The Spacetime Metric

Level 6 · Research preparation · advanced assessment

Microforce round-robin qualification

Treat calibration transfer, laboratory heterogeneity, injections, and shams as prerequisites to any propulsion interpretation.

Complete all three challenges. Show assumptions, units, uncertainty, and the boundary between calculation, model-dependent inference, observation, and unresolved claim.

Challenge 1 · derivation

Reconstruct the calibration-transfer model

Derive a measurement model that maps raw sensor output to force while including scale, offset, drift, thermal coupling, vibration, electromagnetic pickup, and calibration uncertainty. Show which terms are identifiable under the proposed schedule.

Required deliverables

  • Generative measurement equation
  • Identifiability matrix
  • Combined uncertainty expression and limiting checks

Scoring criteria · 20 points

  • Measurement model completeness: 8 points
  • Identifiability reasoning: 7 points
  • Uncertainty propagation: 5 points

Challenge 2 · analysis

Estimate a cross-laboratory residual

Analyze a blinded multi-laboratory dataset containing injections, shams, and candidate runs. Estimate laboratory heterogeneity, qualify laboratories from injections and shams, and compute a combined residual only from prespecified qualified data.

Required deliverables

  • Laboratory qualification table
  • Hierarchical or random-effects estimate
  • Influence, heterogeneity, and leave-one-lab-out diagnostics

Scoring criteria · 20 points

  • Qualification rules applied before outcome inspection: 7 points
  • Heterogeneity model and uncertainty: 7 points
  • Robustness diagnostics: 6 points

Challenge 3 · design

Run a transportable blind round robin

Design a round robin using a shared artifact or simulator, concealed injections, randomized candidate/sham states, and independent analysis. Include shipping, orientation, power, and environmental transitions.

Required deliverables

  • Common protocol and transfer-standard plan
  • Blind schedule and laboratory qualification gates
  • Data package, adjudication, and rerun rules

Scoring criteria · 20 points

  • Cross-site comparability: 7 points
  • Blinding and controls: 7 points
  • Adjudication and replication readiness: 6 points

Instructor solution outlines

Look for reasoning that survives inspection

1. Reconstruct the calibration-transfer model

  • Represent force, calibration, and nuisance channels in one time-indexed model.
  • Use schedule variation to identify terms rather than assuming nuisance coefficients are zero.
  • Propagate calibration-transfer uncertainty into the final residual.

2. Estimate a cross-laboratory residual

  • Unblind condition types only after each laboratory's calibration model is frozen.
  • Exclude or down-weight laboratories using the preregistered qualification rule.
  • Do not interpret a pooled value when heterogeneity or sham failure invalidates pooling.

3. Run a transportable blind round robin

  • Characterize the transfer standard before and after each shipment.
  • Require injection recovery and sham rejection before a site contributes to the candidate estimate.
  • Preserve site-level data and discrepancies rather than reporting only a pooled headline.