2 · Prior Measurement Systems and the Positioning of This Work

2.1 · An ontological map of measurement units

Prior measurement systems can be mapped onto two axes: the measurement unit (model, organization, company, country, or individual) and the measured quantity (capability, readiness, output, or influence). Table 1 lays the map out; it makes the positioning of the present work precise, and it makes the novelty claim checkable rather than rhetorical. The claim the table supports is not “no relative index exists” but “the cell (unit = AI Originator community, quantity = social influence, form = relative + centered + real-time) is empty.”

Table 1. An ontological map of measurement units (rows) and measured quantities (columns) in the AI measurement literature at the time of writing. Shaded cell = the cell this system occupies.

Model level. Pairwise-comparison ratings such as LMArena's Elo attach a score to a model, with an arbitrary scale anchor (Zheng and others, 2023). The measured quantity is capability (or crowd preference); there is no notion of organizational or collective influence, and the scale is relative in the pairwise sense but not centered on a reference population in the aggregate sense used here. The Elo family is formally the closest relative (Appendix E compares the two scales); its level of analysis is the model, and models are not communities. A model that is a component of a larger Originator's portfolio contributes to the Originator's measurement only through the portfolio-level aggregation (Section 6.5); the unit is never the model itself. Society / country level. Annual reports such as the Stanford AI Index (Maslej and others, 2024), the Global AI Index (Tortoise Media, 2024), and the Government AI Readiness Index (Oxford Insights, 2025) measure countries or societies on a yearly cadence. They are authoritative but slow, and they do not name the productive communities that create AI as measured units. Their influence on policy is real and desirable; their granularity is national, which is the wrong granularity for the question “which community is changing how society works.” Company / list level. Company-level trackers (e.g., compute-based analyses of frontier training (Sevilla et al., 2022)) and media lists rank organizations or individuals; they are editorial or research artifacts rather than continuously maintained indexes. A media list may be rigorous, but it is not a measurement system: it has no stated composition rule, no conservation law, no settlement calendar, and no audit protocol. The difference between a ranked list and an index is exactly the difference between an editorial opinion and a repeatable measurement. Individual-influence level. Citation-style measures such as the h-index (Hirsch, 2005) and PageRank (Page et al., 1999) quantify individual influence over an artifact graph (citations, web links). They are the closest formal ancestors of an influence index, and they inherit the well-documented cumulative-advantage dynamics of influence measures (Garfield, 1955; Merton, 1968). None of them targets AI Originators as communities. Two lessons transfer directly into the design of FA: (i) influence measures exhibit path dependence (Matthew dynamics), so a measurement system must decide how much inertia is legitimate — here, the stock dimensions of FA carry inertia deliberately, while the live signal is centered so that discussion reorders but does not compound; and (ii) an influence measure that can be decomposed (the h-index decomposes into citation buckets) is far easier to audit than an opaque scalar.

2.2 · The failure of AI benchmark evaluation as motivation

The strongest empirical argument for “capability $\ne$ influence” comes not from theory but from the recent record of benchmark evaluation failing at its own job. We collect the failure modes here because they are the concrete evidence that a capability score is a manipulable artifact of an evaluation pipeline, and therefore cannot serve as the public's measure of where the field stands. Contamination. Large public benchmark corpora are routinely exposed to models during pretraining or fine-tuning, so that “measuring” a model on a leaked benchmark measures memorization rather than capability. The documentation of the MMLU benchmark (Hendrycks et al., 2021) and of BIG-bench (Srivastava and others, 2023) discusses contamination risk explicitly, and a systematic study of closed-source LLMs found widespread leakage and evaluation malpractices across published leaderboards (Balloccu et al., 2024). Koch et al. (Koch et al., 2021) document the reuse and recycling lifecycle of ML datasets, showing that a benchmark item born as a test item frequently re-enters the training corpus through downstream forks. The consequence is a measurement environment in which a high “capability” number can be manufactured without a real capability increase — precisely the Goodhart failure the system's premise warns about. Over-optimization and reward hacking. Even without leakage, optimizing directly against a proxy objective degrades the objective's validity: this is the empirical content of reward over-optimization (Gao et al., 2023), reward hacking (Skalse et al., 2022), and spontaneous reward hacking in self-refinement (Pan et al., 2024). The mechanism is generic — any score that is targeted stops being a measurement of the underlying quantity and becomes a bargaining chip between the optimizer and the scorer — and it applies with full force to public AI leaderboards, which are optimized against by every serious model developer. Assessor bias. Even a clean benchmark requires a scoring function, and when the scoring function is another model (LLM-as-a-judge) it carries systematic biases: self-preference, position bias, and value contamination (Zheng and others, 2023; Wang and others, 2023; Santurkar and others, 2023). These are not implementation bugs; they are the expected behavior of a model asked to evaluate its peers, and they are the same class of value-contamination the system's second argument (Section 1.2) predicts for any “which is better” assessment. What the failure record implies for design. The record supports three design commitments that recur through this paper. (i) Measure what is hard to fake: an influence measure should lean on inputs whose manipulation cost is high — cumulative stock, cross-referenced third-party data, verified events — and treat fast, easily manufactured signals as a bounded, centered perturbation (Section 7.5). (ii) De-average the sources: because any single benchmark can be gamed, the FA capability block is a weighted mean over seven independent sources with an institutional replaceability mechanism (Sections 6.5 and 6.2); no single benchmark is decisive. (iii) Separate the slow from the fast: the contamination and over-optimization literature is largely a story about fast targets being gamed. The system's two-component design — a slow, stock-like, multi-source FA anchor and a fast, centered, budgeted RI signal — is the structural response: it makes the gaming surface as small as the design can make it.

