In the ledger of evils perpetrated by humans, Operation Reinhard holds a special place. Over the course of 21 months starting in March 1942, Nazi forces and their collaborators rounded up 1.7 million Jews from 393 Polish towns and ghettos and dispatched them in tightly packed rail cars to three camps in German-occupied Poland — Sobibor, Treblinka and Belzec.

At these three killing centres, members of Poland’s once-thriving Jewish community were murdered with such efficiency and ruthlessness that, of roughly 1.5 million Jews who passed through their gates, a mere 102 would survive to bear witness. By November 1943, when Operation Reinhard ended, essentially no Polish Jews were left for the Germans to kill.

In a bid to capture the scope and intensity of genocidal killing sprees, a Tel Aviv University researcher has dissected Operation Reinhard and found its dark heart.

Biomathematician Lewi Stone drew upon a painstaking accounting of Nazi train schedules to analyze the “kill rate” of Jews between February 1942 and December 1944. Within Operation Reinhard’s 21-month campaign of extermination, he discovered a 92-day period that stands out for its ferocity.

In August, September and October of 1942, he calculated, German forces and their allies in Poland killed at least 1.32 million Jews. That averages out to 14,348 per day, every day. Virtually all of the victims were from Poland and its immediate neighbours.

This concentration of murders in a three-month period “likely created substantial confusion among its victims, and its speed would have made the possibility of organized resistance difficult to coordinate in time,” Stone wrote in a study published this week in the journal Science Advances. “The massacre was effectively over before there was time for an organised response.”

Stone uses authoritative estimates of the Holocaust’s toll on Jews — which range from 5.1 million to 6.2 million — to reckon that as many as a quarter of the Nazis’ Jewish victims were murdered during these three months of Operation Reinhard.

It appears to have taken place at roughly the same time that German forces, having invaded the Soviet Union and been thrown back from the outskirts of Moscow, were advancing instead on Stalingrad. Historians have noted that around this time, Adolf Hitler ordered his plan for the “final solution of the Jewish question” to be accelerated.

To clarify the rate at which Jews were murdered in the course of Operation Reinhard, Stone turned to detailed railway schedules compiled by Israeli historian Yitzakh Arad. These schedules included data on 480 train deportations to Sobibor, Belzec and Treblinka carried out by the German National Railway during this period.

In an effort to glean the full extent of the Nazis’ genocidal machine, Stone then incorporated the well-documented death tolls from Auschwitz-Birkenau in western Poland and from the Einsatzgruppen, which were active across the countries that German troops had entered, including the Soviet Union.

By December 1942, long before Operation Reinhard formally ended, the rate of train deportations — and of murders at the three camps — slowed markedly, Stone found. It wasn’t that the Nazis had a change of heart.

The new study is part of an effort to push scholarship on the Holocaust — and on the phenomenon of genocide generally — beyond aggregated numbers of the dead, and to reveal their inner dynamics. Understanding the patterns of violence that lie between a genocidal event’s beginning and end points might uncover what factors touch them off, sustain or accelerate them, or bring them to a close, Stone suggested.

Focusing on pivotal phases of the Holocaust may also offer new perspective on death tolls that have either become the subject of dry academic debate or that defy easy comprehension by the public.