# Probabilistic Recall-Miss Bound -- Primary Yield-Gate Operational Definition

**Scope:** Yield-gate math ONLY. Scope lives in `charter_lock_protocol.md`; contradictions in `contradiction_partial_reset.md`; framing in `saturation_typology.md`; anti-patterns in `anti_patterns_volume_floor.md`.

## 1. Operational definition (load-bearing citation)

Grounded in Callaghan, M.W. & Muller-Hansen, F. (2020). "Statistical stopping criteria for automated screening in systematic reviews." *Systematic Reviews* 9:273. The paper reformulates the screening-stopping problem as a recall-miss hypothesis test over an observed yield curve and publishes the `buscarR` reference implementation.

Operational statement (verbatim adaptation):

- Let `r_target` be the target recall fraction (default 0.95: we want at least 95% of true in-scope claims captured).
- Let `alpha` be the maximum acceptable probability of having missed more than `(1 - r_target)` of the population.
- Null hypothesis H0: `P(miss_rate > (1 - r_target)) >= alpha`.
- Reject H0 -- declare the yield gate CLOSED for the claim -- iff the posterior probability of missing more than `(1 - r_target)` of the true in-scope claim population, given the observed per-batch novel-claim counts, is strictly less than `alpha`.

## 2. Alpha threshold conventions

- **Default (RAM-wide):** `alpha = 0.05`. Matches Callaghan-Muller-Hansen's reported operating point and standard single-gate practice.
- **Conservative:** `alpha = 0.01` when the Charter declares the claim load-bearing for a material decision. Tighter alpha produces later STOP and is SAFE in the Governor's direction of concern.
- **Prohibited:** `alpha > 0.10`. Anything looser does not carry warrant status.
- **Per-claim override:** Charter may declare per-claim alpha overrides. The Governor reads; never mutates.

## 3. Minimum-batches requirement

The estimator requires at least three distinct search-batches with non-degenerate yield counts before a defensible posterior exists. Fewer -> D2 routes to Section 8 fallback with `proxy_rationale = "yield curve has N batches; estimator requires minimum 3"`. Never substitute a count-based shortcut.

## 4. Per-claim aggregation

The yield gate operates PER CLAIM. Each decomposed claim has its own yield curve and posterior. The inquiry-level gate is CLOSED iff EVERY per-claim gate is closed. No inquiry-wide averaging -- averaging masks under-saturated claims behind well-saturated peers.

## 5. What the posterior is NOT

- Not a coverage percentage; do not render as a completeness bar.
- Not a claim confidence score (that is the Output Layer's three-axis computation).
- Not interchangeable with Adversarial Pass nothing-found records (those are contradiction-class).
- Not comparable across inquiries with different Charters.

## 6. Degraded-mode boundary

When the estimator cannot run, the Governor leaves the yield gate OPEN or enters the Section 8 pragmatic proxy -- whichever the Charter authorizes. The proxy is explicitly labeled degraded. No count-based or time-based surrogate is ever promoted to primary.
