Polynomial recent-wire offsets -- definitions

Nested transition wrappers refer to child outputs whose distance from the current frontier is a fixed polynomial in the tableau horizon. These helpers evaluate that polynomial into one scratch value, use the dynamic-offset gate emitter, and restore every owned register.

noncomputable def Complexity.CircuitUnrolling.Serializer.DirectGenerator.preparePolynomialOffset (polynomial : Polynomial ℕ) (extra : ℕ := 0) : BinaryRoutine WorkCount

Evaluate polynomial(T) + extra into the dynamic-offset register.

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noncomputable def Complexity.CircuitUnrolling.Serializer.DirectGenerator.emitPolynomialRecentGate (polynomial : Polynomial ℕ) (extra : ℕ) (op : AndOrOp) (negated₀ negated₁ : Bool) (fixedOffset₁ : ℕ) : BinaryRoutine WorkCount

Emit one raw gate from a polynomial recent offset and a fixed recent offset, then clear the evaluated polynomial value.

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