We introduce Psi-Turing Machines (Psi-TM): classical Turing machines equipped with a constant-depth introspection interface $ ι$ and an explicit per-step information budget $ B(d,n)=c\,d\log_2 n $. With the interface frozen, we develop an information-theoretic lower-bound toolkit: Budget counting, $ Ψ$-Fooling, and $ Ψ$-Fano, with worked examples $ L_k $ and $ L_k^{\mathrm{phase}} $. We prove an oracle-relative separation $ P^Ψ \neq NP^Ψ $ and a strict depth hierarchy, reinforced by an Anti-Simulation Hook that rules out polynomial emulation of $ ι_k $ using many calls to $ ι_{k-1} $ under the budget regime. We also present two independent platforms (Psi-decision trees and interface-constrained circuits IC-AC$^{0}$/IC-NC$^{1}$) and bridges that transfer bounds among machine, tree, and circuit with explicit poly/log losses. The model preserves classical computational power outside $ ι$ yet enables precise oracle-aware statements about barriers (relativization; partial/conditional progress on natural proofs and proof complexity). The aim is a standardized minimal introspection interface with clearly accounted information budgets.

翻译：我们提出Ψ图灵机(Psi-TM)模型：经典图灵机配备常数深度内省接口ι，且每步信息预算显式定义为B(d,n)=c d log₂ n。在接口冻结条件下，我们构建了信息论下界工具集：预算计数法、Ψ-欺骗法与Ψ-法诺法，并给出L_k与L_k^{phase}的实例分析。我们证明了预言机相对化分离P^Ψ≠NP^Ψ及严格深度层次结构，通过反模拟钩机制(在预算约束下，禁止通过多次调用ι_{k-1}多项式模拟ι_k)。同时提出两个独立平台(Ψ决策树与接口约束电路IC-AC^{0}/IC-NC^{1})，并建立机器、树与电路间显式多项式/对数损失的桥接转换。该模型在ι之外保留经典计算能力，同时能精确表述关于障碍(相对化；自然证明与证明复杂性的部分/条件性进展)的预言机感知结论。研究目标是建立具有清晰信息核算的标准化最小内省接口。