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 + 2Aₖ. Experiments confirm that exit residues factor through q* (w): words sharing the same state reach the same exit residue modulo 2ᵐ. 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