Composite Timelike–Spacelike AdS Geodesics For CFT Correlators

Timelike geodesics may offer a natural, observer-centric handle on real-time holography. We introduce a bulk extremization prescription that assembles composite timelike-spacelike geoedsics joining timelike-separated boundary points and show that the resulting total length reproduces the complex length inferred from boundary CFT two-point functions at timelike separation. We validate the construction in Poincaré AdS, for generic pairs of points in global AdS, and for the BTZ geometry where the timelike segment necessarily probes behind the horizon. In AdS₃/CFT₂, the computed lengths coincide with pseudo-entropy. Our evidence indicates the prescription is nontrivial and robust, and it suggests a derivation via a saddle-point analysis of CFT correlators; in particular, this structure points to a boundary definition of a class of timelike bulk observers in terms of an on-shell worldline action.