# Geometry-to-source feasibility review

Translate an exotic line element into source, tidal, and observational requirements before discussing engineering.

## Instructor edition

## 1. Derive the throat requirements

**Task type:** derivation

For a static spherical wormhole ansatz, derive the throat and flare-out conditions and evaluate the radial null-energy contraction at the throat. Preserve frame and sign conventions throughout.

### Deliverables

- Geometric derivation from the metric functions
- Throat-limit stress-energy relation
- A convention audit and two sanity checks

### Scoring criteria

- Geometry and throat conditions: 8 points
- Stress-energy contraction: 7 points
- Conventions and checks: 5 points

### Solution outline

- Apply the minimum-radius and flare-out requirements to the shape function.
- Use the field equation to express the radial null contraction in geometric terms.
- State that a geometric construction is not evidence that the required source exists or is controllable.

## 2. Search the source-tidal trade space

**Task type:** analysis

Sweep throat size and shape parameters to compare integrated source requirement, peak null-energy violation, tidal acceleration, and crossing time. Identify Pareto-efficient points without naming any point feasible unless every declared gate passes.

### Deliverables

- A sweep of at least 30 parameter points
- Four gate metrics and a Pareto plot
- A feasibility table with pass, fail, or unresolved labels

### Scoring criteria

- Correctly computed trade metrics: 7 points
- Pareto and gate logic: 7 points
- No feasibility overclaim: 6 points

### Solution outline

- Compute geometry, source, and traversal quantities from the same parameter record.
- Reject points that optimize one metric by silently worsening another.
- Reserve unresolved for missing material or stability evidence rather than converting it to pass.

## 3. Separate exotic lensing from ordinary structure

**Task type:** design

Design an observing program for a restricted exotic-metric lensing signature and a matched conventional mass-distribution alternative. Include selection effects, reconstruction bias, and a result that would disfavor the exotic model.

### Deliverables

- Competing forward models and observable contrast
- Injection-recovery and selection-bias tests
- Preregistered model-comparison and follow-up rules

### Scoring criteria

- Models make distinct predictions: 7 points
- Bias controls and simulations: 7 points
- Symmetric decision rules: 6 points

### Solution outline

- Simulate both models through the same instrument and reconstruction pipeline.
- Blind the injected class during pipeline tuning.
- Treat an unexplained anomaly as unresolved until conventional structure and systematics are quantitatively excluded.

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