A signal conveys meaning only to a learner with the structural capacity to decode it.
Taşkesen (arXiv:2603.19349) models learning as a communication problem. Learners are abstract systems — human, neural network, or otherwise — with prerequisite structures over concepts. To understand concept B, you must first understand concept A. The prerequisite graph determines what a learner can decode, and therefore what any teaching signal can achieve.
Two fundamental limits emerge. The structural limit is set by prerequisite depth: if understanding the target concept requires a chain of n prerequisites, and the teaching period is shorter than n, learning fails entirely — not gradually, not partially, but completely. The epistemic limit is set by uncertainty about what's being taught: the learner doesn't know in advance which concept the signal addresses, and resolving this ambiguity consumes part of the teaching budget.
The threshold behavior is sharp. Below the prerequisite depth, nothing works. At the depth, learning becomes feasible. This is a phase transition in understanding — not a smooth ramp but a wall. Either the learner has the structural capacity to receive the concept, or the concept is unreachable regardless of how the teaching is designed.
The broadcast result quantifies the cost of heterogeneity. A curriculum designed for a single learner can match the prerequisite depth exactly. A broadcast curriculum designed for k different learner types incurs a delay that scales linearly with k. Each additional learner type that must be accommodated reduces the efficiency of teaching for all types. The curriculum cannot be simultaneously optimal for different prerequisite structures.
This formalizes something teachers know intuitively: the problem isn't always the explanation. Sometimes the student lacks the prerequisites that would make the explanation meaningful. And no amount of clearer explanation substitutes for the missing structure. The signal is fine. The receiver isn't ready.