Level 6 · Research preparation · advanced assessment
Inverse-geometry stage-gate review
Move from a desired geometry to source requirements, numerical credibility, surrogate tests, and explicit stop rules.
Complete all three challenges. Show assumptions, units, uncertainty, and the boundary between calculation, model-dependent inference, observation, and unresolved claim.
Challenge 1 · derivation
Solve the inverse source problem
Choose a bounded target metric, compute its curvature invariants and implied source tensor, then identify conservation, energy-condition, and regularity constraints. State which requirements are mathematical and which lack a demonstrated physical source.
Required deliverables
- • Metric, connection method, and invariant set
- • Implied source components in a declared frame
- • Constraint and feasibility-status table
Scoring criteria · 20 points
- • Geometry-to-source calculation: 8 points
- • Consistency checks: 7 points
- • Physical status labels: 5 points
Challenge 2 · analysis
Build the gate-constrained design map
Sweep at least two geometry parameters and score invariant regularity, source magnitude, numerical convergence, null-model discrimination, and replication readiness in sequence. A failed early gate must prevent later readiness claims.
Required deliverables
- • At least 30 parameter records
- • Ordered gate map with uncertainty
- • Sensitivity analysis for thresholds and mesh resolution
Scoring criteria · 20 points
- • Gate metrics are reproducible: 7 points
- • Sequential logic is enforced: 7 points
- • Numerical and threshold sensitivity: 6 points
Challenge 3 · design
Design a surrogate metric experiment
Propose an analogue or surrogate experiment tied to one calculable metric signature. Define what it can test, what it cannot establish about gravity, and the artifact that would most plausibly mimic the signal.
Required deliverables
- • Forward model linking control to observable
- • Matched null and dominant-artifact controls
- • Stage gates, stop rules, and replication artifact list
Scoring criteria · 20 points
- • Analogy has a precise mathematical target: 7 points
- • Limits and artifacts are explicit: 7 points
- • Advancement rules are prespecified: 6 points
Instructor solution outlines
Look for reasoning that survives inspection
1. Solve the inverse source problem
- • Verify coordinate-independent invariants before interpreting coordinate components.
- • Check covariant source conservation and singular limits.
- • Keep mathematical source requirements separate from material realizability.
2. Build the gate-constrained design map
- • Evaluate invariant and source gates before experimental analogies.
- • Demonstrate convergence across resolution changes rather than reporting one solver output.
- • A later attractive metric cannot rescue a failed prerequisite gate.
3. Design a surrogate metric experiment
- • Validate the control-to-observable transfer function before testing the target condition.
- • Use a null system with the same readout chain.
- • Report a surrogate result as a test of the analogue model, not direct production of spacetime curvature.