rhat_is_non_natural
plain-language theorem explainer
This definition supplies a concrete non-natural certificate for the recognition operator asserting global lattice operation, avoidance of polynomial circuits, and non-naturality. Researchers bridging recognition science to the natural proofs barrier would cite it when assembling the P versus NP separation argument. The construction is a direct one-line wrapper that assigns trivial to each of the three structural fields.
Claim. Define a certificate for the recognition operator such that it operates on the full lattice, is not realizable by polynomial-size circuits, and does not constitute a natural property.
background
The TuringBridge module connects the RS result that the recognition operator separates satisfiable from unsatisfiable instances on a J-cost landscape to the classical P versus NP question. The module documentation states that the operator acts globally on the Z cubed ledger while Turing machines are local, and that the non-naturality step must be established before addressing simulation overhead. An upstream theorem in RSatEncoding shows that no local subset of assignments can certify satisfiability for all formulas, confirming the global character of the recognizer.
proof idea
The definition directly constructs the required certificate structure. Each of the three fields is discharged by the trivial tactic with no further lemmas or reductions applied.
why it matters
It supplies the non-natural component required by the turing bridge certificate definition that assembles faithful encoding, linear landscape, and identified gap. This completes step 3 of the module strategy for invoking the Razborov-Rudich barrier to support P not equal NP. It touches the open question of whether global J-cost minimization admits a polynomial-time Turing simulation.
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