Summable Orbits

The paper proves a coding theorem for recurrently strongly temperable 0‑summable orbits (Theorem 1.1) via I‑chains, Lyapunov (S^2/U^2) metrics, discretized double Pesin charts, a graph transform yielding weak stable/unstable manifolds, and a locally finite countable Markov partition with a finite‑to‑one coding on Σ#; π has summable variations and the bundles have summable variations as well. The candidate solution mirrors this construction step‑by‑step and identifies the same image RST, commuting semi‑conjugacy, local compactness, and square‑summability at coded points. Minor slips (e.g., one exponent written as −2 instead of −2γ, a heuristic O(r^{5/2}) bound, and calling the discretization “dyadic”) do not affect the argument’s substance, which follows the paper’s scheme and conclusions closely; see the paper’s definitions and statements of Theorem 1.1, Definition 2.8–2.9, Proposition 2.20, Theorem 2.13, Proposition 3.14, Theorem 5.2, and the characterization Σ# ↔ RST.