IndisputableMonolith.Complexity.JFrustration
J-Frustration assigns zero to satisfiable CNF formulas and one to unsatisfiable ones via the J-cost landscape on the Boolean hypercube. Complexity researchers pursuing Recognition Science routes to circuit lower bounds and P versus NP would cite this module. It assembles the J-cost Laplacian and RSAT encoding into a binary classifier that supports topological obstruction arguments for unsatisfiability.
claimFor a CNF formula $φ$ on $n$ variables, the J-frustration $J(φ)$ equals 0 when $φ$ is satisfiable and equals 1 when $φ$ is unsatisfiable, where the value is extracted from the weighted graph on the Boolean hypercube whose edge weights are absolute differences of satJCost.
background
The module operates in the Complexity domain of Recognition Science and defines J-frustration as a binary classifier for CNF formulas. It imports the J-cost Laplacian, which places vertices at assignments in {0,1}^n and weights edges by |satJCost(φ,a) - satJCost(φ,a')| for Hamming-distance-1 pairs. The RSatEncoding upstream result supplies the core claim that satisfiable instances reach zero J-cost in linear recognition steps while unsatisfiable instances carry a non-contractible topological obstruction (positive Betti-1). Constants supplies the RS time quantum τ₀ = 1 tick as the underlying discrete unit.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
J-frustration supplies the central object for the P versus NP assembly: it feeds CircuitLowerBound by linking high frustration to super-polynomial circuit size, NonNaturalness by showing the property evades Razborov-Rudich natural-proof criteria, and PvsNPAssembly by enabling the conditional path that UNSAT formulas have frustration at least 1 while SAT formulas reach zero. The module thereby closes the first phase of the Recognition Science resolution structure for P ≠ NP.
scope and limits
- Does not prove the full P versus NP separation.
- Does not compute explicit frustration values for concrete formulas.
- Does not implement the Laplacian or recognition steps.
- Does not address higher-dimensional topological invariants beyond Betti-1.