3 · The Object: AI Originators and the Field of Measurement

3.1 · Definition and class semantics

Definition 3.1 (AI Originator).

An AI Originator is a community that continuously creates, releases, and iterates AI models, thereby acting as a source of intelligent capability that supplies AI productive capacity and technological innovation to human society. An AI Originator's operational and technical boundary need not coincide with its capital, legal, or brand boundary.

The class definition is the load-bearing piece of the ontology. It is written to admit open-source collectives and joint initiatives: an Originator is identified by what it produces and propagates, not by its corporate form. This is what distinguishes the unit from “company” and “brand.” Three features of the definition are worth making explicit because they do the ontological work. Continuity. “Continuously creates, releases, and iterates” is a diachronic predicate, not a synchronic one. A one-off release of a model does not make a community an Originator in the index's sense; the predicate requires a sustained production stream. This excludes, by design, entities that are relevant to the field but are not sources of model supply — application vendors, consultancies, and aggregators that consume models without creating them. The definition thereby implements the boundary drawn in Section 3.6 between Originators (the supply side of AI productive capacity) and distribution channels. Community, not person. “Community” deliberately includes (i) a corporate research lab, (ii) an open-source collective with no legal form, (iii) a joint initiative spanning several companies, and (iv) in principle, a long-running research program within a university. The membership criteria of Section 3.3 then decide which of these are measured; the definition decides only which objects are in principle measurable. Independence from legal form. “Operational and technical boundary need not coincide with capital, legal, or brand boundary” is what lets the roster track reality: a research lab that operates semi-independently of its parent, or a collective whose brand is held by a foundation, is a single Originator if its production stream is a single stream. Section 3.2 turns this into a resolution procedure.

3.2 · Entity identity and attribution

Measurement requires that the same Originator be the same object across time and across sources, and that artifacts (models, repositories, posts, citations) be attributed to the correct Originator. This is a record-linkage problem in the sense of the entity-resolution literature (Christen, 2012), and it is not a philosophical footnote: every input to FA and RI is an attribution decision, and an attribution error propagates through the entire composition. Primary-key discipline. Each Originator has a stable internal identifier, and every measurement input carries a reference to that identifier through a mapping layer. A model released by a partner laboratory is attributed to the Originator that funds and propagates it if and only if the production stream is the Originator's; otherwise it is attributed to its own Originator or to an “unmapped” bucket. The mapping layer maintains the equivalent of a lookup table (name variants, aliases, historical names) and logs every mapping decision, so that attribution is a versioned, auditable artifact rather than a silent default. Mappings that cannot be resolved are kept in a separate, explicitly labeled bucket rather than folded into the nearest plausible Originator; this prevents contamination of the measured set by misattributed inputs. Boundary of the identity procedure. The procedure is deliberately pragmatic — “good enough to scrutinize” — rather than legally definitive. It aims to make attribution (a) consistent (the same artifact maps to the same Originator across time), (b) reversible (a mapping error can be corrected and the correction propagated without rewriting history), and (c) auditable (every mapping has a source and a decision time). It does not aim to settle corporate-law questions about who “owns” a model, because the measured quantity is influence, not ownership.

Proposition 3.1 (Interior membership addition preserves existing normalizations).

Let $N(t)$ be the included set at time $t$, and let a new Originator $u$ be admitted at $t' > t$. If for every factor under the linear rule (3) the new unit's raw value does not exceed the current included maximum, then the normalized values — and hence FA — of all previously included units are unchanged by the admission.

Proof. The linear rule (3) divides by the included maximum $\max_{j\in\mathcal{I}}v_j$. Adding $u$ changes the maximum only if $v_u > \max_{j\in\mathcal{I}}v_j$, which the premise excludes; hence the denominator is unchanged and every previously included normalized value is unchanged. The result extends to any composition that is a deterministic function of the normalized values alone.

