Specification Fibers and System Fingerprinting

Implementations that satisfy the same specification can remain distinguishable because a specification constrains only a particular observation of system behavior. This paper replaces a global linear “implementation null space” with a more general formulation based on specification fibers. A specification observation S:X->Y partitions implementations into equivalence classes S^{-1}(y); a fingerprint probe P:X->Z refines those classes, and an implementation attribute is recoverable only when it is constant on the fibers of the available observation. In linear models, the familiar null-space description reappears as a special case. For stochastic fingerprints, mutual information quantifies target-specific distinguishability, while conditional mutual information measures the incremental value of complementary probes. A Gaussian log-determinant expression is derived only for an explicitly linear-Gaussian measurement model rather than asserted as a universal capacity law. Fingerprint resistance is formulated as channel coarsening under a resource-cost set function, showing why linear defense cost requires separability assumptions rather than following from dimensionality alone. The framework unifies specification deviations, browser and protocol fingerprinting, and cross-layer observation without assuming that all specifications or behaviors form Euclidean subspaces.