The Dimensionality Ceiling: Cross-Domain Synthesis and the Recognition of Value

As language models absorb more of the human record, this paper asks where their reach ends and answers with a falsifiable conjecture: a measurable ceiling on what a corpus-bound system can recognise as worth pursuing, graded by how far across knowledge a synthesis reaches. Generating connections across fields is cheap, and models can produce arrangements in no single source; what stays hard is recognising which is valuable, the judgement that turns reach into use. The standard by which an unprecedented synthesis is judged worthwhile is not yet in the record that the model and any learned evaluator are made from, so recognition at the frontier cannot be read off the corpus, and does not get cheap as generation does. The limit is jagged, not uniform, and tightens with reach: the writing that would value a distant connection is produced by the same rare authors who would draw the bridge, and goes missing with it. The paper calls this reach-graded surface the dimensionality ceiling. It separates three senses in which a bridge can be missing, only one of which is the durable human locus, and places the residue where no automatic test can settle worth. The conjecture is falsifiable, and the test that could overturn it doubles as a map of where human synthesis still matters most. That map, not a forecast about wages, scale, or employment, is the societal stake this paper presses; the labour-market questions stay separate.