Knowledge worth having is held by individuals, institutions, communities, formats and platforms alike. The constraint on learning is seldom the volume of material produced. It is that most of the search space remains invisible to the person searching it.

Learners differ in what they know, what they need and the circumstances in which they are working. The same idea may be conveyed through an explanation, an example, an exercise, a question, a visualisation, a discussion, an annotation, practical experience, a tool or another person.

No single form serves every learner at every moment, which is what makes variation the raw material of an effective search.

Published content is coarse. An explanation, a paper or a course constitutes a large action, and it either lands or it does not.

Annotations record what a reader noticed at the moment they noticed it, and each becomes an inexpensive action for whoever follows. Coarse actions cannot absorb the variation between learners; a dense layer of fine ones can. Content establishes the route, and annotations adjust it for the individual.

An action carries no meaning in isolation. It acquires meaning only in relation to a state, which makes the search space a graph rather than a list. Charting that graph requires collaboration, and collaboration is the only mechanism that scales with the size of the field. Coverage. Many readers attempt combinations no individual would. Elevation. A connection one person has mapped becomes a starting position for the next.

Axi locates and cites existing knowledge, and where nothing suitable exists it reports the gap. Studio allows people to produce the missing material. The gaps then function as a map of what to build next.

Learning lines connect actions so that each prepares the learner for the next. They propose a route without fixing it, and learners may branch away, leave and rejoin.

Ranking. The retrieval model is constructed to mirror the learner's own search. It represents the initial state as the learner's knowledge base, the goal state as the understanding sought through the query, and the transition model as an estimate of how each action may alter what the learner knows. Searching that model returns a ranked list of the actions most likely to reach the goal at low cost. The ranking is advisory and does not decide on the learner's behalf.

Learning styles. Learners differ in how a given action changes their state. Their choices, ratings, annotations and outcomes provide evidence of those differences. That evidence is the subject of research we have planned rather than completed, and we intend to use it to refine the transition model rather than to confirm any existing theory of learning.

Axi. Ranking necessarily proceeds from an estimate of the learner, and conversation is the least costly means of correcting that estimate. In a few sentences a learner can revise every element of their own search: what they already know, what they are seeking, which form would help, what has landed and what constraints apply. Each answer re-ranks immediately, and the correction is retained for subsequent sessions. Axi predicts, directs and cites. It does not conduct the search in the learner's place.

The cost of the actions themselves. Complexity is properly located in the system rather than the interface. Search, the knowledge graph, learning lines and the associated tools open the next action from a single place. The Companion operates on the published page or the local PDF as it stands, without rehosting or reformatting. Annotating, rating, branching and rejoining should cost the learner very little beside the learning itself.