# Instructor guide: Metric-engineering sequential feasibility gate

Course: Metric-engineering research studio

Suggested time: 80–110 minutes

## Learning target

Researchers enforce ordered geometry, source, numerical, null, and replication dependencies instead of accumulating disconnected plausibility arguments.

## Prepare

- Define one invariant observable and stop rule.
- Require a source-to-apparatus systems ledger.
- Prepare an intentionally out-of-order evidence package.

## Facilitation moves

- Reject downstream evidence when an upstream gate is open.
- Require uncertainties on every threshold comparison.
- Separate theoretical feasibility from apparatus readiness.

## Misconception checks

- **A visually compelling metric simulation establishes source feasibility.** Geometry, realizable stress-energy, preparation, stability, and measurement are separate ordered gates.
- **Passing four of five gates is nearly equivalent to passing all five.** A failed dependency can invalidate downstream interpretation; stage gates are sequential, not a popularity score.

## Accessibility and participation

- Provide a text-based gate state machine.
- Pair tensor outputs with invariant observable summaries.
- Use pass/hold labels in addition to color.

## Evidence of learning

- A declared invariant observable
- An ordered five-gate dossier
- A quantitative hold or advance decision

## Extension

Create a competing conventional model that reaches the same observable and design the cheapest discriminating gate.

## Evidence boundary

Assess the learner's reasoning only within the declared model and recorded observations. Do not upgrade a simulation result into a claim about an unmodeled physical system.