Invisible to the Machine: Auditing AI Restaurant, Cafe, and Bar Recommendation Against a Complete Market Census

AI assistants are becoming a primary interface for local discovery, yet almost nothing is known about which venues they surface -- especially in food and drink, where recommendations carry direct revenue consequences. We present the first census-denominated audit of AI venue recommendation: a complete enumeration of 4,776 cafes, restaurants, and bars across two bounded markets (Canggu and Ubud, Bali), against which we evaluate 2,208 search-grounded responses from four production AI systems (ChatGPT, Claude, Gemini, Perplexity) to 96 persona-conditioned queries, collected over seven days under a pre-registered protocol. Because we observe the full market, we can measure what sampled audits cannot: 85.6% of venues were never recommended by any system -- 72.6% even among established venues with fifty or more ratings. Visibility follows a two-margin structure. Entry into answers is associated with documentation: review volume (OR 1.64), an own website (OR 1.92), listed price information (OR 1.54), and third-party web mentions (OR 1.44) -- while star rating is null at this margin (OR 0.89). Rank within answers reverses the pattern: among recommended venues, rating significantly predicts first position (OR 1.17). Presence in an open POI dataset (Foursquare), a folk-theorized visibility factor, shows no positive effect at either margin. Outright fabrication is rare (0.08% of mentions), but systems recommended permanently closed venues 93 times -- staleness, not hallucination, is the practical failure mode. Cross-system agreement is low (top-20 Jaccard 0.33-0.54). A two-week test-retest shows cross-period answer similarity comparable to same-day rerun similarity: the churn is sampling stochasticity, not temporal drift. We release our protocol, registry construction method, and derived data.