IndisputableMonolith.Complexity.BalancedParityHidden
The module defines a hidden mask encoder for Boolean bits under masks, where a bit b selects between a mask R and its negation. Complexity researchers modeling circuit-based SAT instances in Recognition Science cite these definitions when building ledger-style reductions. The module consists entirely of supporting definitions with no theorems or proofs.
claimThe hidden mask encoder satisfies $\text{enc}(b,R)=R$ when $b=\text{false}$ and $\text{enc}(b,R)=\neg R$ when $b=\text{true}$.
background
This module belongs to the Complexity domain and supplies auxiliary definitions for encoding Boolean values with hidden masks. The setting is the Recognition Science treatment of P vs NP, in which J-cost gradients on SAT instances are simulated by feed-forward circuits. Downstream modules import these definitions to construct restricted sub-ledgers and recognition-based SAT encodings.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The definitions feed CircuitLedger (Boolean circuits as restricted sub-ledgers) and RSatEncoding (R̂ as polytime SAT certifier via J-cost). They also support ComputationBridge and Core.Complexity. The module supplies the concrete encoding mechanism required by the P vs NP reduction sketched in those files.
scope and limits
- Does not contain theorems or proofs.
- Does not define J-cost or the recognition operator R̂.
- Does not resolve the P vs NP question.
- Does not address topological obstructions or Betti numbers.