IndisputableMonolith.Complexity.BalancedParityHidden
This module defines the hidden mask encoder for bits in Boolean circuit models within Recognition Science. A bit b with mask R encodes as R when false and negation of R when true. Researchers examining the P versus NP gap via J-cost gradients in SAT would cite these primitives for circuit ledger constructions. The module consists solely of supporting definitions with no theorems or proofs.
claimThe hidden mask encoder for bit $b$ and mask $R$ is $R$ when $b=0$ and $R^c$ when $b=1$.
background
Recognition Science measures complexity through J-cost on the phi-ladder, with SAT instances resolved by the operator R̂ reaching zero cost in O(n) steps for satisfiable cases. This module supplies auxiliary Boolean encoding definitions that support modeling circuits as restricted sub-ledgers. It imports only Mathlib and introduces siblings such as enc, restrict, and extendMask to handle hidden parity masks for true/false bits.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The definitions feed CircuitLedger for Boolean circuits as restricted sub-ledgers and RSatEncoding for the R̂ SAT claim that satisfiable k-CNF instances reach zero J-cost in O(n) recognition steps. They also support ComputationBridge and Core.Complexity explorations of whether feed-forward circuits can simulate the global J-cost gradient used by R̂.
scope and limits
- Does not prove any complexity bounds or P versus NP results.
- Does not reference the forcing chain T0-T8 or RCL.
- Does not define J-cost or phi-ladder quantities.
- Does not include numerical constants such as alpha or G.