The SN home page is an auction

Scoresby

Last night what I shared as $$\text{Rank}_i$$ is  `hot_s`.

$$
\text{Rank}_i \;=\; \sum_j \text{zap\_amount}_{ij}\,e^{\lambda\,\text{zap\_time}_{ij}}
\qquad\text{where}\qquad
\lambda=\frac{\ln 2}{4h}.
$$

We store `hot_t` and `hot_s`:

$$
\text{Rank}_i \;=\; e^{\lambda\,\text{hot\_t}_i}\,\text{hot\_s}_i
$$

with

$$
\text{hot\_t}_i \;=\; \max_j \text{zap\_time}_{ij},
\qquad
\text{hot\_s}_i \;=\; \sum_j \text{zap\_amount}_{ij}\,e^{\lambda(\text{zap\_time}_{ij}-\text{hot\_t}_i)}.
$$

Substituting those definitions directly:

$$
\text{Rank}_i
\;=\;
e^{\lambda\,\max_j \text{zap\_time}_{ij}}
\sum_j \text{zap\_amount}_{ij}\,
e^{\lambda\left(\text{zap\_time}_{ij}-\max_j \text{zap\_time}_{ij}\right)}.
$$