A Delta-State Finite Automaton Framework for High-Energy Collatz Corridors: Exhaustive Symbolic Enumeration and Profinite State Compression

We introduce a Δ-state compression framework for the accelerated Collatz dynamics. High-energy valuation words w = (a₁,...,aₖ) with energy B(w) = k·log₂3 − Σaᵢ ≥ 10 are analyzed via two complementary engines. CPSE (Corridor-exit-compensation symbolic engine) exhaustively enumerates the complete finite domains W(30,{1,2},10) and W(30,{1,...,6},10), covering 1,510,808 and 13,681,233 valuation words respectively. In both cases, every word resolves into convergence to 1 or bounded-delay compensation (v₂(3n+1) ≥ 3) with zero unresolved words and maximum compensation delay at most 53. PCDS (Profinite constrained dynamical system) identifies the corrected finite-state descriptor q*(w) = (u, Δ(w) mod 2^(A(w)+m)) where u is a fixed-length suffix and Δ(w) satisfies the linear recurrence Δₖ₊₁ = 3Δₖ + 2^Aₖ. Experiments confirm that exit residues factor through q*(w): words sharing the same state reach the same exit residue modulo 2^m. Apparent exceptions at low lifting precision (≤ 42 bits) vanish completely at ≥ 64 bits, confirming the factorization is a genuine structural property. This work reduces the Collatz escape problem to a profinite Δ-state safety condition and identifies the remaining open problem: establishing Δ-state factorization in full generality. This paper does not prove the Collatz conjecture. It is Paper B of a four-part series on Collatz obstruction theory. Series:Paper A: https://doi.org/10.5281/zenodo.20068553Paper C: https://doi.org/10.5281/zenodo.20068757Paper D: https://doi.org/10.5281/zenodo.20068845