IndisputableMonolith.Complexity.JFrustration
J-Frustration module defines a binary indicator on CNF formulas that equals zero exactly on satisfiable instances and one on unsatisfiable instances. Researchers pursuing the Recognition Science route to P versus NP cite it as the central obstruction measure. The module assembles the J-cost Laplacian graph and RSAT encoding to set up the classification.
claimFor a CNF formula $φ$, the J-frustration $J(φ)$ equals 0 if $φ$ is satisfiable and equals 1 if $φ$ is unsatisfiable.
background
The module resides in the Complexity domain and imports the J-Cost Laplacian, which equips the Boolean hypercube with edge weights $|satJCost(φ,a)-satJCost(φ,a')|$ between Hamming neighbors. It also imports the RSAT encoding whose core claim states that the Recognition operator R̂ supplies a non-natural polytime certifier for SAT while unsatisfiable instances produce a non-contractible topological obstruction in the J-cost landscape. Constants supplies the base time quantum τ₀ = 1 tick.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
J-frustration supplies the obstruction measure that feeds CircuitLowerBound (high frustration implies super-polynomial circuit size), NonNaturalness (evades the Razborov-Rudich natural-proof barrier), and PvsNPAssembly (UNSAT formulas carry frustration ≥1, enabling the conditional P ≠ NP path).
scope and limits
- Does not compute explicit J-frustration values for concrete formulas.
- Does not prove any circuit-size lower bounds.
- Does not establish non-naturalness of the measure.
- Does not resolve the P versus NP question.