The Reduction Ladder

Fifty theories, from candidate quantum gravity to sociology by way of biophysics, complexity and network science. Each sheet carries its axioms, its hypotheses with their epistemic status, its predictions and whether they were made before or after the fact, the core equations with a notation key, how the theory was actually found, the experiments with their apparatus and numbers, a ledger of what is assumed, a worked example, and the relations running out of it — sorted by whether the limit is smooth, singular, an effective-theory decoupling, or a reduction claim that does not survive inspection.

Downward arrows are not all the same animal. Limit means a regular expansion in a small dimensionless parameter; singular means the limit does not exist pointwise and the interesting physics lives where it fails; EFT means heavy degrees of freedom were integrated out, with a computable error; coarse-grain means degrees of freedom were averaged over; constitutive means composition rather than derivation; contested flags a standard textbook reduction claim that the literature does not support; analogy flags shared mathematics without any reduction relation at all; and one arrow runs upward.