An oscillator is said to be T-nosed if, at one (and only one) point in its evolution stage, a T-pentomino forms at an edge of the pattern, specifically in a way that allows it to interact as a finger.
Currently T-nose oscillators are known for periods 4, 5, 6 and 7.
Oscillators which are not T-nosed
The pentadecathlon is generally not considered a T-nose as, despite the fact that it does produce an isolated T-tetromino in one of its phases that lends itself to catalysis, the cell at the point of that T is also alive four and five generations afterwards, where a true "T-nosed p15" would have these cells dead for all 14 other generations of the oscillator.[1] Instead, the pethadecathlon is a phi-sparker. The same applies to Tanner's p46.
For the same reason, the second oscillator below cannot be called a "T-nosed p8" as a blinker created by it turns the cell at the tip of the T on two extra times.
Oscillators like the pulsar and pulsar quadrant are also not T-nosed as the thumbs they produce come from an L-tetromino, rather than a T-pentomino, even though they can interact in much the same way (see boring p24 and uninteresting p24).
Oscillators such as Rich's p16, this p8, and Karel's p15 can be said to "act" like T-noses, as they do produce a cluster of cells identical to a T-pentomino in one and only one phase and allow for the same catalysis, however as the T-pentomino is in fact a subset of a larger polyomino they are generally not counted among the T-noses.
There are at least three known p4 t-nose reactions, with the T part remaining the same but the immediate hassling region differing. An Octagon 3|5 can support two reactions simultaneously,[2] with the 3 side being the same as the reaction the conventional T-nosed p4 uses.
Reactions for p5, p6 and p7 are known and all have been stabilised as of July 2021. Other true t-nose reactions of this period and true t-nose reactions of any other period are unknown.
No still life (allowing for a "T-nosed p1") can contain a T-pentomino within itself due to the central cell immediately dying of overpopulation and the tip dying of isolation, and no period-2 T-nose can exist because those two cells cause the oscillator to recede two cells, which cannot be made up in a single generation. It seems very likely that no true t-nose reaction can exist for periods 3.