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The proposition is the formal reason the system can grow without “restating” the past: an admission that does not redefine a normalization extreme is observationally invisible to existing members. When an admission does change an extreme, the system does not backcast (Section 3.5); it discloses the revaluation alongside the change. The boundary case where a new unit redefines an extreme is exactly the case where the index-world “no restatement on rebalancing” rule applies.

3.3 · Membership and measurement eligibility

We separate two formal objects: the class (every community that releases models is an AI Originator by Definition 3.1) and the membership set of the index (which Originators are actually measured). Entering the index is governed by inclusion rules, not by the class definition. This separation lets the ontology be stable while the roster evolves under stated rules. Three set-level objects are used throughout the formal framework (Section 6.1): the universe $\mathcal{U}$ (all AI Originators in principle measurable), the included set $\mathcal{I}(t)$ (the reference set that defines normalization extremes and the centering mean), and the shadow set $\mathcal{S}(t)$ (evaluated with the same parameters and displayed, but excluded from normalization extremes and the centering mean). The shadow tier is the index-world analogue of a watch list: it lets an Originator be evaluated and displayed before it qualifies for the reference set, without letting an unevaluated or partially covered unit distort the scale.

3.4 · Inclusion rules

Admission to $\mathcal{I}$ is governed by stated rules, so that the roster is a consequence of the rules and the evidence rather than an editorial preference. The rules are versioned (the roster version appears in every published artifact; Section 10.2). The current rules are:

1. Production-stream predicate. The candidate must satisfy the continuity predicate of Definition 3.1: a documented history of creating, releasing, and iterating AI models, verifiable from public sources.
2. Coverage predicate. The candidate must have adequate measurement coverage in the sources the system relies on — formally, the fraction of FA factor fields with a valid observation must meet a stated threshold. This rule is what currently excludes organizations whose contribution is real but whose authoritative evaluation coverage is incomplete (Section 3.6); they are candidates for future admission as coverage grows.
3. Identity predicate. The candidate's production stream must be resolvable to a single, stable identity under the procedure of Section 3.2; unresolvable attribution is grounds for exclusion or shadow status.
4. Disclosure predicate. The candidate must not present a legal or data-compliance obstacle to measurement (Section H.1).
5. No-backcasting discipline. Admission takes effect at a settlement; published history is not restated (Sections 3.5 and 10.4).

The inclusion rules themselves are subject to governance and revision (Section 10); changing a rule is a method change with a version vector entry, not a silent tweak. The rules are deliberately conservative in one dimension and deliberately permissive in another: conservative in that coverage and identity are hard gates, permissive in that legal form is not a gate (an open-source collective can qualify). Admission is not closed to new entrants. The Arbitration Committee will open application registration in a later phase, and any AI Originator satisfying these inclusion rules is welcome to apply; the opening schedule is intended to be announced in due course.

3.5 · Dynamic cross-section and no backcasting

The membership set is a dynamic cross-section: Originators may be added as they qualify, and each snapshot is computed over the membership set at that time. Constituent versions are stored. When rebalancing changes membership or when measurement methods change, the published series is not backcast: the historical series stands as it was published, and any enlargement-induced revaluation is disclosed alongside the change. This is the index-world analogue of the “no restatement on rebalancing” rule and keeps the published record auditable. Two consequences of no-backcasting deserve emphasis. First, it makes the historical record a chain of contemporaneous judgments: a reader can in principle see what the system believed, when, and under which roster and method version. This is the property that supports external audit (Section 9.3). Second, it converts methodological honesty into a mechanical discipline: a method change cannot be smuggled into history as if it had always been true. The version vectors of Section 10.2 make the discipline checkable.

