Certifying multichannel event coincidence with a shared anchored clock
Year: 2026
Type: article
Abstract: Can an experimenter certify that at least four cross-channel event pairs coincide when the selected events share an acquisition counter and lie between two calibration markers? We study this decision for fixed nonnegative pair weights and a closed coincidence window of radius Δ>0. For n≥1 events at distinct source coordinates strictly inside one open cell between consecutive anchors, we prove that the minimum over continuous strictly increasing shared clocks equals the minimum internal weight of a contiguous partition into at most K=min{n,⌈ D/Δ⌉} blocks, where D is the anchor-label span. The maximum is the total candidate-pair weight. Explicit clocks attain both bounds. In a six-event model, each pair can avoid coincidence, yet every common clock gives at least four coincident pairs. Exact joint difference constraints agree with the partition bounds on the same inputs. We give a span criterion for a prescribed guarantee and specify the calibration and recording-support information needed to apply it to a retained event list. AI tools assisted with mathematical derivation, proof checking, literature comparison, and manuscript preparation.
Author: Xu, Zihuan
Institution: Capital Normal University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223942938