Sanskrit is traditionally described as a free-word-order language, and the indigenous grammatical tradition explains what constrains word combination through three notions: ākāṅkṣā (syntactic expectancy), yogyatā (semantic compatibility), and sannidhi (proximity or contiguity). This study asks whether sannidhi, read as a locality constraint, is empirically supported, and how it relates to the cross-linguistic principle of dependency-length minimization (DLM). Using the Universal Dependencies Treebank of Vedic Sanskrit (27,182 sentences; 206,440 tokens), I compared observed dependency lengths against a random-projective baseline and a minimal-arrangement heuristic, partitioned arcs by grammatical relation, quantified non-projectivity, and traced variation across the corpus's chronological layers. At the whole-sentence level, Vedic showed no dependency-length minimization beyond the projectivity constraint: observed mean length (1.996) was statistically indistinguishable from the random-projective baseline (2.002) and far above the minimal arrangement (1.512). This near-parity, however, masked a systematic relation-specific split. Core verb-argument relations—the kāraka-type expectancy relations—were placed reliably closer than their own random baseline (mean deviation −0.36 tokens, 95% CI [−0.38, −0.34]), whereas coordinate, appositional, and modifier relations were placed at or beyond chance distance (+0.16 tokens, 95% CI [+0.13, +0.18]). Non-projectivity was common (19.4% of sentences) but overwhelmingly mild and well-nested, and it declined sharply from the Ṛgvedic layer (35.9%) to the Sūtra layer (11.0%). An independent classical treebank reproduced both the aggregate parity and the non-projectivity rate. I argue that sannidhi is best understood not as global length optimization but as a selective, expectancy-scoped locality operating over ākāṅkṣā-linked pairs, and that Vedic word order becomes measurably more projective over time.