The Prevalence and Absence of Contiguous Intraday Boundaries Across Bullish Engulfing Risk-Reward Configurations in XAUUSD M15

This study quantified the prevalence and absence of qualifying contiguous intraday boundaries across unfiltered Bullish Engulfing events in XAUUSD M15. The evidence universe contained 5,639 events observed from 24 April 2023 through 1 July 2026 and 50 direction-risk-reward configurations, formed from BUY and SELL directions across a five-by-five absolute risk-reward grid. Each configuration was evaluated using a locked direct qualification rule followed, where necessary, by a controlled fallback procedure. Configurations that produced no qualifying boundary after completion of the full search were retained as no-boundary outcomes rather than excluded from reporting. A qualifying boundary was identified in 21 of 50 configurations, giving an overall prevalence of 42.0%. Ten boundaries met the direct criteria and 11 required fallback qualification; 29 configurations remained no-boundary. BUY prevalence was 56.0%, compared with 28.0% for SELL. Prevalence varied materially across risk-reward geometry. It rose from 10.0% at 1R risk to 60.0% at 4R before declining to 50.0% at 5R. By reward, prevalence decreased from 80.0% at 1R to 10.0% at 5R. All direct boundaries occurred at rewards of 1R or 2R, whereas every detected boundary at rewards of 3R through 5R required fallback qualification. Matched BUY-SELL pairs comprised six dual-boundary pairs, eight BUY-only pairs, one SELL-only pair, and ten pairs with no boundary in either direction. Each of the 29 no-boundary configurations completed 496 audited search attempts, yielding 14,384 unsuccessful attempts in total. These results show that qualifying intraday concentration was selective rather than universal and depended jointly on direction, risk-reward geometry, and evidence threshold. A no-boundary result denotes absence under the specified contiguous-window search and qualification rules; it does not establish the absence of trades, profitable individual hours, or opportunities under alternative definitions. Bullish Engulfing events were generated through a proprietary rule-based identification framework, with the exact logic withheld to protect trade-secret methodology.