# EDH corrected-interval diagnostic — registered disclosure note

**Date:** 11 August 2026. **Status:** REGISTERED AND BINDING at commit, before any
corrected interval for the actual registered split is computed. Operator-directed
(discussion of 11 August): the interval defect was a mechanical error in the
registered construction, identifiable and justifiable by derivation alone; the
minimally entailed correction may therefore be computed and published for the actual
holdout as a **corrected-instrument measurement**, under the same discipline the CIR
applied to the EDR battery's instruments.

## 1. Fix class and scope — the two-layer distinction

The registered semantic of the sixteen Block B intervals was a **prediction
interval** ("across repeated comparable applications of the method, the target
should land inside its stated range about nine times in ten" — supplement, recovery
test). That semantic mechanically entails a predictive variance with **two**
components: Var(θ̂_vis) + Var(θ_hid). The alpha implementation delivered one. Adding
the second is the **minimally entailed correction** — the analogue of a CIR A0 fix:
the registered standard determines the answer; no free parameter is chosen.

Two layers are therefore distinguished, and only the first is in scope:

- **In scope:** the alpha construction + the entailed second variance component,
  exactly as already fixed and measured in `ops/popper/measure_interval_defect.py`
  (the defect note's two-sample construction), applied to the **actual registered
  visible half** instead of random splits.
- **Out of scope:** every further refinement in the v2.x successor protocol
  (finite-population weighting choices, per-tail machinery, fallback rules). Those
  are a **new instrument**, developed with the help of EDH-derived measurements, and
  await the registered v2.3 fresh-population certification. They do not appear in
  this diagnostic.

## 2. Construction — per target family

For every target, the corrected interval is the alpha resampling frame with an
independent future-half draw (the two-sample scheme of
`measure_interval_defect.py`), and nothing else:

- **Whole-population ratio targets** (non-Latin whole, epitaph, votive, dated,
  range-dated precision, bracket density, no-photograph): the defect-note two-sample
  construction, verbatim, on the registered 33 visible provinces.
- **Stratified ratio targets** (non-Latin Latin-West / Greek-East; marble
  Mediterranean / continental): the same construction within the registered stratum
  province sets, per the frozen Block B stratum definitions.
- **Count targets** (provinces ≥1,000; provinces <300) and **concentration targets**
  (largest-province share; top-five share): the alpha construction's resampling
  frame from the frozen Block B script with the independent future-half draw added.
- **Century-mix TV band:** band-only target; same treatment if the second component
  is mechanically derivable in the alpha frame.

**Abstention rule:** if for any target the second component cannot be added without a
discretionary modelling choice (anything beyond mechanical entailment), that cell
publishes **"n/a — no mechanically entailed correction"**. No invented constructions;
park, not tune.

## 3. Blindness of construction, sequencing, execution

The corrected construction consumes **only** frozen visible-half inputs. The
computing code path must not read the scoring/landed-values file; corrected intervals
are written to disk **before** landed values are joined to produce the covered/not
column. One official execution (the A7 void-run precedent governs crashes); the
result publishes whatever it shows. Public seed: SHA-256 of the literal string
`QUINCUNX-EDH-CID-20260811`, big-endian integer, `numpy.random.Generator(PCG64DXSM)`;
resample counts as in the defect-note script.

## 4. Labels — what this measurement is and is not

- It is the **current-best measurement** of the sixteen interval statements, exactly
  as the CIR's corrected execution is the current-best measurement of the EDR
  battery: the repaired instrument run once on the frozen inputs.
- The blind score of record remains **9/16** and is not replaced or annotated as
  superseded; the corrected column publishes beside it, labelled
  **corrected-instrument diagnostic**.
- It is **not** a new blind confirmation, and it does **not** certify the corrected
  method: this holdout selected which defect was repaired, so it cannot measure the
  repaired method's general calibration (defects this split does not punish remain
  invisible; sixteen correlated targets carry no certification power). Certification
  remains the registered v2.3 fresh-population run.

## 5. Consumers

The paper's recovery-test table (one added column plus a short explanatory
paragraph); `docs/generated/quincunx_edh_corrected_interval_diagnostic_20260811.md`
(+ `.json`) as the results record; the paper deposit's source files.

*Registered by the orchestrator on operator direction; computation is unlawful
before this file's commit timestamp.*
