Refactoring the same material across A1, A2, B1, and B2 turns out to move along at least two gradients. One is linguistic: vocabulary, and what modifiers, phrases, and clauses are asked to carry. The other is conceptual: what the reader has to construct. Grade 1 through Grade 12 is a rough curricular axis for the second gradient. Placement on that axis is not itself a measure of conceptual difficulty.

With Grade 1 material it is relatively easy to start at A1 and move toward B2 by adding vocabulary and elaborating the syntax. The ideas need not get more sophisticated. With Grade 12 material the problem runs the other way. A B2 sentence is often available, but an A1 representation has to unpack the assembly that sentence was holding. Concepts leave the sentence and occupy more sentences. Implicit relationships are said out loud.

Let G = (V, E). V is the set of concepts or propositions the reader has to construct. E is the relationships among them: causation, dependency, contrast, qualification, sequence. Where one relationship joins several concepts at once, a hypergraph is the more faithful picture. The point of either picture is the same. Understanding is the assembly of relationships, not the recognition of terms.

A text is then an encoding of that structure at a language level: Tℓ = Encode(G, ℓ). The notation states an objective. It is not a promise that every graph can be said at every CEFR level inside a fixed length.

The passage below is Grade 1 life science. Move from A1 to a legal B2 and the sentences change. The graph does not. Choose the edit that mentions photosynthesis and the graph gains nodes. That second move is not an up-composition. It is a different lesson.

Over a sentence or a passage window W, local concept density can be written

The weights are the demands of introducing a concept and of establishing a relationship. They need annotation rules and empirical calibration. They are not universal constants. Even with equal weights, the ratio says something sentence length cannot: how much conceptual structure is packed into a given amount of language. λ lets a relation count for more or less than a concept. In the plant example, legal A1 and legal B2 have the same sums and different word counts, so D moves while G does not. A readability score aimed at rare words and long sentences can move the other way at the same time.

A list of independent facts and a chain of conditions can put similar structure into similar numbers of words and still ask for different amounts of simultaneous work. What has to stay active as reading proceeds is a second quantity:

Aₜ is the set of conceptual elements and unresolved dependencies that reader r must keep active at t. The cost cᵤ depends on prior knowledge. An expert may hold a familiar assembly as one chunk. A novice keeps the components. In the instrument below, a relation enters the active set once any of its concepts has appeared and it has not yet been established, and it leaves when the text establishes it. Reprise of a concept already built costs 0.3 rather than its full weight.

Shorter sentences do not automatically solve the problem. Breaking one sentence into five can lower local density and still leave the reader to connect all five. The implicit split is that failure. The explicit split is a real refactoring: the links are said, so they can close. Syntax sits in between. A clause can hold an assembly the way a pencil holds a crossword. It can also be a load, if the reader cannot use the frame. For a reader who can, a packed relation is costed here at 0.45 of its weight. For a reader who cannot, that factor is 1.15, plus 0.07 for each word past 18. Those factors are part of the demonstration, not findings.

Cognitive maturation matters, along with education, working memory, and knowledge already chunked. CEFR level is not a measure of that maturation. The same distinction belongs to the long argument about language and intelligence. It does not license a simple causal story about Broca’s and Wernicke’s areas. Those areas sit in broader networks. This page is a model of comprehension one can test, not a neurological claim.

Unpacking a Grade 12 sentence distributes nodes and makes implicit edges explicit. That changes the representation. Deleting a node, or quietly replacing the mechanism, changes what is taught. The two operations can look alike on the page, because both produce shorter or simpler sentences. They are not alike in G.

Some material will not fit a faithful A1 passage at all. The greenhouse effect is the case in the studio. Outgoing longwave radiation, absorption, re-emission, and the comparison to a planet without those gases are the content. A blanket that traps sunlight is a different, false graph that happens to share a name. If the prerequisites take more explanation than a passage can hold, the honest products are a sequence of lessons, or a declared cut. A paraphrase that hides the cut is not an encoding.

Successful refactoring manages both quantities at once: how much meaning arrives locally, and which relationships remain unresolved across the passage. Repetition, explicit referents, definitions, examples, and diagrams externalize work that would otherwise sit in Aₜ.

Unpack the greenhouse effect · Natural selection, including the slogan that changes it

The Lexile Framework puts text and reader on one scale. Its documented text analysis emphasizes word frequency and sentence length. Those are real linguistic demands, and they often correlate with conceptual difficulty. The early-reader extensions add further features. None of that constructs the graph, its prerequisite structure, or the set of relationships a particular reader must keep active. A reader measure can reflect the combined result without separating the two gradients.

The missing measurement is not another readability feature. It is a representation of what must be understood, what survives refactoring, and how the burden of assembling that understanding changes across language levels.

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