Modern Systems-on-Chip (SoCs) employ undocumented linear address-scrambling functions to obfuscate DRAM addressing, which complicates DRAM-aware performance optimizations and hinders proactive security analysis of DRAM-based attacks; most notably, Rowhammer. Although previous work tackled the issue of reversing physical-to-DRAM mapping, existing heuristic-based reverse-engineering approaches are partial, costly, and impractical for comprehensive recovery. This paper establishes a rigorous theoretical foundation and provides efficient practical algorithms for black-box, complete physical-to-DRAM address-mapping recovery. We first formulate the reverse-engineering problem within a linear algebraic model over the finite field GF(2). We characterize the timing fingerprints of row-buffer conflicts, proving a relationship between a bank addressing matrix and an empirically constructed matrix of physical addresses. Based on this characterization, we develop an efficient, noise-robust, and fully platform-agnostic algorithm to recover the full bank-mask basis in polynomial time, a significant improvement over the exponential search from previous works. We further generalize our model to complex row mappings, introducing new hardware-based hypotheses that enable the automatic recovery of a row basis instead of previous human-guided contributions. Evaluations across embedded and server-class architectures confirm our method's effectiveness, successfully reconstructing known mappings and uncovering previously unknown scrambling functions. Our method provides a 99% recall and accuracy on all tested platforms. Most notably, Knock-Knock runs in under a few minutes, even on systems with more than 500GB of DRAM, showcasing the scalability of our method. Our approach provides an automated, principled pathway to accurate DRAM reverse engineering.