ProtocolFinal
Units, estimands, and what marginal checks cannot identify
Deployment → persona prompt → condition → episode → seat → round → request; four estimand families kept distinct.
Unit hierarchyIdentification propositions
The unit chain is deployment → explicit persona prompt (16 + bare control) → condition (6 cells, 160 arms) → episode (1,712 in Phase 5) → seat (2/episode) → round (54,276) → provider request (36,251). These nouns are not interchangeable; calls are operational scale, not subjects.
Four estimand families
| Family | Definition | Status in this program |
|---|---|---|
| Fixed-panel | properties of these sixteen sealed prompts | all registered Phase 5 predicates attach here |
| Persona-generator | a wider persona population | exploratory at n=16; two-stage bootstrap targets it |
| Prompt-indexed | Δi for the same explicit string across conditions | identified; a latent person’s effect is not (invariance untested) |
| Human-substitution | human–LLM equivalence | not claimed; references protocol-nonmatched |
Identification propositions
Proposition A — accepted bands [ℓ₀,u₀], [ℓ₁,u₁] identify only Δ ∈ [ℓ₁−u₀, u₁−ℓ₀]: the interval can contain zero, an attenuated effect, or the wrong sign. Exact mean matching would force the aggregate effect by identity — the failure lives in the slack of coarse criteria. Proposition B — mean and variance identify neither the between/within split, the shape, boundary mass, nor the cross-condition coupling that defines prompt-indexed response (a Fréchet–Hoeffding/Sklar application, not a new theorem).