Appendix RRR — Deterministic High-Energy Event Ranking

To systematically identify the most physically informative neutrino events within the IceCube High-Energy Starting Event (HESE) sample, we introduce a deterministic event-ranking statistic designed to combine deposited energy with directional reconstruction precision.

For each event $i$, we define the KILLER statistic as

<a id="eq-eq-killer-statistic" />

where $E^{\mathrm{dep}}_i$ denotes the deposited energy of the event, and $\sigma_{\theta,i}$ represents the median angular reconstruction uncertainty, expressed in degrees.

By construction, this statistic preferentially ranks events that simultaneously exhibit exceptionally high deposited energy and superior angular localization. Importantly, the definition of $\mathcal{K}_i$ does not rely on probabilistic classification, machine-learning inference, or assumptions regarding astrophysical source populations.

The KILLER statistic is fully deterministic, dataset-internal, and invariant under re-sampling or catalog partitioning. As such, it provides a robust and reproducible method for ordering rare, high-information neutrino events according to their intrinsic physical constraining power.

When applied to the HESE dataset, the resulting ranking reveals a single event that dominates the distribution of $\mathcal{K}_i$, exceeding all other events by a substantial margin. This event is therefore identified as the most physically constraining neutrino observation within the analyzed sample.

At this stage, no assumptions are made regarding astrophysical associations, multi-messenger counterparts, or external source catalogs.