TL;DR: “fast take-off” is defined as AGI to ASI + transformative change in a span of 6 months.
Definitions and clarifications:
This question refers to the timespan between (1) the creation of AGI, and (2) the creation of a transformative Artificial Super-intelligence. Here, a fast take-off scenario is one in which:
An ASI is created within 6 months of the first AGI (or the first AGI is also an ASI), and also
This or another ASI is directly responsible for significant and disruptive social, political, or environmental change, within a 6 month timeframe after the first AGI.
An AI will be considered an AGI if the general consensus among experts is that it meets their criteria for AGI.
Examples of significant and disruptive change include, but are not limited to:
Rapid deployment of new renewable energy tech, or the creation of fusion power or similarly disruptive technologies;
Significant advances in medicine or nanotechnology;
Solutions to long-standing problems in math or physics due to contributions made by the AGI or ASI;
Major and disruptive economic changes (such as mass layoffs or the automation of significant portions of some companies or fields)
This list is not exhaustive, and if only one or two things on the list occur, that will constitute disruptive change for the purposes of this question. This disruptive change must be attributable to an AGI or ASI.