2.3 · AI actor in governance literature

The governance literature uses the concept of an AI actor to allocate responsibility across the lifecycle of an AI system: deployer, provider, and developer roles appear in the EU AI Act (European Union, 2024), the OECD AI Principles (Organisation for Economic Co-operation and Development, 2019), the NIST AI Risk Management Framework (National Institute of Standards and Technology, 2023), and the International AI Safety Report (Bengio and others, 2025); measurement of AI systems is itself studied as a governance mechanism (Kwa and others, 2025; Shevlane and others, 2023), and agent-specific regulatory proposals extend the actor-centric trajectory to autonomous systems (Gardhouse et al., 2026; Hacker and Holweg, 2026). In this literature “actor” is an instrument of responsibility assignment, not a measurement unit. The present system inherits the lifecycle framing but inverts its purpose: instead of assigning blame, it measures cumulative social influence. The two readings are complementary: governance actors are the responsibility-bearing instances of the Originator class, and a governance regime that needs to attribute responsibility to a developer also needs an account of that developer's cumulative footprint. The system does not provide that account in governance form; it provides the measurement form, and the mapping between the two is left to the governance community.

2.4 · Financial AI equity indexes as a formal precedent

Relative, centered, real-time indexing has a mature precedent in financial equity indexes, including industry-vertical equity indexes that track companies engaged in AI (for example, exchange- and index-provider-compiled AI industry indexes). These indexes establish that a relative, center-anchored, real-time scale can be operated publicly and be trusted for its measurement semantics. The present system borrows this form but changes the measured quantity: equity indexes measure market capitalization, i.e., the market's pricing of a company; the Eins Index measures the social influence of an AI Originator. The novelty is therefore in the combination — measurement unit and measured quantity — not in the index form itself. Three transferable lessons come from this precedent, and all three are adopted. First, a relative scale needs an explicit, reproducible composition rule and an explicit rebalancing calendar; the settlement calendar in Section 10.3 plays that role. Second, a center-anchored scale (an index “level” that does not drift for compositional reasons) requires a conservation or normalization discipline; the centering of RI in Section 5.6 is that discipline, and the no-backcasting rule of Section 3.5 keeps the level history auditable. Third, a real-time index needs a halt/suspend mechanism for integrity events; the system's suspend–resume release protocol (Section 10.5) is that mechanism. The differences are equally important and are stated as disclaimers (Section 13.6): equity indexes measure price discovery in a regulated market; the Eins Index measures a social-scientific construct with no market mechanism and no regulatory mandate, and nothing in the formal resemblance implies financial status.

2.5 · Gap positioning and honest boundaries

Relative measures already exist at the model level (pairwise Elo). Therefore the precise claim is not “first relative index”; it is: the Eins Index is, to our knowledge from searchable public information, the first relative, centered, real-time measurement scale for the social influence of AI Originators as contributor-level units. Searches in both English and Chinese did not surface a comparable public-facing AI influence index at the time of writing. Two honest boundaries attach to this claim. First, “search has not found” is not “does not exist”; the claim is deliberately weak. Second, the system's breadth is bounded by its sources: it measures influence to the extent expressible in verifiable public data, not influence in some unrestricted sense. “Comprehensive” is therefore not claimed; measurable social influence bounded by verifiable public sources is. A third boundary is epistemic rather than empirical. The claim “first relative, centered, real-time influence scale for Originators” is a claim about the combination, and a combination claim is only as strong as its weakest component. The relative and real-time components have established precedent (Sections 2.4 and 7.3); the centered conservation discipline and the Originator unit are the components with the least precedent.

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