# Frozen Confirmatory Protocol

**Frozen before execution on 2026-07-26.**

This protocol supersedes the draft status in `05_CONFIRMATORY_RESEARCH_DESIGN.md`. The model lists, evidence lengths, primary outcomes, decision rules, seeds, and asset sample below may not be changed after confirmatory results are observed.

## Study 1: Evidence × Model-Universe Factorial

### Design

- Confirmation seed: `2026072602`.
- Development/test seed: `2026072601`; development output is never pooled with confirmation.
- Replications: 400 per DGP.
- Estimation history: 1,000 observations.
- Two disjoint validation streams: 500 observations each.
- Sealed test block: 250 observations.
- Evidence prefixes: 20, 60, 120, 250, and 500.
- DGPs: stable Gaussian, stable Student-\(t\), stable skew-normal, stable mixture, causally scale-adjusted GARCH, single break, Markov switching, and smooth drift.
- Model universes:
  - U3: Gaussian, Student-\(t\), skew-normal.
  - U5: U3 plus generalized normal and two-component Gaussian mixture.
  - U9: U5 plus KDE, three-component Gaussian mixture, recent-60 Student-\(t\), and recent-120 Student-\(t\).

### Acceptable-model rule

Models are compared by observation-level negative log score. In each universe and evidence prefix, the empirical winner has the lowest mean score.

For every other model \(k\), define the paired score difference \(d_{kt}=S_{kt}-S_{\widehat{k}t}\). Estimate its standard error with a Newey–West long-run variance using

\[
\ell_m=\left\lfloor 4(m/100)^{2/9}\right\rfloor.
\]

The negligible mean-loss margin is fixed at \(\delta=0.02\) nats per observation. This corresponds to an average predictive-density penalty of about \(1-\exp(-0.02)=1.98\%\).

Model \(k\) remains acceptable unless the Bonferroni-adjusted 95% one-sided lower confidence bound for \(E[d_{kt}]\) exceeds \(\delta\). The family contains the \(K-1\) comparisons with the empirical winner.

### Primary outcomes and estimand

Co-primary outcomes:

1. 5% VaR diameter across acceptable models, divided by the estimation-sample standard deviation;
2. acceptable-set cardinality.

The primary contrast for outcome \(Y\) is

\[
\Gamma_Y =
\left[Y_{U9,20}-Y_{U5,20}\right]
-
\left[Y_{U9,500}-Y_{U5,500}\right].
\]

The central hypothesis passes only when \(\Gamma_{\mathrm{VaR}}>0\) with a two-sided 95% paired confidence interval excluding zero and \(\Gamma_{\mathrm{set}}>0\) with the same directional conclusion. The primary estimate averages the four stable DGPs within replication before inference. DGP-specific estimates are reported without selecting a preferred DGP.

Best attainable validation score is the prespecified flexibility benefit. ES diameter, winner reversal across disjoint validation streams, sealed-test regret, score gaps, and score-difference variance are secondary or mechanism outcomes.

### Gates

1. U9 never has a worse best observed score than nested U5 beyond \(10^{-10}\).
2. Both co-primary interactions satisfy the rule above.
3. Numerical failure is below 5%.
4. Stable-DGP estimates and every DGP-specific estimate are shown.
5. No DGP, model, evidence length, or outcome is changed after execution.

## Study 2: Multi-Asset Tail Decision

### Preserved sample

The analysis uses the preserved parsed adjusted-price files for SPY, QQQ, IWM, EFA, TLT, IEF, LQD, HYG, GLD, EURUSD, and BTC. Every series has at least 2,000 usable prices. No asset may be dropped except for a logged data-integrity failure that prevents the frozen algorithm from running.

### Rolling design

- Estimation history: 1,000 daily returns.
- Validation evidence: 120 daily returns.
- Sealed decision block: 20 daily returns.
- Primary blocks are non-overlapping.
- Returns are divided by a causal EWMA volatility estimate with decay 0.94.
- The U9 universe and acceptable-set rule from Study 1 are used without retuning.

### Policies

1. Gaussian reference.
2. Lowest-validation-loss model.
3. Exponential-score-weighted predictive ensemble.
4. Most conservative 5% threshold among acceptable models.

The primary tail outcome is VaR coverage. ES diagnostics are secondary.

### Primary outcomes and decision rule

For each asset and policy, report:

- absolute distance between the observed violation rate and 5%;
- mean standardized capital, defined as the positive 5% loss threshold in residual standard-deviation units.

The acceptable-set policy supports a financial-value claim only if:

1. its equal-weight mean asset coverage error is below both the Gaussian and selected-model policies;
2. both paired two-stage bootstrap comparisons have one-sided Holm-adjusted \(p<0.05\);
3. its mean capital is no more than 10% above selected-model capital, using the upper bound of a 95% bootstrap interval;
4. coverage error improves for a majority of assets against each comparator;
5. every leave-one-asset-out aggregate retains the direction of both coverage improvements.

Two-stage bootstrap inference resamples assets and, within sampled assets, non-overlapping decision blocks. The bootstrap seed is `2026072603` and the number of replicates is 2,000.

## Reporting rule

All results are reported once. If Study 1 fails, the manuscript removes the evidence-budget interaction as an established empirical result. If Study 1 passes and Study 2 fails, the manuscript becomes a measurement-and-governance paper and makes no financial-value claim. Null and adverse results remain in the manuscript and replication package.
