MARKED LENGTH PATTERN RIGIDITY FOR ARITHMETIC MANIFOLDS

The uploaded paper states and proves Theorem A: if (M,g0) is a closed arithmetic rank‑one locally symmetric manifold and g is any negatively curved metric on M with R_{g0} ⊂ R_g, then (M,g) is isometric to (M,λ g0) by an isometry isotopic to the identity. This is explicitly stated in the introduction (Theorem A) and proved via a cocycle extension-and-classification argument in Sections 6–7, culminating in proportional marked length spectra followed by marked length spectrum (MLS) rigidity to obtain an isometry (see Theorem A statement and the Section 7 proof sketch: , , , ). The candidate solution follows the same structure: (1) R_{g0} ⊂ R_g ⇒ proportional marked length spectra, (2) rescale, (3) invoke MLS rigidity for rank‑one locally symmetric spaces, (4) conclude isotopy to identity via the marking and an injectivity result for Isom(M) → Out(π1(M)). Minor differences: the candidate attributes step (1) to “Theorem A” whereas in the paper proportionality is an intermediate step within the proof of Theorem A; and it cites Dal’Bo–Kim for MLS rigidity while the paper cites Hamenstädt. These do not affect correctness. Overall, both are correct and essentially the same proof strategy.