An answer reduction stage exists for five-level normal form verifiers

MIPRE.AnswerReduction ℓ (blueprint thm:answer-reduction) records the data and guarantees of answer reduction for $\ell$-level verifiers: constants $a \ge 1$, $0 < b \le 1$ of the soundness loss $\delta(\varepsilon, n) = \sigma^a\bigl((\lambda n)^{\mu a}\varepsilon^b + (\lambda n)^{-\mu b}\bigr)$; a threshold $C$; a polynomial bound and degree deg for the output bound $\mathrm{bound}\bigl((\lambda n+1)^\mu + \sigma + \lambda + n\bigr)^{\mu+1}$ at degree $\deg\cdot(\mu+1)$; the answer-reduced sampler, a function of the input sampler and $(\lambda, \mu, \sigma)$ with polynomial-time program; the polynomial-time compute of the answer-reduced decider from the input programs and $(\lambda, \mu, \sigma)$; and the output verifier of level $\max(\ell+2, 5)$. For an input $\mathcal{V}$ within the budget $\mathrm{inBudget}(\lambda,\mu,n)$ at index $n$ (sampler and dimension within $(\lambda n+1)^\mu$, decider and accepted answers within $2^{(\lambda n+1)^\mu}$, degree $\mu$): if $|\mathcal{V}| \le \sigma$ the output is within the output bound, rejecting longer answers (complexity); for $n \ge C$, $\lambda, \mu \ge 1$ and $|\mathcal{D}| \le \sigma$, a value-$1$ PCC strategy for $\mathcal{V}_n$ gives one for the output at $n$ (completeness); for $n \ge \max(C, 2)$, $\lambda \ge 1$, $|\mathcal{D}| \le \sigma$ and $\varepsilon > 0$, $\mathrm{val}^*(\text{output}_n) > 1 - \varepsilon$ implies $\mathrm{val}^*(\mathcal{V}_n) \ge 1 - \delta(\varepsilon, n)$ (soundness). The statement: the contract holds at $\ell = 5$:

The level $5$ is the introspective verifier's, and the output is read at $\max(5+2, 5) = 7$ levels, as GapCompression.ofPipeline requires. In MIPRE/Background/Pipeline.lean every chapter 7 consequence is stated with an AnswerReduction 5 as its single remaining hypothesis; this leaf is that hypothesis.

Formalization Note In the repository the inhabitant is MIPRE.AnswerReduction.answerReduction, arVerifier over the classical PCP decider TM.CookLevin.Pad.classicalPcpDecider. The contract adapts the paper's absolute-time hypothesis $\mathrm{TIME}_{\mathcal{D}}(n) \le (2^{\lambda n})^\mu$ to degrees in the input size, bounds the input sampler's size by $\sigma$ too, and keeps the paper's threshold $C_{\mathrm{ar}}$ and regime $\lambda, \mu \ge 1$. The platform holds the statement only: the development proves it, in code the platform cannot host yet.