Copenhagen text messages had more sender changes for gaps of 10 to 300 seconds than random order with fixed pair times and daily sender counts

We tested sender order in four weeks of Copenhagen text-message records. The analysis used 24,312 distinct records from 568 participants. The primary window contained 13,069 consecutive message transitions within the same pair and day, with gaps of 10 to 300 seconds. Sender changed in 76.72% of these transitions. A reference model that fixes each pair event time and both daily sender counts predicted 52.50%. The excess was 24.22 percentage points. A two-sided test with 4,999 random label orders gave p = 0.0002, the sampling resolution limit. The test assumes uniform sender order within each pair-day group and independent reference assignments across groups. It is not a population test. The excess was 20.98 points with hourly sender counts and 22.77 points with equal pair weight. All 28 daily effects were positive. Gaps of 1 to 9 seconds instead had 12.56 points fewer sender changes than expected. Prior work already studied temporal reciprocity in these data. This contribution adds a count and time control, exact reference checks, and a reproducible audit package. A separate calculation matched the primary result. A repeat from fresh source bytes reproduced all ten numerical files byte for byte. The package preserves source data, provenance, code, reference draws, and figures. The results concern this student cohort and do not establish causal replies or a universal human behavior law.

temporal networks · text messages · sender order · Copenhagen Networks Study · conditional randomization · temporal reciprocity