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module module moderate

IndisputableMonolith.Complexity.TuringBridge

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The TuringBridge module defines SAT instances and their J-cost structures to connect classical complexity problems to Recognition Science. It introduces SATInstance with n variables and m clauses, plus JCostLandscape and related certificates using the J-cost from JcostCore. Researchers mapping computability bounds to RS-native units would cite these definitions. The module contains only definitions and no proofs.

claimA SAT instance is denoted $SATInstance(n,m)$ with $n$ variables and $m$ clauses. The module defines associated objects $JCostLandscape$, $ResolutionTime$, $NaturalProperty$, and $RHatCertificate$ built from the J-cost measure and the time quantum $τ_0=1$.

background

The module sits in the Complexity domain and imports the RS time quantum $τ_0=1$ tick from Constants together with J-cost definitions from JcostCore. It introduces SATInstance as the standard encoding of boolean satisfiability. Sibling definitions include JCostLandscape for the cost surface over instances, ResolutionTime for the associated cost, and RHatCertificate for verification objects. The setting uses the J-cost formalism to translate classical complexity questions into RS terms.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the base objects that support downstream claims such as rhat_is_non_natural and the_open_gap inside the Complexity domain. It supplies the interface that lets SAT problems be expressed using the J-cost and phi-ladder structures of the broader Recognition framework.

scope and limits

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (13)