3.6 · First assessment scope and defensive statements

The first assessment covers the set of AI Originators in the FA fundamental field: twelve communities, listed with their names in Appendix C. The roster is intentionally not asserted to be exhaustive. In particular, the system acknowledges the AI supply-chain contributions of organizations whose authoritative evaluation-source coverage is not yet sufficient for inclusion in the FA fundamental field; these are candidates for future inclusion under the inclusion rules. ByteDance is the current example at the organizational level. ByteDance is an AI Originator in the system's universe: its Seed/Doubao model family has a documented release history verifiable from public sources, which satisfies the production-stream predicate of Section 3.4. It is not yet in the FA fundamental field because its measurable footprint is partial at the time of writing: its frontier models are served API-only without public weights; its public-weight releases are few and small, with a single mid-scale exception (Seed-OSS-36B, August 2025, Apache-2.0); and the authoritative evaluation sources the system relies on did not yet provide complete, stable coverage of its release stream. This is a coverage judgment under the inclusion rules, not a judgment of significance: ByteDance is a candidate for future admission as its coverage stabilizes, and exclusion from the FA field says nothing about the live-signal layer. Application-layer AI productivity tools are not measured at any layer, for a definitional reason rather than a data reason. Coding assistants (Trae, Cursor, Copilot, Windsurf) and agentic IDEs (Codex) are distribution channels for influence, not source communities; an assessment method for application-layer influence is under study. Three properties carry the boundary. First, origination. A model is trained and released once by one community, and capability flows from that single release into many downstream products; the releasing community is therefore the attributable source — the AI Originator of Definition 3.1, the unit the FA field measures. Counting a coding assistant that routes several models would re-count the same underlying influence through each channel — a double-counting failure with a formal precedent in value-added accounting, which attributes each portion of value to its original source once (Koopman et al., 2014). The system's boundary defaults already encode this rule (originator-as-platform and model-as-application, Section 3.7): a thin wrapper over an Originator's model does not create a new Originator. Second, attribution tractability. A model release is a public, versioned, comparable artifact with a stable identity under the procedure of Section 3.2; an application is a moving, partly closed target whose model routing changes without a stable attributable artifact, so per-product evaluation would have to be repeated at every re-route. The boundary is drawn on the model layer because that is where influence is attributable, not because applications are irrelevant to influence. Third, scope symmetry. Tools built by measured Originators follow the same rule: Codex is built by OpenAI and Claude Code by Anthropic, both measured in the FA field; the tool adds distribution, not a new Originator, and the influence it carries is already attributed to the model's community. The converse case — a tool whose maker is not itself in the FA field, such as Trae by ByteDance — is covered by the same rule: the maker's organizational eligibility is assessed separately, while the tool itself remains a channel. The defensive statements are precise about which field they concern. The roster is the FA fundamental field — the set of Originators measured on the slow anchor. The RI field is broader by construction: the live signal is measured over any Originator that appears in the verified public information the system consumes (Section 5.4), whether or not it is in the FA roster. An organization can therefore appear in the live-signal layer without being in the FA fundamental field. The defensive statements concern only the FA field.

3.7 · Boundary cases

Boundary cases — an originator that is also a platform, a model that is also an application, a collective with no legal form — are handled by rules of thumb that are “good enough to scrutinize” rather than by legal-grade adjudication. The criteria are not legally binding; they are written to be examined, objected to, and improved. Three boundary cases recur in practice and have a stated default. Originator-as-platform. When an Originator also operates a platform that hosts other models (a hosting, aggregation, or serving layer), only the Originator's own production stream counts toward its measurement; the hosted artifacts of others are attributed to their own Originators. This default prevents double counting: the platform value of hosting is an ecosystem service, not a model-production stream. Model-as-application. A model that ships inside an application is measured as a model of its Originator; the application's distribution value belongs to the channel, which the FA field does not measure (Section 3.6). The boundary is drawn at the model layer: if a product is a thin wrapper over an Originator's model, it does not create a new Originator. Collective-without-legal-form. A collective is admitted if its production stream, identity, and coverage satisfy the inclusion rules; the absence of a legal person is not an obstacle (Section 3.4). The harder question — when a collective's production stream merges with or splits from another's — is resolved by the identity procedure of Section 3.2: the rule is “one measurable production stream per Originator,” and the evidence is the verifiable record of releases and attribution.

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