A right answer isn't the same as knowing it.

What the colors mean

Every multiplication fact gets a dot. As the learner practices, the dot moves through four states:

• New Not practiced yet.
• Warming up Answered correctly at least once, but recall is not yet automatic.
• Fix-it Missed recently. The fact is due back soon.
• Mastered Recalled quickly and correctly on several separate occasions.

The states are easy to read. The rules that move a dot from one to the next are where the real decisions are made.

Speed is part of fluency

There are two ways to answer 6 × 7. You can recall 42 directly, or you can rebuild it: 7, 14, 21, 28, 35, 42. Both produce the right number. Only one of them is fluency.

Fluency is fast, automatic recall. A fluent fact is retrieved, not reconstructed. This is the same standard that applies everywhere skill matters. A pianist who has to work out where each note lives has not yet learned the piece. A fact you have to count your way back to is a fact you do not yet know.

So Fact Lab measures time. A correct answer that arrives within a few seconds, straight from memory, counts toward mastery. A correct answer that takes longer is still correct, and it still moves the dot to Warming up, but it earns no mastery credit and the fact returns later in the session. Speed is not pressure for its own sake. It is the clearest evidence that recall has become automatic.

Mastery requires spacing

You cannot reach Mastered in a single session. A fact becomes mastered only after it has been recalled, quickly and correctly, on several separate occasions spaced hours apart.

This is the most reliable finding in the science of memory. Practice packed into one sitting produces recall that feels strong and fades within days. The same practice spread out over time produces recall that lasts. The reason is counterintuitive: a memory strengthens most when you retrieve it after you have started to forget it. The effort of reaching for a fading fact is exactly what makes it durable.

So repeating a fact ten times in a row will not turn its dot green. It will warm the fact up and then set it aside until enough time has passed for the next repetition to do real work.

Errors are information

When the learner answers incorrectly, the dot turns to Fix-it and the fact is scheduled to return within minutes, while the attempt is still fresh. There is no penalty and no streak to protect. An error tells the system one thing: this fact needs another repetition soon. The way out of Fix-it is the same as the way to mastery, a handful of fast, correct recalls spaced over time.

Intervals grow as recall strengthens

Facts the learner keeps getting right return less and less often. The gap between repetitions widens, from hours, to later the same day, to the next day, to several days out. This is spaced repetition working as intended. Time and attention go to the few facts that are still weak, and the facts that are solid step out of the way. Practice stays short because it stays aimed at what the learner has not yet mastered.