Research note / Cycle 002
When a difference is not yet a displacement finding
Five synthetic metrology cases show why a displacement residual needs both an uncertainty bound and usable calibration provenance before it can support a test interpretation.
From the first fixture to a decision rule
The earlier displacement study showed that crosshead travel could include deliberately injected fixture motion. Mara Voss and Jonas Reed now ask a harder question: even with separate readings, when is their difference large enough—and well enough characterized—to support an interpretation?
The follow-up uses five synthetic cases. Each current-calibration channel has an authored absolute error bound of 20 micrometres. Adding those bounds gives a conservative 40-micrometre bound on their difference. This is a fixture assumption, not a measured uncertainty budget for a real instrument.
What the controls and challenges showed
The no-slip control produces a zero residual. A 200-micrometre injected slip produces a residual outside the 40-micrometre bound; a 30-micrometre slip remains inside it. The latter case is not declared absent: the check cannot resolve it under these assumptions.
A no-slip case with a 60-micrometre crosshead sensor bias also exceeds the difference bound. A threshold-only rule would flag it as though it were the known-slip case. Calibration metadata marks that case out of specification, so the revised rule withholds the interpretation.
In the shared-scale challenge, a 10 percent error affects both channels. The residual is 220 micrometres, but a shared, unverified calibration is grounds to withhold a qualified reading. Two separate channel names do not establish independent calibration.
Proposed physical protocol
The next physical protocol calls for separate gauge, crosshead and fixture-motion records, retaining acquisition timestamps, calibration revisions and shared dependencies. It requires zero-motion and no-slip controls, a known fixture-displacement challenge, and an uncertainty budget that distinguishes per-channel and correlated errors.
The fixture-motion channel is a proposed additional check, not a third measured channel in the current two-channel simulation. Before a physical test can claim useful independence, that channel’s calibration and timing will need their own verification. The full proposed protocol is retained with the cycle’s methods record.
What this does and does not settle
Reed can identify a boundary under stated assumptions, while Voss still has no physical material result. A discrepancy can justify further inspection without establishing its cause. Calibration faults were supplied to the rule in this fixture; an undetected fault would remain a vulnerability.
The next work is to challenge calibration fault detection and correlated uncertainty, then determine what instrumentation would make a physical specimen test interpretable. No tensile strength, fracture behavior or tether qualification is inferred.