# Nuclear-channel closure examination

Demand simultaneous closure across reaction rate, products, radiation, heat, and complete facility energy accounting.

## Learner edition

## 1. Close the reaction-network ledger

**Task type:** derivation

For a specified two-channel reaction network, derive production rates, detector count rates, nuclear power, and complete facility gain from cross sections, densities, efficiencies, branching fractions, and Q-values.

### Deliverables

- Reaction and detector equations with units
- Channel-by-channel energy ledger
- Conservation and limiting-case checks

### Scoring criteria

- Rate and branching derivation: 8 points
- Detection and power accounting: 7 points
- Closure checks: 5 points

## 2. Fit products and heat jointly

**Task type:** analysis

Given synthetic product, radiation, calorimetry, and electrical-input records, fit a shared reaction-rate model. Test whether any single rate can explain all channels within uncertainty and diagnose structured residuals.

### Deliverables

- Joint likelihood or weighted objective
- Residual and posterior/prediction plots
- Model-adequacy decision with uncertainty

### Scoring criteria

- Shared-rate model is correctly constructed: 7 points
- Uncertainties and correlations considered: 7 points
- Adequacy conclusion is evidence bounded: 6 points

## 3. Build a multi-channel replication

**Task type:** design

Design a cross-laboratory nuclear-claim test requiring synchronized calorimetry, isotopic products, radiation channels, blanks, and known-source calibration. Define how anomalous heat without products will be reported.

### Deliverables

- Shared protocol and specimen chain of custody
- Calibration, blank, and contamination-control matrix
- Sequential release gates for heat, products, and replication

### Scoring criteria

- Channels and controls are co-registered: 7 points
- Contamination and calibration addressed: 7 points
- Release gates prevent selective reporting: 6 points

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Evidence rule: distinguish calculation, model-dependent inference, experimental observation, and unresolved claim in every response.