The Relational Theory of Information Integrity

We establish that fabrication resistance—the difficulty of forging an information system so that the forgery passes as authentic—is not an intrinsic property of the authentic system. We prove a No-Go result: no measurable property computed from a dataset alone predicts its resistance across adversaries. Six distinct intrinsic constructions (spectral gap, spectral entropy,
a verifiability index, collapse distance, an automorphism dimension, and a computational-depth tower) each fail, and each fails on the same counterexample—a domain whose structure is rich yet cheaply reproducible. This forces the Relational Axiom: resistance is a binary relation R(X,A) between a system and an adversary’s model class. We then give the mechanism. For
a fixed model class Ak (rank-k subspace capture), resistance is governed by the orthogonality of the system’s structure to the adversary’s subspace: a system is authentic-against-Ak exactly to the extent that its structured energy lies outside the adversary’s reach. The counterexample is resolved geometrically—its structure, though high-rank, is collinear with the low-rank adversary and is fully absorbed at rank three, while resistant systems retain structured energy orthogonal to the adversary at the same rank. The mechanism is demonstrated on the four cases that defeated every intrinsic theory. The universality of the resulting threshold across diverse domains is the open frontier