UNITAL SHIFT EQUIVALENCE

The paper proves that unital shift equivalence (USE) of square N-matrices with no zero rows implies a continuous orbit equivalence (COE) of the associated one-sided shifts that preserves eventual periodic points (Theorem 5.2). Its proof proceeds via: (i) reduction to an augmented standard form by out-splits and balanced in-splits, (ii) deriving an SL-equivalence from Boyle’s partitioned polynomial shift equivalence, then refining to an SL_+-equivalence between augmented pairs using K-web/poset-block techniques, (iii) implementing this equivalence by AER graph moves to obtain a diagonal-preserving *-isomorphism of Cuntz–Krieger algebras, and (iv) invoking groupoid/C*-algebra results to get COE preserving eventual periodic points. The candidate solution follows the same route and cites the same core tools. The only differences are stylistic and in the granularity of Step 2 (the model compresses some intermediate reductions that the paper spells out). No substantive mathematical discrepancy was found.