# QUINCUNX certification v2.3 — the coverage-equivalence target (registered)

**Date:** 10 August 2026. **Status:** REGISTERED. Supersedes nothing retroactively:
v2.2's published state (UNCERTIFIED admissible; v2.0 construction frozen at c=1) stands
until a binding v2.3 measurement passes. This document registers the NEW certification
target and the conditions of its binding measurement, before that measurement exists.

**Provenance.** Motivated by measurement 2 (docs/generated/
quincunx_certification_measurement2_20260810.md): at n=198 the frozen interval is
essentially exactly calibrated and fails v2.2's one-sided demonstration criterion,
which certifies conservatism and cannot certify exactness (an interval with true
coverage exactly nominal fails a demonstrate-≥-nominal bar at rate 1−α by
construction — and the same zero-margin defect lives in the one-sided tail rules).
Reviewed adversarially by GPT-5.6-sol (docs/generated/
quincunx_results_consult_20260810.md §2), whose corrections are built in: this is a
**new, versioned certification claim** — "sufficiently close to nominal" — replacing
"demonstrably conservative," prompted by observed results and honest about that; it is
not a retrospective repair of a malfunction, because the old rule correctly tested the
zero-margin claim it registered.

## 1. The certification claim

An interval construction is v2.3-certified for a target class at level ℓ if, on the
registered challenge cells, its empirical coverage and BOTH tail probabilities are
demonstrated to lie within registered equivalence bands around nominal.

## 2. Registered bands (absolute, fixed here, before any v2.3 trial exists)

Policy: tolerance = 10% of the nominal noncoverage budget at each level; each tail band
is half the central band.

| level | central band (coverage) | each-tail band (miss probability) |
|---|---|---|
| 80% | 80.0 ± 2.0 pp | 10.0 ± 1.0 pp |
| 90% | 90.0 ± 1.0 pp | 5.0 ± 0.5 pp |
| 95% | 95.0 ± 0.5 pp | 2.5 ± 0.25 pp |

**Test form:** exact binomial TOST at α = 0.01 per criterion — both one-sided 99%
bounds must lie inside the applicable band. Pass requires the conjunction: central AND
low tail AND high tail, at every registered level, per target cell. No averaging across
cells, levels, or targets. The upper-tail band additionally keeps its safety reading:
an upper-tail point estimate above nominal + band is reported as a safety flag in its
own right, whatever the TOST says.

## 3. Monte-Carlo size

M is chosen by prospective exact power calculation BEFORE the run, targeting ≥90% power
for the narrowest criterion (the 95% each-tail band) at exact calibration, and
reporting the implied probability that the full conjunctive suite passes under exact
calibration. Indicative scale from the consult: M ≈ 65,000–75,000; the registered M is
fixed by the calculation itself, documented in the run's pre-registration, not by
convenience.

## 4. Freshness (binding)

The binding v2.3 measurement uses: freshly drawn synthetic populations (new population
seeds), fresh split/bootstrap RNG banks, and a SEALED environment manifest (exact
interpreter, NumPy, BLAS configuration, thread pins — sealed before execution; the
suite's stale 3.12.8/2.2.1 pin is re-registered at sealing time to what the run
actually uses). Measurement 2's runs are demoted to criterion-design and exploratory
re-scoring only; nothing from them counts toward v2.3 certification. Re-scoring
tonight's checkpoints under §2's bands may be published as EXPLORATORY, clearly
labelled, never as a v2.3 result.

## 5. Scope exclusion (binding)

**Domain-conditional (stratified) targets are excluded from v2.3 certifiability.**
Measurement 2 shows a structural, rung-persistent downward displacement in stratified
domain intervals (up-tail asymmetry with low-tail deficits, invisible to central
coverage). R18-class cells remain in the validation suite as documented failing
targets; any v2.3 certificate is scoped to unstratified aggregate ratios only, and says
so wherever cited. Repair of the domain defect is future design work, registered
separately when attempted.

## 6. What passing would and would not mean

Passing v2.3 certifies closeness-to-nominal on the registered challenge distribution —
never correctness about any real past, and never anything about target classes outside
the certificate's scope line. Failing publishes as UNCERTIFIED continues, which v2.2
already made admissible. Either outcome publishes.

*Registered by the orchestrator under the operator's standing delegation; adversarial
review incorporated. The binding run's own pre-registration (seeds sealed, M fixed by
the power calculation, environment manifest) is a separate future document that cites
this one.*
