IndisputableMonolith.Complexity.SAT.Isolation
This module defines XOR families and isolating structures for SAT instances of fixed size n. Researchers in Recognition Science complexity reductions cite it when constructing deterministic isolation layers for backpropagation. It imports CNF (variables as Fin n) and XOR (parity constraints) modules and supplies definitions to the Completeness module. The module contains only definitions with no theorems or proofs.
claimAn XOR family for instances of size $n$ is a collection of parity constraints over variables indexed by Fin $n$, together with isolating families and deterministic isolation maps that separate satisfying assignments.
background
The module sits inside the SAT complexity layer of Recognition Science. It builds directly on the CNF module, where variable indices are elements of Fin n for a problem of size n, and on the XOR module, whose doc-comment states that an XOR constraint enforces that the parity of a variable subset equals a given parity value. These supply the basic objects for constructing families that isolate solutions.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the isolation primitives required by the downstream Completeness module, whose doc-comment states it builds a fully-determined backpropagation state from a total assignment. It therefore occupies the isolation step in the SAT reduction chain inside the Recognition framework.
scope and limits
- Does not contain any theorems or proofs.
- Does not treat variable counts outside the fixed-n setting.
- Does not address general SAT solvers or numerical benchmarks.
- Does not define reduction maps to other complexity classes.