IndisputableMonolith.Complexity.SAT.SmallBias
This module supplies placeholder definitions for an explicit small-bias family of XOR systems on n variables. Researchers building geometric or linear SAT families in the Recognition framework cite it when adding bias control to parity constraints. It is a definition module containing no proofs.
claimLet $H_{sb}(n)$ be the small-bias family of XOR parity systems on $n$ variables, extending the linear mask family with controlled bias.
background
The module imports CNF (variables indexed by Fin n) and XOR (parity of a subset equals a target bit). These supply the base objects for constructing families of linear constraints. The local setting is the SAT complexity layer of Recognition Science, where XOR systems serve as building blocks for completeness and geometric extensions.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module feeds the Completeness module (backpropagation from total assignments) and the GeoFamily module (Morton octant masks). It supplies the small-bias component required for poly-size linear families in the SAT chain.
scope and limits
- Does not supply concrete instances or generators for the family.
- Does not prove size or bias bounds.
- Does not link to phi-ladder or Recognition constants.
- Does not contain theorems discharging the placeholder.