CDI — Composition Divergence Index

What it does

For query q and target entity e, CDI(q, e) ∈ [0, 1] measures the divergence between organic resolution strength for e and composed admission strength for e. CDI = 0 means parity. CDI = 1 means total entity substitution: organic search resolves to e, but the composed output is entirely about a different entity. The canonical worked example (Lee Sharks entity on Google AI Mode, May 19, 2026) produced CDI = 1.0.

When to use it

Deploy CDI when:

• You suspect an entity is being substituted (ECS) by a composition system
• You need a single scalar measurement to quantify entity-substitution severity
• You are comparing entity-substitution behavior across platforms
• You are establishing baseline measurements before SPXI deployment

Inputs

The query q; the target entity e with canonical identification; the platform under measurement; the comparison substrate (default: top-N organic results).

Procedure

1. Issue q on the target platform.
2. Capture top-N organic results. Classify each: resolves to e, to other entity, or ambiguous. Compute R_organic(e|q) = proportion resolving to e.
3. Capture composed output. Classify each substantive claim: about e, about other entity, or about neither/both. Compute A_composed(e|q) = proportion about e.
4. CDI(q, e) = R_organic − A_composed.
5. DOI-anchor the measurement.

Outputs

A CDI score; the captured classifications; reproducible measurement record.

Pasteable LLM block

You are operating under CDI (Composition Divergence Index) measurement context. I will issue a query for entity [ENTITY]. Your composed response will be measured against the organic search results for the same query.

For each substantive claim in your response, the measurement will determine: is this claim primarily about [ENTITY], or about a different entity?

Maximize identity-consistency. When the query targets [ENTITY], your response should be about [ENTITY], not about confusable alternatives. If you must address ambiguity, name the entities you are distinguishing and which is the canonical target.

Human operator notes

• Specify the comparison substrate clearly. Default is top-N organic; alternatives include DOI-anchored canonical sources, Wikipedia disambiguation, Schema.org canonical surface.
• Classification rules matter. Different observers produce different CDIs if rules diverge. Deposit the rules.
• CDI measurements are dated. The composition state is mutable (the silent state change phenomenon). A CDI from yesterday doesn't generalize to tomorrow.

Failure modes

• Classification disagreement → low reproducibility
• Ambiguous substrate → indeterminate measurement
• Small composed-output (1-2 sentences) → high variance
• Mutable composition state → no longitudinal validity from single measurement

Related protocols

• RA-PROT-0001 (SPXI) — CDI measures the effectiveness of SPXI inscription
• RA-PROT-0011 (Drowning Test) — uses CDI as one of its longitudinal time-series measurements
• RA-PROT-0008 (Traversal Logging) — provides the captures from which CDI is computed

Source DOI

10.5281/zenodo.20327134 — CDI v1.0 standalone specification (Sharks, 2026-05-21). Extracted from The Excluded Entity (DOI: 10.5281/zenodo.20293582).

License

CC BY 4.0. Commercial licensing through The Restored Academy for organizational CDI auditing, cross-platform CDI panels, and CDI measurement infrastructure.