Many of the words below are familiar. The intent is not to redefine them but to fix their meaning rigorously enough that arguments built from them can be checked.
The process by which attention, effort, and reflection accumulate into durable intellectual capability over time. The defining property is that the residue persists: a week, a month, a year later, the capability remains recoverable without assistance.
Contrast: activities that produce the feeling of progress without leaving residue behind.
The smoothness with which a topic can be followed, recognised, or talked about. Fluency is real and useful, but it tracks recognition rather than reconstruction.
Often mistaken for understanding because the felt experience is similar.
The state in which a structure can be reconstructed from its primitives without external aid; in which deviations from the structure are detectable; and in which the structure transfers to adjacent problems. Operationally diagnosed by what one can produce a week later, alone.
The act of producing a structure from its constituent parts using only what one already possesses. The most reliable diagnostic of understanding, and the operation around which the Lab is organised.
The naming of the postulate, definition, prior result, or common notion that licenses an inference. A step is justified when its dependency is explicit and recoverable, not merely plausible.
The minimal set of prior results, axioms, and definitions a proof actually relies on. Mapping dependencies is one of the cheapest ways to upgrade the granularity of one's understanding.
The condition under which difficulty is doing work — surfacing gaps, forcing reconstruction, exposing assumption — rather than merely producing frustration. Marked by the property that the learner is, in fact, the agent of the construction.
Distinct from obstruction, which produces the feeling of struggle without the cognitive operation behind it.
The match between confidence and accuracy. A calibrated learner is no less likely to be wrong than an uncalibrated one, but is appropriately surprised when wrong, and appropriately unmoved when right by accident.
A specific case that demonstrates a general claim does not hold. Searching for counterexamples is one of the most efficient ways of testing whether one has understood a claim or merely accepted it.
A use of an external tool that performs a cognitive operation in place of the user. Useful when capability is not the goal; corrosive when capability is the goal and the substitution is unrecognised.
A use of an external tool that increases the difficulty, feedback density, or specificity of practice without performing the cognitive operation in the user's place. The same tool can be either; the difference is in the design of the interaction.
Of a belief or practice: that it tends to converge on what is actually true, rather than on what is locally rewarded. The aim of cognitive compounding is to produce truth-tracking capability rather than merely persuasive output.
The state of being able to construct, evaluate, and defend one's own reasoning without dependence on tools, authorities, or environments that may not always be available. The point is not isolation; the point is capability that is genuinely one's own.