AAC: Admissible-by-Architecture Differentiable Landmark Compression for ALT

We introduce AAC (Architecturally Admissible Compressor), a differentiable landmark-selection module for ALT (A*, Landmarks, and Triangle inequality) shortest-path heuristics whose outputs are admissible by construction: each forward pass is a row-stochastic mixture of triangle-inequality lower bounds, so the heuristic is admissible for every parameter setting without requiring convergence, calibration, or projection. At deployment, the module reduces to classical ALT on a learned subset, composing end-to-end with neural encoders while preserving the classical toolchain. The construction is the first differentiable instance of the compress-while-preserving-admissibility tradition in classical heuristic search. Under a matched per-vertex memory protocol, we establish that ALT with farthest-point-sampling landmarks (FPS-ALT) has provably near-optimal coverage on metric graphs, leaving at most a few percentage points of headroom for any selector. AAC operates near this ceiling: the gap is 0.9--3.9 percentage points on 9 road networks and ≤1.3 percentage points on synthetic graphs, with zero admissibility violations across 1,500+ queries and all logged runs. At matched memory, AAC is also 1.2--1.5× faster than FPS-ALT at the median query on DIMACS road networks, amortizing its offline cost within 170--1,924 queries. A controlled ablation isolates the binding constraint: training-objective drift under default initialization, not architectural capacity; identity-on-first-m initialization closes the expansion-count gap entirely. We release the module, a reusable matched-memory benchmarking protocol with paired two-one-sided-test (TOST) equivalence and pre-registration, and a reference compressed-differential-heuristics baseline.