The structural landscape of equity index derivatives has undergone a fundamental transformation due to the proliferation of same-day expiry options, universally categorized as Zero-Days-to-Expiration (0DTE) contracts. This paper formalizes the unique mathematical and microstructural characteristics of 0DTE options, focusing specifically on the localized singularities that occur as time-to-maturity approaches zero ($\tau \to 0$). We demonstrate that under dense 0DTE open-interest distributions, traditional assumptions regarding asset price continuity and linear market depth break down. By modeling the non-linear expansion of option Gamma ($\Gamma$) and Speed ($\text{Speed}$), we map the mechanics of intraday liquidity distortions and delta-neutral hedging cascades executed by institutional market makers. Finally, this paper provides an empirical framework for systematic risk managers to isolate 0DTE-induced structural drift and anticipate intraday trend reversals driven entirely by order flow mechanics within the derivatives complex.