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Autonomous indoor mobile robots can navigate reliably to metric coordinates using established frameworks such as ROS 2 Navigation 2, yet they lack the ability to interpret natural language instructions that express intent rather than positions. Vision-Language Models offer the semantic reasoning required to bridge this gap, but their inference latency (2-9 seconds per decision on consumer hardware) and session-by-session amnesia limit practical deployment. This paper presents the Semantic Autonomy Stack, a six-layer reference framework for semantically autonomous indoor navigation, and validates a complete instance featuring hybrid deterministic-VLM reasoning and cross-robot adaptive memory on physical robots with off-the-shelf edge hardware. A seven-step parametric resolver handles 88% of instructions in under 0.1 milliseconds without invoking a language model, camera, or GPU; only genuinely ambiguous instructions escalate to VLM reasoning. A five-category semantic memory framework with explicit scope taxonomy (global environment knowledge, per-operator preferences, per-robot capabilities) enables cross-session learning and cross-robot knowledge transfer: preferences learned through VLM interactions on one robot are promoted to deterministic resolution and transferred to a second robot via a shared compiled digest, achieving a measured latency reduction of 103,000-fold. Experimental validation on two custom-built differential-drive robots across 82 scenario-level decisions and three sessions demonstrates 100% semantic transfer accuracy (33/33, 95% CI [0.894, 1.000]), 100% semantic resolution accuracy, and concurrent multi-robot operation feasibility - all on Raspberry Pi 5 platforms with no onboard GPU, requiring zero training data.