The formal property that the three audiences in the Nested Audience Model are nested, not parallel: content must pass the Bot gate before reaching the Algorithm, and the Algorithm gate before reaching the Person. Notation: Person ⊂ Algorithm ⊂ Bot.

Jason Barnard formalized Sequential Gating as Proposition 3.1 in the academic paper on Cascading Confidence. The proposition states that audiences are nested, not parallel. This is not a metaphor - it is a structural property of the pipeline. Content that a bot cannot access will never be processed by an algorithm. Content that an algorithm does not trust will never be presented to a person. Each audience is a gate: pass or fail, with no bypass. This corrects the industry assumption that bots, algorithms, and people are three parallel tracks requiring separate strategies. They are one nested system requiring one unified strategy executed in the right order.

Audiences are nested: Bot ⊂ Algorithm ⊂ Person. Content must pass each gate before reaching the next. Proposition 3.1 in the arXiv paper. The academic formalization of the Nested Audience Model.