Derivable Residuals and Survivor Contamination: Noise as Primary Structure in Bottom-Up World Modelling

Scientific modelling treats randomness as residue: the part of the data left over once law has been extracted. This paper argues for the inverted ontology. Variability carries structure of its own, part of it derivable from constraint structure before any observation is made, and the standard practice of reading regularities off surviving configurations conflates that structure with the history of the selection that produced the survivors. Three claims follow. First, constraint systems generate derivable residual structure of three distinct kinds: violation floors where constraints conflict, as in the net disclination charge +12 required of a triangulated spherical crystal with local sixfold order and the frustrated bond per triangle of the triangular antiferromagnet; residual degeneracy where constraints are satisfiable but underdetermine the state, as in the configurational entropy of ice; and budget-indexed approximation profiles where constraints are incommensurable, as in the Pythagorean comma read as the residual of the 7/12 convergent. Each is determined by a declared constraint specification and, in tractable cases, computable without survivor data; none is read off survivors. Second, survivor distributions are contaminated evidence: an observed survivor measure combines a declared possibility-space measure, generator density and selection function, which are not separately identifiable from the survivors alone, and a recent materials-music analysis is shown to reproduce its cultural corridor from its own non-cultural site-percolation null model. Third, the programme generates falsifiable transportability tests: whether constraint-derived residual descriptors, expressed as dimensionless ratios or structure-preserving maps fixed in advance, recur across bounded scales and domains, with effective laws conjectured to be fixed points of the residual flow under coarse-graining. A test protocol and failure conditions are given.