Read the equation
Subtracting declaration time from the independently detected change time gives a signed lag. Positive lag means change follows declaration; negative lag means it precedes declaration; zero means coincidence at the observation resolution. When either event is unobserved, a numerical lag is not identified.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| ell | Signed event lag |
| t_Delta | Independent persistent-change time |
| t_D | Declaration time |
How it works
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Assumptions & limits
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Original context
Read the surrounding source passage
(2.4) This locates the first observed qualifying window in the eligible record. When both event times are observed, their difference is ℓ=tΔ−tD. (2.5) A positive ℓ places declaration first, a negative value places persistent discrepancy first, and zero places them at the same measured update. The detector must permit all three results. Searching only at t>tD would instead locate the first qualifying window after declaration. That conditional endpoint can measure subsequent persistence, but it cannot establish that declaration preceded the first qualifying discrepancy. The distinction also matters for δt0. Because its reference is defined at declaration, it is a secondary endpoint for displacement from that declaration, not an independent test for onset before declaration. Temporal precedence must be tested with a reference and comparison space defined without using the declaration to exclude earlier events.
Exact original notation
ℓ={t}_{\Delta }-{t}_{D}.Related builds
Sources & provenance
ℓ={t}_{\Delta }-{t}_{D}.
ℓ={t}_{\Delta }-{t}_{D}.