G · FA Snapshot

This table reproduces the FA snapshot of the case study (Section 11, specifically Section 11.1). It is the value at the 2026-08-29 settlement, verified computationally from the V1 production inputs; it is a snapshot, not a time series. The table reports the raw anchor FA; at this settlement the sustained-leadership adjustment $D$ is small — at most a few percent of FA — and no confirmed incident is recorded ($R = 0$), so the adjusted anchor differs from the raw anchor only marginally. The two shadow units are marked with an asterisk; the ten included units define the normalization extremes and the centering mean. The full code–symbol binding for the published family is in Appendix A (Table 11).

Table 24. FA snapshot, 2026-08-29 settlement (V1 production values, verified computationally). The $\mathrm{cap}_{\mathrm{pts}}$, $\mathrm{eco}_{\mathrm{pts}}$ columns are the two composite channels expressed in FA points ($\mathrm{cap}_{\mathrm{pts}} = 60\,\mathrm{cap}^\ast$, $\mathrm{eco}_{\mathrm{pts}} = 40\,\mathrm{eco}^\ast$) and sum to the FA column up to display rounding. Units marked $*$ are shadow.

First, the top of the board is close: the top four units lie within a band of about eight points and the top two within one point; ranks inside that band should be read as “indistinguishable given the current window,” per the boundary disclosure (Section 8.9). Second, the shadow units are computed with the same parameters but against the included set's extremes, so their values are comparable in method but not in set-membership (Section 3.3). Third, the conservation law has an empirical instance here: with $D$ small and $R = 0$, Proposition 6.11 bounds the gap between $\sum_{i\in\mathcal{I}}\Theta_i$ and $\sum_{i\in\mathcal{I}}\mathrm{FA}_i$ by the size of the adjustment, so the table can be read as a near-conservative reallocation of the pool. Fourth, the balance reading of Remark 6.2 has a concrete instance. The block column sums over the included set are $S_{\mathrm{cap}}=8.29$, $S_{\mathrm{edge}}=2.15$, $S_{\mathrm{eco}}=5.83$, $S_{\mathrm{com}}=3.01$, so the pool is $\sum_{i\in\mathcal{I}}\mathrm{FA}_i = 657.7$, i.e. $65.8\%$ of the maximal pool $1000$ (Table 25). Among the capability benchmarks the extremes bound the spread: LMA-01 (crowd Elo) has column sum $9.83$, the most evenly spread source — every unit near the crowd-Elo leader — whereas HFL-01 (open-source downloads/likes) has $3.64$, the most concentrated within the block, covered by only four of the ten included units.

Table 25. FA pool and block column sums over the included set ($N=10$); shares are of the maximal block sum $10$ and the maximal pool $1000$.

G.1 · Block-level plausibility audit

The formal validity of the composite is established by the propositions (Section 6.9); this subsection adds a plausibility audit at block level: for each of the four blocks the leader's identity should line up with a defensible, independently checkable real-world position, and a systematic coincidence across all four blocks would be unlikely if the composite were measuring something other than influence stock.

Table 26. Block-level plausibility audit: for each of the four blocks, the leader, its normalized value, and the observable basis for the leadership. Values are normalized over the included set $\mathcal{I}$ (Section 6.5); a value of $1.0$ means the unit is maximal on every source entering the block.

Capability block. The capability block $\mathrm{cap}_i$ is led by Anthropic at $0.979$. The lead rests on dispersed sources rather than a single benchmark: Anthropic leads four of the seven capability sources (the two model-capability-evaluation indices, SWE-bench, and LMArena Elo), while OpenAI leads two and Qwen leads one. No single unit owns all seven sources, consistent with a leader value of $0.979$ rather than $1.000$; the multi-source structure means the block's reading is not hostage to any one benchmark. Edge block. The edge block $\mathrm{edge}_i$ is led by Qwen at $1.000$ — the only unit with a best-in-class model in every one of the four parameter bands ($s_{i,c}=1$ in each). This is an explicit reward for edge competence: with the edge weight in (13) at $0.05$ and $\mathrm{edge}_i=1.0$, the block contributes $5.0$ FA points, visible in the $\mathrm{cap}_{\mathrm{pts}}$ column of Table 24. Units with no model in any measured band — Anthropic, MiniMax, xAI, Zhipu — contribute zero by design: a missing band is a true zero about participation, not a discount. Ecosystem block. The ecosystem block $\mathrm{eco}_i$ is led by Google DeepMind at $0.874$ on the academic side: its academic sub-block is $1.000$ (leading on both ripple citations and the adjudicated ledger), its developer side is lifted by open releases (Gemma), and DeepSeek leads the developer sub-block, first on all five developer sources. The block is not a blanket closed-source penalty; it rewards open engagement and academic impact jointly. OpenAI ($0.611$) is carried by academic impact despite being closed, while Anthropic ($0.398$) and xAI ($0.349$) sit at the bottom for different reasons: xAI's academic sub-block is near zero ($0.008$) despite a strong developer sub-block, and Anthropic's open-release presence is thin, with only moderate developer and academic sub-blocks. Commerce block. The commerce block $\mathrm{com}_i$ is led by DeepSeek at $0.900$ on the strongest price–quality blend in the set (raw value $592$ against a next-best $118.7$, at a blend price of $0.0875$ USD) and the widest usage momentum ($20.9$T tokens); its only zero factor is $\mathrm{free}$, so the block value is $0.900$ rather than $1.000$. The four block leaders are four different units — Anthropic (capability), Qwen (edge), Google DeepMind (ecosystem), DeepSeek (commerce) — exactly what one expects from a composite that is not a proxy for any single company. Block-level values and sub-blocks are published in full, so the snapshot is transparent at block level, while the timing signal RI remains undisclosed per the disclosure posture (Section 7.2; Appendix H).

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