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module module high

IndisputableMonolith.Core.Complexity

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The Core.Complexity module assembles Recognition Science results on computational complexity by showing that J-frustration on SAT formulas forces super-polynomial Boolean circuit size. Researchers examining the P versus NP question inside the RS framework cite it as the central collection point. The module composes imported submodules on the J-cost Laplacian, frustration measures, non-naturalness, and explicit lower bounds without internal proofs.

claimJ-frustration on a CNF formula φ is the topological depth of the J-cost barrier on the Boolean hypercube; when JFrust(φ) = 1 the formula is unsatisfiable and any circuit simulating the global J-cost gradient requires size super-polynomial in n.

background

The module operates inside the Recognition Science treatment of P versus NP. It imports definitions of the J-cost Laplacian: a weighted graph on {0,1}^n whose vertices are assignments and whose edge weights equal the absolute difference in satJCost(φ,·). J-frustration is defined as the binary indicator that equals 0 precisely when a satisfying assignment exists and 1 otherwise; it quantifies the minimal depth of the J-cost landscape barrier surrounding the satisfying region.

proof idea

This is a definition module, no proofs. Its structure is the ordered import and re-export of eleven submodules that separately establish the hypercube graph, the frustration measure, the non-naturalness of that measure, and the resulting circuit-size lower bound.

why it matters in Recognition Science

The module supplies the core technical content that feeds the PvsNPAssembly and the larger claim that high J-frustration implies super-polynomial circuit size. It directly addresses the question posed in the CircuitLedger motivation: whether a feed-forward Boolean circuit can simulate the global J-cost gradient used by recognition to resolve SAT in linear steps.

scope and limits

depends on (11)

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