, the reference parameters, and the snapshot are sufficient to check the system's central invariant, even though the live signal is not reproduced.

11.5 · What the case study does and does not show

The snapshot evidences: (i) the composition is computable and bounded (Proposition 6.12); (ii) the channel structure is discriminant in practice; (iii) the conservation invariant holds on released data; and (iv) the missing-value taxonomy is exercised by real coverage gaps. It does not evidence: (i) the validity of the index as a measure of influence (that is the running program of Section 4 and Section 8.6); (ii) any dynamic property (one snapshot has no time dimension); or (iii) any claim about the live signal. The boundary is drawn so that the reader does not over-read the snapshot.

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